wspCPEXPANSIONPTPEFF(p0, t0,
p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97.
Function returns a parameter at the end of the expansion process from initial
point with arguments p0, t0 to pressure p1 with relative efficiency eff. The
process is calculated by the formula: h1 = h0 - eff * (h0 - h1isoent), where h0
- specific enthalpy in initial point, h1 - specific enthalpy in finite point of
the expansion, eff - efficiency, h1isoentr - specific enthalpy in finite point
at isoentropic equilibrium expansion (s = Const). For compression process
calculation it is necessary to use the value inverse to the efficiency eff
(i.e. 1/eff). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations (functions
wspGETTOLERANCE and wspSETTOLERANCE).
wspCPEXPANSIONPTXPEFF(p0, t0,
x0, p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97.
Function returns a parameter at the end of the expansion process from initial
point with arguments p0, t0, x0 to pressure p1 with relative efficiency eff.
The process is calculated by the formula: h1 = h0 - eff * (h0 - h1isoent),
where h0 - specific enthalpy in initial point, h1 - specific enthalpy in finite
point of the expansion, eff - efficiency, h1isoentr - specific enthalpy in
finite point at isoentropic equilibrium expansion (s = Const). For compression
process calculation it is necessary to use the value inverse to the efficiency
eff (i.e. 1/eff). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
where:
It
is a function. The range of the validity is within that described in IF-97.
Function works as follows. For first the IF-97 region is determined by function
wspWATERSTATEAREAHS. Then the original variables are defined for basic equation
of IF-97 region at this point (by functions wspPTxHS and wspRT3HS). Then the
sought quantity is calculated on these data. Since at some stages the function
use iterations, to speed up calculations you may disable precision mode
(functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
where:
The
range of the validity is within that described in IF-97. The function
wspWATERSTATEAREAPH is used to determine the IF-97 region. Then the necessary
function (wspTxPH) is used. Finally, the necessary function (wspCPxPT or
wspCPSTX) is called. Since at some stages the function use iterations, to speed
up calculations you may disable precision mode (functions wspGETTOLERANCEMODE
and wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
where:
The
range of the validity is within that described in IF-97. The function
wspWATERSTATEAREAPS is used to determine the IF-97 region. Then the necessary
function (wspTxPS) is used. Finally, the necessary function (wspCPxPT or
wspCPSTX) is called. Since at some stages the function use iterations, to speed
up calculations you may disable precision mode (functions wspGETTOLERANCEMODE
and wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
4.
Specific isobaric heat capacity
[J/(kg·K)] as function of pressure p [Pa], temperature t [K]:
wspCPPT(p, t)
where:
The range of the validity is within that described in IF-97. The function wspWATERSTATEAREA2 is used to determine the IF-97 region. Then the necessary function (wspCPxPT) is used.
wspCPPTX(p, t, x)
where:
The
range of the validity is within that described in IF-97. The function wspWATERSTATEAREA
is used to determine the IF-97 region. Then the necessary function (wspCPxPT or
wspCPSTX) is used. If the point is out of the double-phase area the value of
vapor fraction is ignored.
wspCVEXPANSIONPTPEFF(p0, t0,
p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97.
Function returns a parameter at the end of the expansion process from initial
point with arguments p0, t0 to pressure p1 with relative efficiency eff. The
process is calculated by the formula: h1 = h0 - eff * (h0 - h1isoent), where h0
- specific enthalpy in initial point, h1 - specific enthalpy in finite point of
the expansion, eff - efficiency, h1isoentr - specific enthalpy in finite point
at isoentropic equilibrium expansion (s = Const). For compression process
calculation it is necessary to use the value inverse to the efficiency eff
(i.e. 1/eff). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
wspCVEXPANSIONPTXPEFF(p0, t0,
x0, p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97.
Function returns a parameter at the end of the expansion process from initial
point with arguments p0, t0, x0 to pressure p1 with relative efficiency eff.
The process is calculated by the formula: h1 = h0 - eff * (h0 - h1isoent),
where h0 - specific enthalpy in initial point, h1 - specific enthalpy in finite
point of the expansion, eff - efficiency, h1isoentr - specific enthalpy in finite
point at isoentropic equilibrium expansion (s = Const). For compression process
calculation it is necessary to use the value inverse to the efficiency eff
(i.e. 1/eff). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
where:
It
is a function. The range of the validity is within that described in IF-97.
Function works as follows. For first the IF-97 region is determined by function
wspWATERSTATEAREAHS. Then the original variables are defined for basic equation
of IF-97 region at this point (by functions wspPTxHS and wspRT3HS). Then the
sought quantity is calculated on these data. Since at some stages the function
use iterations, to speed up calculations you may disable precision mode
(functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
where:
The
range of the validity is within that described in IF-97. The function
wspWATERSTATEAREAPH is used to determine the IF-97 region. Then the necessary
function (wspTxPH) is used. Finally, the necessary function (wspCVxPT or
wspCVSTX) is called. Since at some stages the function use iterations, to speed
up calculations you may disable precision mode (functions wspGETTOLERANCEMODE
and wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
where:
The
range of the validity is within that described in IF-97. The function wspWATERSTATEAREAPS
is used to determine the IF-97 region. Then the necessary function (wspTxPS) is
used. Finally, the necessary function (wspCVxPT or wspCVSTX) is called. Since
at some stages the function use iterations, to speed up calculations you may disable
precision mode (functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary
relative precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
11. Specific isochoric heat capacity
[J/(kg·K)] as function of pressure p [Pa], temperature t [K]:
wspCVPT(p, t)
where:
The range of the validity is within that described in IF-97. The function wspWATERSTATEAREA2 is used to determine the IF-97 region. Then the necessary function (wspCVxPT) is used.
wspCVPTX(p, t, x)
where:
The
range of the validity is within that described in IF-97. The function wspWATERSTATEAREA
is used to determine the IF-97 region. Then the necessary function (wspCVxPT or
wspCVSTX) is used. If the point is out of the double-phase area the value of
vapor fraction is ignored.
where:
Function
is based upon the function wspDCRT(r, t). The latest in it's turn is based upon
the "Release on the Static Dielectric Constant of Ordinary Water Substance
for Temperatures from 238K to 873K and Pressures up to 1000 MPa", 1997
from IAPWS. The range of validity is from 238 to 273K in the metastable liquid
at atmospheric pressure (0.101325 MPa); from 273 to 323 K at pressures up to
the lower of the ice IV melting pressure or 1000 MPa; above 323 K at pressures
up to 600 MPa. The formulation also extrapolates smoothly up to at least 1200 K
and 1200 MPa.
14. Density [kg/m3] as function of
pressure p [Pa], temperature t [K]:
where:
The range of the validity is within that described in IF-97. The function wspWATERSTATEAREA2 is used to determine the IF-97 region. Then the necessary function (wspDENSxPT) is used.
15. Density [kg/m3] as function of
pressure p [Pa], temperature t [K], vapor fraction x [-]:
where:
The
range of the validity is within that described in IF-97. The function wspWATERSTATEAREA
is used to determine the IF-97 region. Then the necessary function (wspDENSxPT
or wspDENSSTX) is used. If the point is out of the double-phase area the value
of vapor fraction is ignored.
wspDYNVISEXPANSIONPTPEFF(p0, t0,
p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97 and
in formulation for dynamic viscosity (see function wspDYNVISRT). Function
returns a parameter at the end of the expansion process from initial point with
arguments p0, t0 to pressure p1 with relative efficiency eff. The process is
calculated by the formula: h1 = h0 - eff * (h0 - h1isoent), where h0 - specific
enthalpy in initial point, h1 - specific enthalpy in finite point of the
expansion, eff - efficiency, h1isoentr - specific enthalpy in finite point at
isoentropic equilibrium expansion (s = Const). For compression process
calculation it is necessary to use the value inverse to the efficiency eff
(i.e. 1/eff). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
wspDYNVISEXPANSIONPTXPEFF(p0, t0,
x0, p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97 and
in formulation for dynamic viscosity (see function wspDYNVISRT). Function
returns a parameter at the end of the expansion process from initial point with
arguments p0, t0, x0 to pressure p1 with relative efficiency eff. The process
is calculated by the formula: h1 = h0 - eff * (h0 - h1isoent), where h0 -
specific enthalpy in initial point, h1 - specific enthalpy in finite point of
the expansion, eff - efficiency, h1isoentr - specific enthalpy in finite point
at isoentropic equilibrium expansion (s = Const). For compression process
calculation it is necessary to use the value inverse to the efficiency eff
(i.e. 1/eff). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
where:
It
is a function. The range of the validity is within that described in IF-97 and
in formulation for dynamic viscosity (see function wspDYNVISRT). Function works
as follows. For first the IF-97 region is determined by function
wspWATERSTATEAREAHS. Then the original variables are defined for basic equation
of IF-97 region at this point (by functions wspPTxHS and wspRT3HS). Then the
sought quantity is calculated on these data. Since at some stages the function
use iterations, to speed up calculations you may disable precision mode
(functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
19. Dynamic viscosity [Pa·sec] as
function of pressure p [Pa], specific enthalpy h [J/kg]:
where:
The
range of the validity is within that described in IF-97 and in formulation for
dynamic viscosity (see function wspDYNVISRT). The function wspWATERSTATEAREAPH
is used to determine the IF-97 region. Then the necessary function (wspTxPH) is
used. Finally, the necessary function (wspDYNVISPT or wspDYNVISSTX) is called.
Since at some stages the function use iterations, to speed up calculations you
may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
20. Dynamic viscosity [Pa·sec] as
function of pressure p [Pa], specific entropy s [J/(kg·K)]:
where:
The
range of the validity is within that described in IF-97 and in formulation for
dynamic viscosity (see function wspDYNVISRT). The function wspWATERSTATEAREAPS
is used to determine the IF-97 region. Then the necessary function (wspTxPS) is
used. Finally, the necessary function (wspDYNVISPT or wspDYNVISSTX) is called.
Since at some stages the function use iterations, to speed up calculations you
may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
21. Dynamic viscosity [Pa·sec] as
function of pressure p [Pa], temperature t [K]:
wspDYNVISPT(p, t)
where:
The
range of the validity is within that described in IF-97 and in formulation for
dynamic viscosity (see function wspDYNVISRT). The function wspDYNVISRT is used
for calculation the argument of which is density defined by reverse value of
the function wspVPT.
wspDYNVISPTX(p, t, x)
where:
The
range of the validity is within that described in IF-97 and in formulation for
dynamic viscosity (see function wspDYNVISRT). The function wspWATERSTATEAREA is
used to determine the IF-97 region. Then the necessary function (wspDYNVISPT or
wspDYNVISSTX) is used. If the point is out of the double-phase area the value
of vapor fraction is ignored.
wspHEXPANSIONPTPEFF(p0, t0,
p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97.
Function returns a parameter at the end of the expansion process from initial
point with arguments p0, t0 to pressure p1 with relative efficiency eff. The
process is calculated by the formula: h1 = h0 - eff * (h0 - h1isoent), where h0
- specific enthalpy in initial point, h1 - specific enthalpy in finite point of
the expansion, eff - efficiency, h1isoentr - specific enthalpy in finite point
at isoentropic equilibrium expansion (s = Const). For compression process
calculation it is necessary to use the value inverse to the efficiency eff
(i.e. 1/eff). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
wspHEXPANSIONPTXPEFF(p0, t0,
x0, p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97.
Function returns a parameter at the end of the expansion process from initial
point with arguments p0, t0, x0 to pressure p1 with relative efficiency eff.
The process is calculated by the formula: h1 = h0 - eff * (h0 - h1isoent),
where h0 - specific enthalpy in initial point, h1 - specific enthalpy in finite
point of the expansion, eff - efficiency, h1isoentr - specific enthalpy in
finite point at isoentropic equilibrium expansion (s = Const). For compression
process calculation it is necessary to use the value inverse to the efficiency
eff (i.e. 1/eff). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
25. Specific enthalpy [J/kg] as function
of pressure p [Pa], specific entropy s [J/(kg·K)]:
where:
The
range of the validity is within that described in IF-97. The function
wspWATERSTATEAREAPS is used to determine the IF-97 region. Then the necessary
function (wspTxPS) is used. Finally, the necessary function (wspHxPT or
wspHSTX) is called. Since at some stages the function use iterations, to speed
up calculations you may disable precision mode (functions wspGETTOLERANCEMODE
and wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
26. Specific enthalpy [J/kg] as function
of pressure p [Pa], temperature t [K]:
wspHPT(p, t)
where:
The range of the validity is within that described in IF-97. The function wspWATERSTATEAREA2 is used to determine the IF-97 region. Then the necessary function (wspHxPT) is used.
wspHPTX(p, t, x)
where:
The
range of the validity is within that described in IF-97. The function
wspWATERSTATEAREA is used to determine the IF-97 region. Then the necessary
function (wspHxPT or wspHSTX) is used. If the point is out of the double-phase
area the value of vapor fraction is ignored.
wspJOULETHOMPSONEXPANSIONPTPEFF(p0, t0,
p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97.
Function returns a parameter at the end of the expansion process from initial
point with arguments p0, t0 to pressure p1 with relative efficiency eff. The process
is calculated by the formula: h1 = h0 - eff * (h0 - h1isoent), where h0 -
specific enthalpy in initial point, h1 - specific enthalpy in finite point of
the expansion, eff - efficiency, h1isoentr - specific enthalpy in finite point
at isoentropic equilibrium expansion (s = Const). For compression process
calculation it is necessary to use the value inverse to the efficiency eff
(i.e. 1/eff). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
wspJOULETHOMPSONEXPANSIONPTXPEFF(p0, t0,
x0, p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97.
Function returns a parameter at the end of the expansion process from initial
point with arguments p0, t0, x0 to pressure p1 with relative efficiency eff.
The process is calculated by the formula: h1 = h0 - eff * (h0 - h1isoent),
where h0 - specific enthalpy in initial point, h1 - specific enthalpy in finite
point of the expansion, eff - efficiency, h1isoentr - specific enthalpy in
finite point at isoentropic equilibrium expansion (s = Const). For compression
process calculation it is necessary to use the value inverse to the efficiency
eff (i.e. 1/eff). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
where:
It
is a function. The range of the validity is within that described in IF-97.
Function works as follows. For first the IF-97 region is determined by function
wspWATERSTATEAREAHS. Then the original variables are defined for basic equation
of IF-97 region at this point (by functions wspPTxHS and wspRT3HS). Then the
sought quantity is calculated on these data. Since at some stages the function
use iterations, to speed up calculations you may disable precision mode
(functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
31. Joule-Thomson coefficient [K/Pa] as
function of pressure p [Pa], specific enthalpy h [J/kg]:
where:
The
range of the validity is within that described in IF-97. The function wspWATERSTATEAREAPH
is used to determine the IF-97 region. Then the necessary function (wspTxPH) is
used. Finally, the necessary function (wspJOULETHOMPSONPT or
wspJOULETHOMPSONSTX) is called. Since at some stages the function use
iterations, to speed up calculations you may disable precision mode (functions
wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative precision for
internal iterations (functions wspGETTOLERANCE and wspSETTOLERANCE).
32. Joule-Thomson coefficient [K/Pa] as
function of pressure p [Pa], specific entropy s [J/(kg·K)]:
where:
The
range of the validity is within that described in IF-97. The function
wspWATERSTATEAREAPS is used to determine the IF-97 region. Then the necessary
function (wspTxPS) is used. Finally, the necessary function (wspJOULETHOMPSONPT
or wspJOULETHOMPSONSTX) is called. Since at some stages the function use
iterations, to speed up calculations you may disable precision mode (functions
wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative precision for
internal iterations (functions wspGETTOLERANCE and wspSETTOLERANCE).
33. Joule-Thomson coefficient [K/Pa] as
function of pressure p [Pa], temperature t [K]:
where:
The range of the validity is within that described in IF-97. The function wspWATERSTATEAREA2 is used to determine the IF-97 region. Then the necessary function (wspJOULETHOMPSONxPT) is used.
where:
The
range of the validity is within that described in IF-97. The function
wspWATERSTATEAREA is used to determine the IF-97 region. Then the necessary
function (wspJOULETHOMPSONPT or wspJOULETHOMPSONSTX) is used. If the point is
out of the double-phase area the value of vapor fraction is ignored.
wspKEXPANSIONPTPEFF(p0, t0,
p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97.
Function returns a parameter at the end of the expansion process from initial
point with arguments p0, t0 to pressure p1 with relative efficiency eff. The
process is calculated by the formula: h1 = h0 - eff * (h0 - h1isoent), where h0
- specific enthalpy in initial point, h1 - specific enthalpy in finite point of
the expansion, eff - efficiency, h1isoentr - specific enthalpy in finite point
at isoentropic equilibrium expansion (s = Const). For compression process
calculation it is necessary to use the value inverse to the efficiency eff
(i.e. 1/eff). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
wspKEXPANSIONPTXPEFF(p0, t0,
x0, p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97.
Function returns a parameter at the end of the expansion process from initial
point with arguments p0, t0, x0 to pressure p1 with relative efficiency eff.
The process is calculated by the formula: h1 = h0 - eff * (h0 - h1isoent), where
h0 - specific enthalpy in initial point, h1 - specific enthalpy in finite point
of the expansion, eff - efficiency, h1isoentr - specific enthalpy in finite
point at isoentropic equilibrium expansion (s = Const). For compression process
calculation it is necessary to use the value inverse to the efficiency eff
(i.e. 1/eff). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
where:
It
is a function. The range of the validity is within that described in IF-97.
Function works as follows. For first the IF-97 region is determined by function
wspWATERSTATEAREAHS. Then the original variables are defined for basic equation
of IF-97 region at this point (by functions wspPTxHS and wspRT3HS). Then the
sought quantity is calculated on these data. Since at some stages the function
use iterations, to speed up calculations you may disable precision mode
(functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
wspKINVISEXPANSIONPTPEFF(p0, t0,
p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97 and
in formulation for dynamic viscosity (see function wspDYNVISRT). Function
returns a parameter at the end of the expansion process from initial point with
arguments p0, t0 to pressure p1 with relative efficiency eff. The process is
calculated by the formula: h1 = h0 - eff * (h0 - h1isoent), where h0 - specific
enthalpy in initial point, h1 - specific enthalpy in finite point of the
expansion, eff - efficiency, h1isoentr - specific enthalpy in finite point at
isoentropic equilibrium expansion (s = Const). For compression process
calculation it is necessary to use the value inverse to the efficiency eff
(i.e. 1/eff). Since at some stages the function use iterations, to speed up calculations
you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
wspKINVISEXPANSIONPTXPEFF(p0, t0,
x0, p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97 and
in formulation for dynamic viscosity (see function wspDYNVISRT). Function
returns a parameter at the end of the expansion process from initial point with
arguments p0, t0, x0 to pressure p1 with relative efficiency eff. The process
is calculated by the formula: h1 = h0 - eff * (h0 - h1isoent), where h0 -
specific enthalpy in initial point, h1 - specific enthalpy in finite point of
the expansion, eff - efficiency, h1isoentr - specific enthalpy in finite point
at isoentropic equilibrium expansion (s = Const). For compression process
calculation it is necessary to use the value inverse to the efficiency eff
(i.e. 1/eff). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
where:
It
is a function. The range of the validity is within that described in IF-97 and
in formulation for dynamic viscosity (see function wspDYNVISRT). Function works
as follows. For first the IF-97 region is determined by function wspWATERSTATEAREAHS.
Then the original variables are defined for basic equation of IF-97 region at
this point (by functions wspPTxHS and wspRT3HS). Then the sought quantity is
calculated on these data. Since at some stages the function use iterations, to speed
up calculations you may disable precision mode (functions wspGETTOLERANCEMODE
and wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
41. Kinematic viscosity [m2/sec] as
function of pressure p [Pa], specific enthalpy h [J/kg]:
where:
The
range of the validity is within that described in IF-97 and in formulation for
dynamic viscosity (see function wspDYNVISRT). The function wspWATERSTATEAREAPH
is used to determine the IF-97 region. Then the necessary function (wspTxPH) is
used. Finally, the necessary function (wspKINVISPT or wspKINVISSTX) is called.
Since at some stages the function use iterations, to speed up calculations you
may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
42. Kinematic viscosity [m2/sec] as
function of pressure p [Pa], specific entropy s [J/(kg·K)]:
where:
The
range of the validity is within that described in IF-97 and in formulation for
dynamic viscosity (see function wspDYNVISRT). The function wspWATERSTATEAREAPS
is used to determine the IF-97 region. Then the necessary function (wspTxPS) is
used. Finally, the necessary function (wspKINVISPT or wspKINVISSTX) is called.
Since at some stages the function use iterations, to speed up calculations you
may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
43. Kinematic viscosity [m2/sec] as
function of pressure p [Pa], temperature t [K]:
wspKINVISPT(p, t)
where:
The
range of the validity is within that described in IF-97 and in formulation for
dynamic viscosity (see function wspDYNVISRT). The equation is: KINVIS = DYNVIS
· V is used for calculation, where DYNVIS defined by the function wspDYNVISPT
and V - by wspVPT.
wspKINVISPTX(p, t, x)
where:
The
range of the validity is within that described in IF-97 and in formulation for
dynamic viscosity (see function wspDYNVISRT). The function wspWATERSTATEAREA is
used to determine the IF-97 region. Then the necessary function (wspKINVISPT or
wspKINVISSTX) is used. If the point is out of the double-phase area the value
of vapor fraction is ignored.
45. Isoentropic exponent [-] as function
of pressure p [Pa], specific enthalpy h [J/kg]:
where:
The
range of the validity is within that described in IF-97. The function
wspWATERSTATEAREAPH is used to determine the IF-97 region. Then the necessary
function (wspTxPH) is used. Finally, the necessary function (wspKPT or wspKSTX)
is called. Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
46. Isoentropic exponent [-] as function
of pressure p [Pa], specific entropy s [J/(kg·K)]:
where:
The
range of the validity is within that described in IF-97. The function
wspWATERSTATEAREAPS is used to determine the IF-97 region. Then the necessary
function (wspTxPS) is used. Finally, the necessary function (wspKPT or wspKSTX)
is called. Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
47. Isoentropic exponent [-] as function
of pressure p [Pa], temperature t [K]:
wspKPT(p, t)
where:
The
range of the validity is within that described in IF-97. Used equation is: K =
W · W / (P · V) is used for calculation, where W (sound velocity) is defined by
the function wspWPT, P - pressure and V (specific volume) - by wspVPT.
wspKPTX(p, t, x)
where:
The
range of the validity is within that described in IF-97. The function
wspWATERSTATEAREA is used to determine the IF-97 region. Then the necessary
function (wspKPT or wspKSTX) is used. If the point is out of the double-phase
area the value of vapor fraction is ignored.
49. Ion product of water substance
[mole2/kg2] as function of pressure p [Pa], temperature t [K]:
where:
Function is based upon the function wspKWRT(r, t). The latest in it's turn based upon the "Release on the Ion Product of Water Substance, May 1980" from IAPWS. The range of validity is for pressure from 1 to 10000 bar, temperature is from 0 to 1000°C. Also is recommended do not use this formulation for densities less than 0.45 g/cm3. Warning! Function return ion product constant in SI base units (mole/kg)^2 (molality^2) but usually used the dimension (mole/dm^3)^2 (molarity^2). To convert from (mole/kg)^2 to (mole/dm^3)^2 you must to multiply value by squared density (r * r). Density must be in kg/dm^3.
50. Pressure [Pa] as function of
specific enthalpy h [J/kg], specific entropy s [J/(kg·K)]:
where:
It
is a function. The range of the validity is within that described in IF-97.
Function works as follows. For first the IF-97 region is determined by function
wspWATERSTATEAREAHS. Then the original variables are defined for basic equation
of IF-97 region at this point (by functions wspPTxHS and wspRT3HS). Then the
sought quantity is calculated on these data. Since at some stages the function
use iterations, to speed up calculations you may disable precision mode
(functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
wspPRANDTLEEXPANSIONPTPEFF(p0, t0,
p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97 and
in formulations for the properties included in the equation to calculate sought
quantity (see function wspPRANDTLEPT, wspTHERMCONDRT, wspDYNVISRT). Function
returns a parameter at the end of the expansion process from initial point with
arguments p0, t0 to pressure p1 with relative efficiency eff. The process is
calculated by the formula: h1 = h0 - eff * (h0 - h1isoent), where h0 - specific
enthalpy in initial point, h1 - specific enthalpy in finite point of the
expansion, eff - efficiency, h1isoentr - specific enthalpy in finite point at
isoentropic equilibrium expansion (s = Const). For compression process
calculation it is necessary to use the value inverse to the efficiency eff
(i.e. 1/eff). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
wspPRANDTLEEXPANSIONPTXPEFF(p0, t0,
x0, p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97 and
in formulations for the properties included in the equation to calculate sought
quantity (see function wspPRANDTLEPT, wspTHERMCONDRT, wspDYNVISRT). Function
returns a parameter at the end of the expansion process from initial point with
arguments p0, t0, x0 to pressure p1 with relative efficiency eff. The process
is calculated by the formula: h1 = h0 - eff * (h0 - h1isoent), where h0 -
specific enthalpy in initial point, h1 - specific enthalpy in finite point of
the expansion, eff - efficiency, h1isoentr - specific enthalpy in finite point
at isoentropic equilibrium expansion (s = Const). For compression process
calculation it is necessary to use the value inverse to the efficiency eff
(i.e. 1/eff). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
53. Prandtl number [-] as function of
specific enthalpy h [J/kg], specific entropy s [J/(kg·K)]:
where:
It
is a function. The range of the validity is within that described in IF-97 and
in formulations for the properties included in the equation to calculate sought
quantity (see function wspPRANDTLEPT, wspTHERMCONDRT, wspDYNVISRT). Function
works as follows. For first the IF-97 region is determined by function
wspWATERSTATEAREAHS. Then the original variables are defined for basic equation
of IF-97 region at this point (by functions wspPTxHS and wspRT3HS). Then the
sought quantity is calculated on these data. Since at some stages the function use
iterations, to speed up calculations you may disable precision mode (functions
wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative precision for
internal iterations (functions wspGETTOLERANCE and wspSETTOLERANCE).
54. Prandtl number [-] as function of
pressure p [Pa], specific enthalpy h [J/kg]:
where:
The
range of the validity is within that described in IF-97 and in formulations for
the properties included in the equation to calculate sought quantity (see
function wspPRANDTLEPT, wspTHERMCONDRT, wspDYNVISRT). The function wspWATERSTATEAREAPH
is used to determine the IF-97 region. Then the necessary function (wspTxPH) is
used. Finally, the necessary function (wspPRANDTLEPT or wspPRANDTLESTX) is
called. Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
55. Prandtl number [-] as function of
pressure p [Pa], specific entropy s [J/(kg·K)]:
where:
The
range of the validity is within that described in IF-97 and in formulations for
the properties included in the equation to calculate sought quantity (see
function wspPRANDTLEPT, wspTHERMCONDRT, wspDYNVISRT). The function
wspWATERSTATEAREAPS is used to determine the IF-97 region. Then the necessary
function (wspTxPS) is used. Finally, the necessary function (wspPRANDTLEPT or
wspPRANDLTESTX) is called. Since at some stages the function use iterations, to
speed up calculations you may disable precision mode (functions
wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative precision for
internal iterations (functions wspGETTOLERANCE and wspSETTOLERANCE).
56. Prandtl number [-] as function of
pressure p [Pa], temperature t [K]:
wspPRANDTLEPT(p, t)
where:
The
range of the validity is within that described in IF-97 and in formulations for
the properties included in the equation to calculate sought quantity. The
equation is: Pr = DYNVIS · CP / THERMCOND is used for calculation, where DYNVIS
is calculated by the function wspDYNVISPT, CP - by wspCPPT and THERMCOND - by
wspTHERMCONDPT.
57. Prandtl number [-] as function of
pressure p [Pa], temperature t [K], vapor fraction x [-]:
wspPRANDTLEPTX(p, t, x)
where:
The
range of the validity is within that described in IF-97 and in formulations for
the properties included in the equation to calculate sought quantity (see
function wspPRANDTLEPT, wspTHERMCONDRT, wspDYNVISRT). The function
wspWATERSTATEAREA is used to determine the IF-97 region. Then the necessary
function (wspPRANDTLEPPT or wspPRANDTLEPSTX) is used. If the point is out of
the double-phase area the value of vapor fraction is ignored.
where:
It
is a function. The range of the validity is within that described in IF-97.
Function works as follows. For first the IF-97 region is determined by function
wspWATERSTATEAREAHS. Then the original variables are defined for basic equation
of IF-97 region at this point (by functions wspPTxHS and wspRT3HS). Then the
sought quantities are calculated on these data. Since at some stages the
function use iterations, to speed up calculations you may disable precision
mode (functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
Note: In
Mathcad the function have only parameters (h, s) and return an array containing
output (return) parameters in SI units system.
Note: In Excel
the function have only parameters (h, s) and return an array which contains
output (return) parameters in SI units system. By default you will receive only
first output parameter (only one element from array). To retrieve all values in
array do next: 1) Enter formula with this function to any cell (as example B2).
2) Select cells: first cell with inputted formula and some cells on right hand
(as example 2 cells from B2 to C2). 3) Press F2. 4) Press Ctrl+Shift+Enter. If
you want to retrive values in vertical way (as example for cells from B2 to B3)
please use the Excel built-in "TRANSPOSE" function.
wspSEXPANSIONPTPEFF(p0, t0,
p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97.
Function returns a parameter at the end of the expansion process from initial
point with arguments p0, t0 to pressure p1 with relative efficiency eff. The
process is calculated by the formula: h1 = h0 - eff * (h0 - h1isoent), where h0
- specific enthalpy in initial point, h1 - specific enthalpy in finite point of
the expansion, eff - efficiency, h1isoentr - specific enthalpy in finite point
at isoentropic equilibrium expansion (s = Const). For compression process
calculation it is necessary to use the value inverse to the efficiency eff
(i.e. 1/eff). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
wspSEXPANSIONPTXPEFF(p0, t0,
x0, p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97.
Function returns a parameter at the end of the expansion process from initial
point with arguments p0, t0, x0 to pressure p1 with relative efficiency eff.
The process is calculated by the formula: h1 = h0 - eff * (h0 - h1isoent),
where h0 - specific enthalpy in initial point, h1 - specific enthalpy in finite
point of the expansion, eff - efficiency, h1isoentr - specific enthalpy in
finite point at isoentropic equilibrium expansion (s = Const). For compression
process calculation it is necessary to use the value inverse to the efficiency
eff (i.e. 1/eff). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
61. Specific entropy [J/(kg·K)] as
function of pressure p [Pa], specific enthalpy h [J/kg]:
where:
The
range of the validity is within that described in IF-97. The function
wspWATERSTATEAREAPH is used to determine the IF-97 region. Then the necessary
function (wspTxPH) is used. Finally, the necessary function (wspSPTX) is
called. Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
62. Specific entropy [J/(kg·K)] as
function of pressure p [Pa], temperature t [K]:
wspSPT(p, t)
where:
The range of the validity is within that described in IF-97. The function wspWATERSTATEAREA2 is used to determine the IF-97 region. Then the necessary function (wspSxPT) is used.
wspSPTX(p, t, x)
where:
The
range of the validity is within that described in IF-97. The function
wspWATERSTATEAREA is used to determine the IF-97 region. Then the necessary
function (wspSxPT or wspSSTX) is used. If the point is out of the double-phase
area the value of vapor fraction is ignored.
64. Surface tension [N/m] as function of
temperature t [K]:
wspSURFTENT(t)
where:
The
function is based on the IAPWS Release on The Surface Tension of Ordinary Water
Substance 1995. The range of validity is from triple point (0.01°C) to 647.096
K.
wspTEXPANSIONPTPEFF(p0, t0,
p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97.
Function returns a parameter at the end of the expansion process from initial
point with arguments p0, t0 to pressure p1 with relative efficiency eff. The
process is calculated by the formula: h1 = h0 - eff * (h0 - h1isoent), where h0
- specific enthalpy in initial point, h1 - specific enthalpy in finite point of
the expansion, eff - efficiency, h1isoentr - specific enthalpy in finite point
at isoentropic equilibrium expansion (s = Const). For compression process
calculation it is necessary to use the value inverse to the efficiency eff
(i.e. 1/eff). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
wspTEXPANSIONPTXPEFF(p0, t0,
x0, p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97.
Function returns a parameter at the end of the expansion process from initial
point with arguments p0, t0, x0 to pressure p1 with relative efficiency eff.
The process is calculated by the formula: h1 = h0 - eff * (h0 - h1isoent),
where h0 - specific enthalpy in initial point, h1 - specific enthalpy in finite
point of the expansion, eff - efficiency, h1isoentr - specific enthalpy in
finite point at isoentropic equilibrium expansion (s = Const). For compression
process calculation it is necessary to use the value inverse to the efficiency
eff (i.e. 1/eff). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
wspTHERMCONDEXPANSIONPTPEFF(p0, t0,
p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97 and
in formulation for thermal conductivity (see function wspTHERMCONDRT). Function
returns a parameter at the end of the expansion process from initial point with
arguments p0, t0 to pressure p1 with relative efficiency eff. The process is
calculated by the formula: h1 = h0 - eff * (h0 - h1isoent), where h0 - specific
enthalpy in initial point, h1 - specific enthalpy in finite point of the
expansion, eff - efficiency, h1isoentr - specific enthalpy in finite point at
isoentropic equilibrium expansion (s = Const). For compression process
calculation it is necessary to use the value inverse to the efficiency eff
(i.e. 1/eff). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
wspTHERMCONDEXPANSIONPTXPEFF(p0, t0,
x0, p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97 and
in formulation for thermal conductivity (see function wspTHERMCONDRT). Function
returns a parameter at the end of the expansion process from initial point with
arguments p0, t0, x0 to pressure p1 with relative efficiency eff. The process
is calculated by the formula: h1 = h0 - eff * (h0 - h1isoent), where h0 -
specific enthalpy in initial point, h1 - specific enthalpy in finite point of
the expansion, eff - efficiency, h1isoentr - specific enthalpy in finite point
at isoentropic equilibrium expansion (s = Const). For compression process
calculation it is necessary to use the value inverse to the efficiency eff
(i.e. 1/eff). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
where:
It
is a function. The range of the validity is within that described in IF-97 and
in formulation for thermal conductivity (see function wspTHERMCONDRT). Function
works as follows. For first the IF-97 region is determined by function
wspWATERSTATEAREAHS. Then the original variables are defined for basic equation
of IF-97 region at this point (by functions wspPTxHS and wspRT3HS). Then the
sought quantity is calculated on these data. Since at some stages the function
use iterations, to speed up calculations you may disable precision mode
(functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
where:
The
range of the validity is within that described in IF-97 and in formulation for
thermal conductivity (see function wspTHERMCONDRT). The function
wspWATERSTATEAREAPH is used to determine the IF-97 region. Then the necessary
function (wspTxPH) is used. Finally, the necessary function (wspTHERMCONDPT or
wspTHERMCONDSTX) is called. Since at some stages the function use iterations,
to speed up calculations you may disable precision mode (functions
wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative precision for
internal iterations (functions wspGETTOLERANCE and wspSETTOLERANCE).
where:
The
range of the validity is within that described in IF-97 and in formulation for
thermal conductivity (see function wspTHERMCONDRT). The function
wspWATERSTATEAREAPS is used to determine the IF-97 region. Then the necessary
function (wspTxPS) is used. Finally, the necessary function (wspTHERMCONDPT or
wspTHERMCONDSTX) is called. Since at some stages the function use iterations,
to speed up calculations you may disable precision mode (functions wspGETTOLERANCEMODE
and wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
72. Thermal conductivity coefficient
[W/(m·K)] as function of pressure p [Pa], temperature t [K]:
wspTHERMCONDPT(p, t)
where:
The
range of the validity is within that described in IF-97 and in formulation for
thermal conductivity (see function wspTHERMCONDRT). The function wspTHERMCONDRT
is used for calculation the argument of which is density defined by the reverse
value of function wspVPT.
wspTHERMCONDPTX(p, t, x)
where:
The
range of the validity is within that described in IF-97 and in formulation for
thermal conductivity (see function wspTHERMCONDRT). The function
wspWATERSTATEAREA is used to determine the IF-97 region. Then the necessary
function (wspTHERMCONDPT or wspTHERMCONDSTX) is used. If the point is out of
the double-phase area the value of vapor fraction is ignored.
74. Temperature [K] as function of
specific enthalpy h [J/kg], specific entropy s [J/(kg·K)]:
where:
It
is a function. The range of the validity is within that described in IF-97. Function
works as follows. For first the IF-97 region is determined by function
wspWATERSTATEAREAHS. Then the original variables are defined for basic equation
of IF-97 region at this point (by functions wspPTxHS and wspRT3HS). Then the
sought quantity is calculated on these data. Since at some stages the function
use iterations, to speed up calculations you may disable precision mode
(functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
75. Temperature [K] as function of
pressure p [Pa], specific enthalpy h [J/kg]:
where:
The
range of the validity is within that described in IF-97. The function
wspWATERSTATEAREAPH is used to determine the IF-97 region. Then the necessary
function (wspTxPH) is used. Since at some stages the function use iterations,
to speed up calculations you may disable precision mode (functions
wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative precision for
internal iterations (functions wspGETTOLERANCE and wspSETTOLERANCE).
76. Temperature [K] as function of
pressure p [Pa], specific entropy s [J/(kg·K)]:
where:
The
range of the validity is within that described in IF-97. The function
wspWATERSTATEAREAPS is used to determine the IF-97 region. Then the necessary
function (wspTxPS) is used. Since at some stages the function use iterations,
to speed up calculations you may disable precision mode (functions
wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative precision for
internal iterations (functions wspGETTOLERANCE and wspSETTOLERANCE).
wspUEXPANSIONPTPEFF(p0, t0,
p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97.
Function returns a parameter at the end of the expansion process from initial
point with arguments p0, t0 to pressure p1 with relative efficiency eff. The
process is calculated by the formula: h1 = h0 - eff * (h0 - h1isoent), where h0
- specific enthalpy in initial point, h1 - specific enthalpy in finite point of
the expansion, eff - efficiency, h1isoentr - specific enthalpy in finite point
at isoentropic equilibrium expansion (s = Const). For compression process
calculation it is necessary to use the value inverse to the efficiency eff
(i.e. 1/eff). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
wspUEXPANSIONPTXPEFF(p0, t0,
x0, p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97.
Function returns a parameter at the end of the expansion process from initial
point with arguments p0, t0, x0 to pressure p1 with relative efficiency eff.
The process is calculated by the formula: h1 = h0 - eff * (h0 - h1isoent), w-
specific enthalpy in initial point, h1 - specific enthalpy in final point of
the expansion, eff - efficiency, h1isoentr - specific enthalpy in final point
with isoentropic expansion (s = Const). For the calculating the process of
compression you must to use instead the efficiency eff the inverse number (i.e.
1/eff). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
where:
It
is a function. The range of the validity is within that described in IF-97.
Function works as follows. For first the IF-97 region is determined by function
wspWATERSTATEAREAHS. Then the original variables are defined for basic equation
of IF-97 region at this point (by functions wspPTxHS and wspRT3HS). Then the
sought quantity is calculated on these data. Since at some stages the function
use iterations, to speed up calculations you may disable precision mode
(functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
80. Specific internal energy [J/kg] as
function of pressure p [Pa], specific enthalpy h [J/kg]:
where:
The
range of the validity is within that described in IF-97. The function
wspWATERSTATEAREAPH is used to determine the IF-97 region. Then the necessary
function (wspTxPH) is used. Finally, the necessary function (wspUxPT or
wspUSTX) is called. Since at some stages the function use iterations, to speed
up calculations you may disable precision mode (functions wspGETTOLERANCEMODE
and wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
81. Specific internal energy [J/kg] as
function of pressure p [Pa], specific entropy s [J/(kg·K)]:
where:
The
range of the validity is within that described in IF-97. The function
wspWATERSTATEAREAPS is used to determine the IF-97 region. Then the necessary
function (wspTxPS) is used. Finally, the necessary function (wspUxPT or
wspUSTX) is called. Since at some stages the function use iterations, to speed
up calculations you may disable precision mode (functions wspGETTOLERANCEMODE
and wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
82. Specific internal energy [J/kg] as
function of pressure p [Pa], temperature t [K]:
wspUPT(p, t)
where:
The range of the validity is within that described in IF-97. The function wspWATERSTATEAREA2 is used to determine the IF-97 region. Then the necessary function (wspUxPT) is used.
wspUPTX(p, t, x)
where:
The
range of the validity is within that described in IF-97. The function
wspWATERSTATEAREA is used to determine the IF-97 region. Then the necessary
function (wspUxPT or wspUSTX) is used. If the point is out of the double-phase
area the value of vapor fraction is ignored.
wspVEXPANSIONPTPEFF(p0, t0,
p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97.
Function returns a parameter at the end of the expansion process from initial
point with arguments p0, t0 to pressure p1 with relative efficiency eff. The
process is calculated by the formula: h1 = h0 - eff * (h0 - h1isoent), where h0
- specific enthalpy in initial point, h1 - specific enthalpy in finite point of
the expansion, eff - efficiency, h1isoentr - specific enthalpy in finite point
at isoentropic equilibrium expansion (s = Const). For compression process calculation
it is necessary to use the value inverse to the efficiency eff (i.e. 1/eff).
Since at some stages the function use iterations, to speed up calculations you
may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
wspVEXPANSIONPTXPEFF(p0, t0,
x0, p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97.
Function returns a parameter at the end of the expansion process from initial
point with arguments p0, t0, x0 to pressure p1 with relative efficiency eff.
The process is calculated by the formula: h1 = h0 - eff * (h0 - h1isoent),
where h0 - specific enthalpy in initial point, h1 - specific enthalpy in finite
point of the expansion, eff - efficiency, h1isoentr - specific enthalpy in
finite point at isoentropic equilibrium expansion (s = Const). For compression
process calculation it is necessary to use the value inverse to the efficiency
eff (i.e. 1/eff). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
where:
It
is a function. The range of the validity is within that described in IF-97.
Function works as follows. For first the IF-97 region is determined by function
wspWATERSTATEAREAHS. Then the original variables are defined for basic equation
of IF-97 region at this point (by functions wspPTxHS and wspRT3HS). Then the
sought quantity is calculated on these data. Since at some stages the function
use iterations, to speed up calculations you may disable precision mode
(functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
87. Specific volume [m3/kg] as function
of pressure p [Pa], specific enthalpy h [J/kg]:
where:
The
range of the validity is within that described in IF-97. The function
wspWATERSTATEAREAPH is used to determine the IF-97 region. Then the necessary
function (wspTxPH) is used. Finally, the necessary function (wspVPTX) is
called. Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
88. Specific volume [m3/kg] as function
of pressure p [Pa], specific entropy s [J/(kg·K)]:
where:
The
range of the validity is within that described in IF-97. The function
wspWATERSTATEAREAPS is used to determine the IF-97 region. Then the necessary
function (wspTxPS) is used. Finally, the necessary function (wspVxPT or
wspVPTX) is called. Since at some stages the function use iterations, to speed
up calculations you may disable precision mode (functions wspGETTOLERANCEMODE
and wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
89. Specific volume [m3/kg] as function
of pressure p [Pa], temperature t [K]:
wspVPT(p, t)
where:
The range of the validity is within that described in IF-97. The function wspWATERSTATEAREA2 is used to determine the IF-97 region. Then the necessary function (wspVxPT) is used.
90. Specific volume [m3/kg] as function
of pressure p [Pa], temperature t [K], vapor fraction x [-]:
wspVPTX(p, t, x)
where:
The
range of the validity is within that described in IF-97. The function
wspWATERSTATEAREA is used to determine the IF-97 region. Then the necessary
function (wspVxPT or wspVSTX) is used. If the point is out of the double-phase
area the value of vapor fraction is ignored.
91. Properties calculation result as
function of pressure p [Pa], temperature t [K]:
wspVUSHCVWDERPTPT(p, t, *v,
*u, *s, *h, *Cv, *w,
*DVDPt, *DUDPt, *DSDPt, *DHDPt,
*DVDTp, *DUDTp, *DSDTp, *DHDTp)
where:
The
range of the validity is within that described in IF-97. The function
wspWATERSTATEAREA2 is used to determine the IF-97 region. Then the necessary
function (wspVUSHDERPTxPT) is used to return the set of properties and so speed
up calculation of several values in one point.
Note: In
Mathcad the function have only parameters (p, t) and return an array containing
output (return) parameters in SI units system.
Note: In
Excel the function have only parameters (p, t) and return an array which
contains output (return) parameters in SI units system. By default you will
receive only first output parameter (only one element from array). To retrieve
all values in array do next: 1) Enter formula with this function to any cell
(as example B2). 2) Select cells: first cell with inputted formula and some
cells on right hand (as example 2 cells from B2 to C2). 3) Press F2. 4) Press
Ctrl+Shift+Enter. If you want to retrive values in vertical way (as example for
cells from B2 to B3) please use the Excel built-in "TRANSPOSE" function.
wspWEXPANSIONPTPEFF(p0, t0,
p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97.
Function returns a parameter at the end of the expansion process from initial
point with arguments p0, t0 to pressure p1 with relative efficiency eff. The
process is calculated by the formula: h1 = h0 - eff * (h0 - h1isoent), where h0
- specific enthalpy in initial point, h1 - specific enthalpy in finite point of
the expansion, eff - efficiency, h1isoentr - specific enthalpy in finite point
at isoentropic equilibrium expansion (s = Const). For compression process
calculation it is necessary to use the value inverse to the efficiency eff
(i.e. 1/eff). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
wspWEXPANSIONPTXPEFF(p0, t0,
x0, p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97.
Function returns a parameter at the end of the expansion process from initial
point with arguments p0, t0, x0 to pressure p1 with relative efficiency eff.
The process is calculated by the formula: h1 = h0 - eff * (h0 - h1isoent),
where h0 - specific enthalpy in initial point, h1 - specific enthalpy in finite
point of the expansion, eff - efficiency, h1isoentr - specific enthalpy in
finite point at isoentropic equilibrium expansion (s = Const). For compression
process calculation it is necessary to use the value inverse to the efficiency
eff (i.e. 1/eff). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
94. Speed of sound [m/sec] as function
of specific enthalpy h [J/kg], specific entropy s [J/(kg·K)]:
where:
It
is a function. The range of the validity is within that described in IF-97.
Function works as follows. For first the IF-97 region is determined by function
wspWATERSTATEAREAHS. Then the original variables are defined for basic equation
of IF-97 region at this point (by functions wspPTxHS and wspRT3HS). Then the
sought quantity is calculated on these data. Since at some stages the function
use iterations, to speed up calculations you may disable precision mode (functions
wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative precision for
internal iterations (functions wspGETTOLERANCE and wspSETTOLERANCE).
95. Speed of sound [m/sec] as function
of pressure p [Pa], specific enthalpy h [J/kg]:
where:
The
range of the validity is within that described in IF-97. The function
wspWATERSTATEAREAPH is used to determine the IF-97 region. Then the necessary
function (wspTxPH) is used. Finally, the necessary function (wspWxPT or
wspWSTX) is called. Since at some stages the function use iterations, to speed
up calculations you may disable precision mode (functions wspGETTOLERANCEMODE
and wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
96. Speed of sound [m/sec] as function
of pressure p [Pa], specific entropy s [J/(kg·K)]:
where:
The
range of the validity is within that described in IF-97. The function
wspWATERSTATEAREAPS is used to determine the IF-97 region. Then the necessary
function (wspTxPS) is used. Finally, the necessary function (wspWxPT or
wspWSTX) is called. Since at some stages the function use iterations, to speed
up calculations you may disable precision mode (functions wspGETTOLERANCEMODE
and wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
97. Speed of sound [m/sec] as function
of pressure p [Pa], temperature t [K]:
wspWPT(p, t)
where:
The range of the validity is within that described in IF-97. The function wspWATERSTATEAREA2 is used to determine the IF-97 region. Then the necessary function (wspWxPT) is used.
98. Speed of sound [m/sec] as function
of pressure p [Pa], temperature t [K], vapor fraction x [-]:
wspWPTX(p, t, x)
where:
The
range of the validity is within that described in IF-97. The function
wspWATERSTATEAREA is used to determine the IF-97 region. Then the necessary
function (wspWxPT or wspWSTX) is used. If the point is out of the double-phase
area the value of vapor fraction is ignored.
wspXEXPANSIONPTPEFF(p0, t0,
p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97.
Function returns a parameter at the end of the expansion process from initial
point with arguments p0, t0, x0 to pressure p1 with relative efficiency eff.
The process is calculated by the formula: h1 = h0 - eff * (h0 - h1isoent),
where h0 - specific enthalpy in initial point, h1 - specific enthalpy in finite
point of the expansion, eff - efficiency, h1isoentr - specific enthalpy in
finite point at isoentropic equilibrium expansion (s = Const). For compression
process calculation it is necessary to use the value inverse to the efficiency
eff (i.e. 1/eff). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
wspXEXPANSIONPTXPEFF(p0, t0,
x0, p1, eff)
where:
It
is a function. The range of the validity is within that described in IF-97.
Function returns a parameter at the end of the expansion process from initial
point with arguments p0, t0, x0 to pressure p1 with relative efficiency eff.
The process is calculated by the formula: h1 = h0 - eff * (h0 - h1isoent),
where h0 - specific enthalpy in initial point, h1 - specific enthalpy in finite
point of the expansion, eff - efficiency, h1isoentr - specific enthalpy in
finite point at isoentropic equilibrium expansion (s = Const). For compression
process calculation it is necessary to use the value inverse to the efficiency
eff (i.e. 1/eff). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
101.
Vapor
fraction [-] as function of specific enthalpy h [J/kg], specific entropy s
[J/(kg·K)]:
where:
It
is a function. The range of the validity is within that described in IF-97.
Function works as follows. For first the IF-97 region is determined by function
wspWATERSTATEAREAHS. Then the original variables are defined for basic equation
of IF-97 region at this point (by functions wspPTxHS and wspRT3HS). Then the
sought quantity is calculated on these data. Since at some stages the function
use iterations, to speed up calculations you may disable precision mode
(functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
102.
Vapor
fraction [-] as function of pressure p [Pa], specific enthalpy h [J/kg]:
where:
It
is a function. The range of the validity is within that described in IF-97. The
IF-97 region is determined for given p and h (by function wspWATERSTATEAREAPH).
If the region is double-phase the sought parameter is calculated. Since at some
stages the function use iterations, to speed up calculations you may disable
precision mode (functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary
relative precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
103.
Vapor
fraction [-] as function of pressure p [Pa], specific entropy s [J/(kg·K)]:
where:
It
is a function. The range of the validity is within that described in IF-97. The
IF-97 region is determined for given p and s (by function wspWATERSTATEAREAPS).
If the region is double-phase the sought parameter is calculated. Since at some
stages the function use iterations, to speed up calculations you may disable
precision mode (functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary
relative precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
wspCPSST(t)
where:
The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
wspCPSWT(t)
where:
The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
where:
Function
returns the sum of specific isochoric heat capacity of steam from one-phase
region (function wspCVSST) and additional increment calculated by corresponding
thermodynamic formulas. The range of validity is from triple point of water
(0.01°C) to critical point (647.096K or 373.946°C).
where:
Function
returns the sum of specific isochoric heat capacity of water from one-phase
region (function wspCVSWT) and additional increment calculated by corresponding
thermodynamic formulas. The range of validity is from triple point of water
(0.01°C) to critical point (647.096K or 373.946°C).
wspCVSST(t)
where:
The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
wspCVSWT(t)
where:
The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
110.
Density
of steam at saturation line [kg/m3] as function of temperature t [K]:
where:
The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
111.
Density
of water at saturation line [kg/m3] as function of temperature t [K]:
where:
The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
where:
Function
is based upon "Supplementary Release on Saturation Properties of Ordinary
Water Substance" from International Association for the Properties of
Water and Steam. The range of validity is from triple point of water (0.01°C)
to critical point (647.096K or 373.946°C).
113.
Dynamic
viscosity of steam at saturation line [Pa·sec] as function of temperature t
[K]:
wspDYNVISSST(t)
where:
The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
114.
Dynamic
viscosity of water at saturation line [Pa·sec] as function of temperature t
[K]:
wspDYNVISSWT(t)
where:
The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
115.
Specific
enthalpy of steam at saturation line [J/kg] as function of temperature t [K]:
wspHSST(t)
where:
The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
116.
Specific
enthalpy of water at saturation line [J/kg] as function of temperature t [K]:
wspHSWT(t)
where:
The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
117.
Joule-Thomson
coefficient of steam at saturation line [K/Pa] as function of temperature t
[K]:
where:
The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
118.
Joule-Thomson
coefficient of water at saturation line [K/Pa] as function of temperature t
[K]:
where:
The
range of validity is from triple point of water (0.01°C) to critical point (647.096K
or 373.946°C).
119.
Kinematic
viscosity of steam at saturation line [m2/sec] as function of temperature t
[K]:
wspKINVISSST(t)
where:
The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
120.
Kinematic
viscosity of water at saturation line [m2/sec] as function of temperature t
[K]:
wspKINVISSWT(t)
where:
The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
121.
Isoentropic
exponent of steam at saturation line [-] as function of temperature t [K]:
wspKSST(t)
where:
The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
122.
Isoentropic
exponent of water at saturation line [-] as function of temperature t [K]:
wspKSWT(t)
where:
The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
123.
Prandtl
number of steam at saturation line [-] as function of temperature t [K]:
wspPRANDTLESST(t)
where:
The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
124.
Prandtl
number of water at saturation line [-] as function of temperature t [K]:
wspPRANDTLESWT(t)
where:
The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
125.
Pressure
at saturation line [Pa] as function of temperature t [K]:
wspPST(t)
where:
Function
is based upon the Supplementary Release on Saturation Properties of Ordinary
Water Substance from IAPWS. The range of validity is from triple point of water
(0.01°C) to critical point (647.096K or 373.946°C).
where:
Function
uses the special equation from Supplementory Release for IF-97 Formulation. The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
where:
Function
uses the special equation from Supplementory Release for IF-97 Formulation. The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
128.
Rough
value of density of steam at saturation line [kg/m3] as function of temperature
t [K]:
where:
This
function allows to calculate quickly rough value of steam density at saturation
line. The range of validity is from triple point of water (0.01°C) to critical
point (647.096K or 373.946°C).
129.
Rough
value of density of water at saturation line [kg/m3] as function of temperature
t [K]:
where:
This
function allows to calculate quickly rough value of steam density at saturation
line. The range of validity is from triple point of water (0.01°C) to critical
point (647.096K or 373.946°C).
130.
Specific
evaporation heat [J/kg] as function of temperature t [K]:
wspRST(t)
where:
The
result of function is calculated by formula r = (hs - hw), where hs - specific
enthalpy of steam at saturation line, hw - specific enthalpy of water at
saturation line. The range of validity is from triple point of water (0.01°C)
to critical point (647.096K or 373.946°C).
131.
Specific
entropy of steam at saturation line [J/(kg·K)] as function of temperature t
[K]:
wspSSST(t)
where:
The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
132.
Specific
entropy of water at saturation line [J/(kg·K)] as function of temperature t
[K]:
wspSSWT(t)
where:
The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
wspTHERMCONDSST(t)
where:
The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
wspTHERMCONDSWT(t)
where:
The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
where:
Function
calculates saturation temperature on a base of thermodunamic formulas. Newton
method is used to determine the root. The range of validity is from triple
point of water (0.01°C) to critical point (647.096K or 373.946°C). Since at
some stages the function use iterations, to speed up calculations you may
disable precision mode (functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE)
or vary relative precision for internal iterations (functions wspGETTOLERANCE
and wspSETTOLERANCE).
136.
Temperature
at saturation line [K] as function of pressure p [Pa]:
wspTSP(p)
where:
Function
is based upon the Supplementary Release on Saturation Properties of Ordinary Water
Substance from IAPWS. The range of validity is from triple point of water
(0.01°C or 611.657 Pa) to critical point (647.096K or 373.946°C or 22.064 MPa).
137.
Specific
internal energy of steam at saturation line [J/kg] as function of temperature t
[K]:
wspUSST(t)
where:
The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
138.
Specific
internal energy of water at saturation line [J/kg] as function of temperature t
[K]:
wspUSWT(t)
where:
The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
139.
Specific
volume of steam at saturation line [m3/kg] as function of temperature t [K]:
wspVSST(t)
where:
The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
140.
Specific
volume of water at saturation line [m3/kg] as function of temperature t [K]:
wspVSWT(t)
where:
The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
141.
Properties
calculation result for steam at saturation line as function of temperature t
[K]:
wspVUSHCVWDERPTSST(t, *v, *u,
*s, *h, *Cv, *w, *DVDPt,
*DUDPt, *DSDPt, *DHDPt, *DVDTp,
*DUDTp, *DSDTp, *DHDTp)
where:
The
function is based upon IF-97 formulation. It returns the property set that
speed up calculation considerably. The range of validity is from triple point
of water (0.01°C) to critical point (647.096K or 373.946°C).
Note: In
Mathcad the function have only parameters (t) and return an array containing
output (return) parameters in SI units system.
Note: In
Excel the function have only parameters (t) and return an array which contains
output (return) parameters in SI units system. By default you will receive only
first output parameter (only one element from array). To retrieve all values in
array do next: 1) Enter formula with this function to any cell (as example B2).
2) Select cells: first cell with inputted formula and some cells on right hand
(as example 2 cells from B2 to C2). 3) Press F2. 4) Press Ctrl+Shift+Enter. If
you want to retrive values in vertical way (as example for cells from B2 to B3)
please use the Excel built-in "TRANSPOSE" function.
142.
Properties
calculation result for water at saturation line as function of temperature t
[K]:
wspVUSHCVWDERPTSWT(t, *v, *u,
*s, *h, *Cv, *w, *DVDPt,
*DUDPt, *DSDPt, *DHDPt, *DVDTp,
*DUDTp, *DSDTp, *DHDTp)
where:
The
function is based upon IF-97 formulation. It returns the property set that
speed up calculation considerably. The range of validity is from triple point
of water (0.01°C) to critical point (647.096K or 373.946°C).
Note: In
Mathcad the function have only parameters (t) and return an array containing
output (return) parameters in SI units system.
Note: In
Excel the function have only parameters (t) and return an array which contains
output (return) parameters in SI units system. By default you will receive only
first output parameter (only one element from array). To retrieve all values in
array do next: 1) Enter formula with this function to any cell (as example B2).
2) Select cells: first cell with inputted formula and some cells on right hand
(as example 2 cells from B2 to C2). 3) Press F2. 4) Press Ctrl+Shift+Enter. If
you want to retrive values in vertical way (as example for cells from B2 to B3)
please use the Excel built-in "TRANSPOSE" function.
143.
Sound
velocity in steam at saturation line [m/sec] as function of temperature t [K]:
wspWSST(t)
where:
The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
144.
Sound
velocity in water at saturation line [m/sec] as function of temperature t [K]:
wspWSWT(t)
where:
The
range of validity is from triple point of water (0.01°C) to critical point
(647.096K or 373.946°C).
where:
Function
uses functions wspCPSST and wspCPSWT which return specific heat capacities at
constant pressure (Cp) of steam and water at saturation line. The function uses
following formula: CPx = (1 - X)·CPw + X·CPs, where CPs = wspCPSST, CPw =
wspCPSWT and X - vapor fraction. The range of calculation is double-phase
(water-vapor) area.
wspCVSTX(t, x)
where:
Function
uses functions wspCVDPSST and wspCVDPSWT which return specific heat capacities
at constant volume (Cv) of steam and water at saturation line in the
double-phase region area. The function uses following formula: CVx = (1 -
X)·CVDPw + X·CVDPs, where CVDPs = wspCVDPSST, CVDPw = wspCVDPSWT and X - vapor
fraction. This function used functions wspCVSST and wspCVSWT until version 5.6
which is not conform to thermodynamic, because it neglects the jump of
properties at saturation line. The range of validity is double-phase
(water-vapor) area.
147.
Density
in double-phase area [kg/m3] as function of temperature t [K], vapor fraction x
[-]:
where:
Function
uses the function named wspVSTX which return specific volume in double-phase
area. The function uses following formula: DENSx = 1 / Vx, where Vx =
wspVSTX(t, x). The range of validity is double-phase (water-vapor) area.
where:
Function
uses functions wspDYNVISSST and wspDYNVISSWT which return dynamic viscosity of
steam and water at saturation line. The function uses following formula:
DYNVISx = (1 - X)·DYNVISw + X·DYNVISs, where DYNVISs = wspDYNVISSST, DYNVISw =
wspDYNVISSWT and X - vapor fraction. The range of calculation is double-phase
(water-vapor) area.
wspHSTX(t, x)
where:
Function
uses functions wspHSST and wspHSWT which return specific enthalpies of steam
and water at saturation line. The function uses following formula: Hx = (1 -
X)·Hw + X·Hs, where Hs = wspHSST, Hw = wspHSWT and X - vapor fraction. The
range of validity is double-phase (water-vapor) area.
where:
Function
calculate the Joule-Thomson coefficient in double-phase area by equation at saturation
line: JT = (dT/dP)h. Until version 5.6 the function used wspJOULETHOMPSONSST
and wspJOULETHOMPSONSWT and returned value from following formula: JTx = (1 -
X)·JOULETHOMPSONw + X·JOULETHOMPSONs, where JOULETHOMPSONs =
wspJOULETHOMPSONSST, JOULETHOMPSONw = wspJOULETHOMPSONSWT and X - vapor vapor
fraction that did not conform to definition of Joule-Thomson coefficient. Now
it calculates correctly. The range of validity is double-phase (water-vapor)
area.
where:
Function
uses functions wspKINVISSST and wspKINVISSWT which return kinematic viscosities
of steam and water at saturation line. The function uses next formula: KINVISx
= (1 - X)·KINVISw + X·KINVISs, where KINVISs = wspKINVISSST, KINVISw =
wspKINVISSWT and X - vapor fraction. The range of calculation is double-phase
(water-vapor) area.
wspKSTX(t, x)
where:
Function
calculate isoentropic exponent in double-phase area considering property jump
at saturation line. Until version 5.6 this function uses following formula: Kx
= (1 - X)·Kw + X·Ks, where Ks = wspKSST, Kw = wspKSWT and X - vapor fraction.
But that is not agree with thermodynamic. Now it is calculated properly. The
range of validity is double-phase (water-vapor) area.
153.
Prandtl
number in double-phase area [-] as function of temperature t [K], vapor
fraction x [-]:
where:
Function
uses functions wspPRANDTLESST and wspPRANDTLESWT which returns Prandtl numbers of
steam and water at saturation line. The function uses following formula:
PRANDTLEx = (1 - X)·PRANDTLEw + X·PRANDTLEs, where PRANDTLEs = wspPRANDTLESST,
PRANDTLEw = wspPRANDTLESWT and X - vapor fraction. The range of calculation is
double-phase (water-vapor) area.
wspSSTX(t, x)
where:
Function
uses functions wspSSST and wspSSWT which return specific entropies of steam and
water at saturation line. The function uses following formula: Sx = (1 - X)·Sw
+ X·Ss, where Ss = wspSSST, Sw = wspSSWT and X - vapor fraction. The range of
validity is double-phase (water-vapor) area.
where:
Function
uses functions wspTHERMCONDSST and wspTHERMCONDSWT which return thermal
conductivity of steam and water at saturation line. The function uses following
formula: THERMCONDx = (1 - X)·THERMCONDw + X·THERMCONDs, where THERMCONDs =
wspTHERMCONDSST, THERMCONDw = wspTHERMCONDSWT and X - vapor fraction. The range
of calculation is double-phase (water-vapor) area.
where:
Function
calculates saturation temperature and vapor fraction on the base of
thermodunamic formulas. Newton method is used to determine the root. Since at
some stages the function use iterations, to speed up calculations you may
disable precision mode (functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE)
or vary relative precision for internal iterations (functions wspGETTOLERANCE
and wspSETTOLERANCE). The range of validity is double-phase (water-vapor) area.
Note: In
Mathcad the function have only parameters (h, s) and return an array containing
output (return) parameters in SI units system.
Note: In
Excel the function have only parameters (h, s) and return an array which
contains output (return) parameters in SI units system. By default you will
receive only first output parameter (only one element from array). To retrieve
all values in array do next: 1) Enter formula with this function to any cell
(as example B2). 2) Select cells: first cell with inputted formula and some
cells on right hand (as example 2 cells from B2 to C2). 3) Press F2. 4) Press
Ctrl+Shift+Enter. If you want to retrive values in vertical way (as example for
cells from B2 to B3) please use the Excel built-in "TRANSPOSE"
function.
wspUSTX(t, x)
where:
Function
uses functions wspUSST and wspUSWT which return specific internal energies of
steam and water at saturation line. The function uses following formula: Ux =
(1 - X)·Uw + X·Us, where Us = wspUSST, Uw = wspUSWT and X - vapor fraction. The
range of validity is double-phase (water-vapor) area.
wspVSTX(t, x)
where:
Function
uses the functions wspVSST and wspVSWT which return specific volumes of steam
and water at saturation line. The function uses following formula: Vx = (1 -
X)·Vw + X·Vs, where Vs = wspVSST, Vw = wspVSWT and X - vapor fraction. The
range of validity is double-phase (water-vapor) area.
wspWSTX(t, x)
where:
Function
uses function wspKSTX to calculate sound velocity in double-phase area
conforming with thermodynamic. The function neglects the flow structure. Until
version 5.6 this function used following formula: Wx = (1 - X)·Ww + X·Ws, where
Ws = wspWSST, Ww = wspWSWT and X - vapor fraction, which disagrees with
thermodynamic because it neglects the property jump at saturation line. The
range of validity is double-phase (water-vapor) area.
where:
This
function uses formula: X = (CP - CPw)/(CPs - CPw), where CPw = wspCPSWT, CPs =
wspCPSST. The range of calculation is double-phase (water-vapor) area.
wspXSTCV(t, Cv)
where:
This
function uses formula: X = (CV - CVDPw)/(CVDPs - CVDPw), where CVDPw =
wspCVDPSWT, CVDPs = wspCVDPSST. The range of validity is double-phase
(water-vapor) area.
162.
Vapor
fraction [-] as function of temperature t [K], density r [kg/m3]:
where:
This
function uses formula: X = rs * (rw - r) / (r * (rw - rs)), where rw =
wspDENSSWT, rs = wspDENSSST. The range of validity is double-phase
(water-vapor) area.
163.
Vapor
fraction [-] as function of temperature t [K], dynamic viscosity dv [Pa·sec]:
where:
This
function uses formula: X = (DV - DVw)/(DVs - DVw), where DVw = wspDYNVISSWT,
DVs = wspDYNVISSST. The range of calculation is double-phase (water-vapor)
area.
164.
Vapor
fraction [-] as function of temperature t [K], specific enthalpy h [J/kg]:
wspXSTH(t, h)
where:
This
function uses formula: X = (H - Hw)/(Hs - Hw), where Hw = wspHSWT, Hs =
wspHSST. The range of validity is double-phase (water-vapor) area.
165.
Vapor
fraction [-] as function of temperature t [K], Joule-Thomson coefficient jt
[K/Pa]:
where:
This
function uses formula: X = (JOULETHOMPSON - JOULETHOMPSONw)/(JOULETHOMPSONs -
JOULETHOMPSONw), where JOULETHOMPSONw = wspJOULETHOMPSONSWT, JOULETHOMPSONs =
wspJOULETHOMPSONSST. The range of validity is double-phase (water-vapor) area.
166.
Vapor
fraction [-] as function of temperature t [K], isoentropic exponent k [-]:
wspXSTK(t, k)
where:
This
function uses formula: X = (K - Kw)/(Ks - Kw), where Kw = wspKSWT, Ks =
wspKSST. The range of validity is double-phase (water-vapor) area.
167.
Vapor
fraction [-] as function of temperature t [K], kinematic viscosity kv [m2/sec]:
where:
This
function uses formula: X = (KV - KVw)/(KVs - KVw), where KVw = wspKINVISSWT,
KVs = wspKINVISSST. The range of calculation is double-phase (water-vapor)
area.
168.
Vapor
fraction [-] as function of temperature t [K], Prandtl number pr [-]:
where:
This
function uses formula: X = (PR - PRw)/(PRs - PRw), where PRw = wspPRANDTLESWT,
PRs = wspPRANDTLESST. The range of calculation is double-phase (water-vapor)
area.
169.
Vapor
fraction [-] as function of temperature t [K], specific entropy s [J/(kg·K)]:
wspXSTS(t, s)
where:
This
function uses formula: X = (S - Sw)/(Ss - Sw), where Sw = wspSSWT, Ss = wspSSST.
The range of validity is double-phase (water-vapor) area.
where:
This
function uses formula: X = (TC - TCw)/(TCs - TCw), where TCw = wspTHERMCONDSWT,
TCs = wspTHERMCONDSST. The range of calculation is double-phase (water-vapor)
area.
171.
Vapor
fraction [-] as function of temperature t [K], specific internal energy u
[J/kg]:
wspXSTU(t, u)
where:
This
function uses formula: X = (U - Uw)/(Us - Uw), where Uw = wspUSWT, Us =
wspUSST. The range of validity is double-phase (water-vapor) area.
172.
Vapor
fraction [-] as function of temperature t [K], specific volume v [m3/kg]:
wspXSTV(t, v)
where:
This
function uses formula: X = (V - Vw)/(Vs - Vw), where Vw = wspVSWT, Vs =
wspVSST. The range of validity is double-phase (water-vapor) area.
173.
Vapor
fraction [-] as function of temperature t [K], speed of sound w [m/sec]:
wspXSTW(t, w)
where:
From
version 5.6 this function calculates value of sound velocity in double-phase
region from isoentropic exponent that is conform to thermodynamic. Until
version 5.6 this function used formula: X = (W - Ww)/(Ws - Ww), where Ww =
wspWSWT, Ws = wspWSST which was not right. Now it is calculated correctly. The
range of validity is double-phase (water-vapor) area.
174.
Pressure
at melting line of ice I [Pa] as function of temperature t [K]:
where:
Function
is based on "Release on the Pressure along the Melting and the Sublimation
Curves of Ordinary Water Substance" IAPWS (Milan, Italy, September 1993).
175.
Pressure
at sublimation line [Pa] as function of temperature t [K]:
where:
Function
is based on "Release on the Pressure along the Melting and the Sublimation
Curves of Ordinary Water Substance" IAPWS (Milan, Italy, September 1993).
where:
This
function calculates the properties of super-cooled steam (in meta-stable
region). The parameters range: pressure up to 10 MPa, vapor fraction above 95%.
Special equation for meta-stable vapor region is used for calculation which is
based upon IAPWS IF-97.
where:
This
function calculates the properties of super-cooled steam (in meta-stable
region). The parameters range: pressure up to 10 MPa, vapor fraction above 95%.
Special equation for meta-stable vapor region is used for calculation which is
based upon IAPWS IF-97.
where:
This
function calculates the properties of super-cooled steam (in meta-stable region).
The parameters range: pressure up to 10 MPa, vapor fraction above 95%. Special
equation for meta-stable vapor region is used for calculation which is based
upon IAPWS IF-97.
where:
This
function calculates the properties of super-cooled steam (in meta-stable
region). The parameters range: pressure up to 10 MPa, vapor fraction above 95%.
Special equation for meta-stable vapor region is used for calculation which is
based upon IAPWS IF-97.
where:
This
function calculates the properties of super-cooled steam (in meta-stable
region). The parameters range: pressure up to 10 MPa, vapor fraction above 95%.
Special equation for meta-stable vapor region is used for calculation which is
based upon IAPWS IF-97.
where:
This
function calculates the properties of super-cooled steam (in meta-stable
region). The parameters range: pressure up to 10 MPa, vapor fraction above 95%.
Special equation for meta-stable vapor region is used for calculation which is
based upon IAPWS IF-97.
where:
This
function calculates the properties of super-cooled steam (in meta-stable
region). The parameters range: pressure up to 10 MPa, vapor fraction above 95%.
Special equation for meta-stable vapor region is used for calculation which is
based upon IAPWS IF-97.
where:
This
function calculates the properties of super-cooled steam (in meta-stable
region). The parameters range: pressure up to 10 MPa, vapor fraction above 95%.
Special equation for meta-stable vapor region is used for calculation which is
based upon IAPWS IF-97.
where:
This
function calculates the properties of super-cooled steam (in meta-stable
region). The parameters range: pressure up to 10 MPa, vapor fraction above 95%.
Special equation for meta-stable vapor region is used for calculation which is
based upon IAPWS IF-97.
where:
This
function calculates the properties of super-cooled steam (in meta-stable
region). The parameters range: pressure up to 10 MPa, vapor fraction above 95%.
Special equation for meta-stable vapor region is used for calculation which is
based upon IAPWS IF-97.
where:
This
function calculates the properties of super-cooled steam (in meta-stable
region). The parameters range: pressure up to 10 MPa, vapor fraction above 95%.
Special equation for meta-stable vapor region is used for calculation which is
based upon IAPWS IF-97.
where:
This
function calculates the properties of super-cooled steam (in meta-stable
region). The parameters range: pressure up to 10 MPa, vapor fraction above 95%.
Special equation for meta-stable vapor region is used for calculation which is
based upon IAPWS IF-97.
wspVUSHCVWDERPTMSPT(p, t, *v,
*u, *s, *h, *Cv, *w,
*DVDPt, *DUDPt, *DSDPt, *DHDPt,
*DVDTp, *DUDTp, *DSDTp, *DHDTp)
where:
This
function calculates the properties of super-cooled steam (in meta-stable
region). The parameters range: pressure up to 10 MPa, vapor fraction above 95%.
Special equation for meta-stable vapor region is used for calculation which is
based upon IAPWS IF-97.
Note: In
Mathcad the function have only parameters (p, t) and return an array containing
output (return) parameters in SI units system.
Note: In
Excel the function have only parameters (p, t) and return an array which
contains output (return) parameters in SI units system. By default you will
receive only first output parameter (only one element from array). To retrieve
all values in array do next: 1) Enter formula with this function to any cell
(as example B2). 2) Select cells: first cell with inputted formula and some
cells on right hand (as example 2 cells from B2 to C2). 3) Press F2. 4) Press
Ctrl+Shift+Enter. If you want to retrive values in vertical way (as example for
cells from B2 to B3) please use the Excel built-in "TRANSPOSE"
function.
where:
This
function calculates the properties of super-cooled steam (in meta-stable
region). The parameters range: pressure up to 10 MPa, vapor fraction above 95%.
Special equation for meta-stable vapor region is used for calculation which is
based upon IAPWS IF-97.
wspCP1PT(p, t)
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic
Properties of Water and Steam.
wspCP2PT(p, t)
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic
Properties of Water and Steam.
wspCP3PT(p, t)
where:
Function
is based upon functions wspR3PT and wspU3RT. Since at some stages the function
use iterations, to speed up calculations you may disable precision mode
(functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
wspCP3RT(r, t)
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic
Properties of Water and Steam.
wspCP5PT(p, t)
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic
Properties of Water and Steam.
wspCV1PT(p, t)
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic
Properties of Water and Steam.
wspCV2PT(p, t)
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic
Properties of Water and Steam.
wspCV3PT(p, t)
where:
Function
is based upon functions wspR3PT and wspU3RT. Since at some stages the function
use iterations, to speed up calculations you may disable precision mode
(functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
wspCV3RT(r, t)
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic
Properties of Water and Steam.
wspCV5PT(p, t)
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic
Properties of Water and Steam.
where:
Function
is based upon the "Release on the Static Dielectric Constant of Ordinary
Water Substance for Temperatures from 238K to 873K and Pressures up to 1000
MPa", 1997 from IAPWS. The range of validity is from 238 to 273K in the
metastable liquid at atmospheric pressure (0.101325 MPa); from 273 to 323 K at
pressures up to the lower of the ice IV melting pressure or 1000 MPa; above 323
K at pressures up to 600 MPa. The formulation also extrapolates smoothly up to
at least 1200 K and 1200 MPa.
201.
Density
in IF-97 region 1 [kg/m3] as function of pressure p [Pa], temperature t [K]:
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic Properties
of Water and Steam.
202.
Density
in IF-97 region 2 [kg/m3] as function of pressure p [Pa], temperature t [K]:
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic
Properties of Water and Steam.
203.
Density
in IF-97 region 3 [kg/m3] as function of pressure p [Pa], temperature t [K]:
where:
Function
calculates the density in region 3 by calling the function wspR3PTR0 with the
corresponding initial estimate for density. Used for unification of the
functions in all IF-97 regions. Since at some stages the function use
iterations, to speed up calculations you may disable precision mode (functions
wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative precision for
internal iterations (functions wspGETTOLERANCE and wspSETTOLERANCE).
204.
Density
in IF-97 region 5 [kg/m3] as function of pressure p [Pa], temperature t [K]:
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic
Properties of Water and Steam.
205.
Dynamic
viscosity [Pa·sec] as function of density r [kg/m3], temperature t [K]:
wspDYNVISRT(r, t)
where:
Function
is based upon the Revised Release on the IAPS Formulation 1985 for the
Viscosity of Ordinary Water Substance with correction for ITS-90 (International
Temperature Scale). The range of validity is for pressure up to 500 MPa
temperature is from 0 to 150°C, for pressure up to 350 MPa temperature is from
150 to 600°C, for pressure up to 300 MPa temperature is from 600 to 900°C.
206.
Specific
enthalpy in IF-97 region 1 [J/kg] as function of pressure p [Pa], temperature t
[K]:
wspH1PT(p, t)
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic
Properties of Water and Steam.
207.
Specific
enthalpy at line between areas 2b and 2c [J/kg] as function of pressure p [Pa]:
where:
Function
is based upon additional equations of the IAPWS Industrial Formulation 1997 for
Thermodynamic Properties of Water and Steam.
208.
Specific
enthalpy in IF-97 region 2 [J/kg] as function of pressure p [Pa], temperature t
[K]:
wspH2PT(p, t)
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic
Properties of Water and Steam.
209.
Specific
enthalpy in IF-97 region 3 [J/kg] as function of pressure p [Pa], temperature t
[K]:
wspH3PT(p, t)
where:
Function
is based upon functions wspR3PT and wspU3RT. Since at some stages the function
use iterations, to speed up calculations you may disable precision mode
(functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
210.
Specific
enthalpy in IF-97 region 3 [J/kg] as function of density r [kg/m3], temperature
t [K]:
wspH3RT(r, t)
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic
Properties of Water and Steam.
211.
Specific
enthalpy in IF-97 region 5 [J/kg] as function of pressure p [Pa], temperature t
[K]:
wspH5PT(p, t)
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic Properties
of Water and Steam.
where:
Function
is based upon "Supplementary Release on Backward Equations for p(h, s) for
Region 3, Equations as a Function of h and s for the Region Boundaries, and a
Equation Tsat(h, s) for Wet Steam of the IAPWS Industrial Formulation 1997 for
the Thermodynamic Properties of Water and Steam" (September 2004).
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic
Properties of Water and Steam. The equation: JT = (T*dV/dT - V)/Cp is used,
where T - temperature, dV/dT - differential quotient (dV/dT)p, V - volume, Cp -
isobaric heat capacity (Cp).
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic
Properties of Water and Steam. The equation: JT = (T*dV/dT - V)/Cp is used,
where T - temperature, dV/dT - differential quotient (dV/dT)p, V - volume, Cp -
isobaric heat capacity (Cp).
where:
Function
calculates Joule-Thomson coefficient for region 3 of IF-97 Formulation. This
function uses function wspR3PT(p, t) to calculate density and then returns the
value from the function wspJOULETHOMPSON3RT(r, t). Since at some stages the
function use iterations, to speed up calculations you may disable precision
mode (functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
where:
Function
calculates the Joule-Thomson coefficient for region 3 of IF-97 Formulation.
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic
Properties of Water and Steam. The equation: JT = (T*dV/dT - V)/Cp is used,
where T - temperature, dV/dT - differential quotient (dV/dT)p, V - volume, Cp -
isobaric heat capacity (Cp).
218.
Ion
product of water substance [mole2/kg2] as function of density r [kg/m3],
temperature t [K]:
where:
Function is based upon the "Release on the Ion Product of Water Substance, May 1980" from IAPWS. The range of validity is for pressure from 1 to 10000 bar, temperature is from 0 to 1000°C. Also is recommended do not use this formulation for densities less than 0.45 g/cm3. Warning! Function return ion product constant in SI base units (mole/kg)^2 (molality^2) but usually used the dimension (mole/dm^3)^2 (molarity^2). To convert from (mole/kg)^2 to (mole/dm^3)^2 you must to multiply value by squared density (r * r). Density must be in kg/dm^3.
where:
Function
is based upon "Supplementary Release on Backward Equations for Pressure as
a Function of Enthalpy and Entropy p(h,s) to the IAPWS Industrial Formulation
1997 for the Thermodynamic Properties of Water and Steam" (September
2001). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations (functions
wspGETTOLERANCE and wspSETTOLERANCE).
220.
Pressure
at line between areas 2 and 3 [Pa] as function of temperature t [K]:
wspP23T(t)
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for the Thermodynamic
Properties of Water and Steam. Used in function wspWATERSTATEAREA when region
of IF-97 is determined.
221.
Pressure
at line between areas 2b and 2c [Pa] as function of specific enthalpy h [J/kg]:
where:
Function
is based upon additional equations of the IAPWS Industrial Formulation 1997 for
Thermodynamic Properties of Water and Steam.
where:
Function
is based upon "Supplementary Release on Backward Equations for Pressure as
a Function of Enthalpy and Entropy p(h,s) to the IAPWS Industrial Formulation
1997 for the Thermodynamic Properties of Water and Steam" (September 2001)
and used the functions: wspP2AHS(h, s), wspP2BHS(h, s) and wspP2CHS(h, s).
Since at some stages the function use iterations, to speed up calculations you
may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
where:
Function
is based upon "Supplementary Release on Backward Equations for p(h, s) for
Region 3, Equations as a Function of h and s for the Region Boundaries, and a
Equation Tsat(h, s) for Wet Steam of the IAPWS Industrial Formulation 1997 for
the Thermodynamic Properties of Water and Steam" (September 2004). Since
at some stages the function use iterations, to speed up calculations you may
disable precision mode (functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE)
or vary relative precision for internal iterations (functions wspGETTOLERANCE
and wspSETTOLERANCE).
224.
Pressure
in IF-97 region 3 [Pa] as function of density r [kg/m3], temperature t [K]:
wspP3RT(r, t)
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic
Properties of Water and Steam.
where:
Function
is used to find the pressure in region 5 by Newton method. Since at some stages
the function use iterations, to speed up calculations you may disable precision
mode (functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
where:
Function
is based upon "Supplementary Release on Backward Equations for p(h, s) for
Region 3, Equations as a Function of h and s for the Region Boundaries, and a
Equation Tsat(h, s) for Wet Steam of the IAPWS Industrial Formulation 1997 for
the Thermodynamic Properties of Water and Steam" (September 2004).
227.
Area
of phase state as function of pressure p [Pa], temperature t [K]:
where:
Function
returns code of phase state in point with given p, t. If pressure p or
temperature t are above critical (Prk or Tkr), the result is "3"
(phase state - supercritical). If the point is situated above the saturation
line (in P-T diagramm) the result is "1" (phase state - liquid). If
the point is situated below the saturation line (in P-T diagram) the result is
"2" (phase state - steam). If point is situated below triple point,
the return is error value ("-1").
where:
Function
is used to find parameters in region 1 by Newton method. Since at some stages
the function use iterations, to speed up calculations you may disable precision
mode (functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
Note: In
Mathcad the function have only parameters (h, s) and return an array containing
output (return) parameters in SI units system.
Note: In
Excel the function have only parameters (h, s) and return an array which
contains output (return) parameters in SI units system. By default you will
receive only first output parameter (only one element from array). To retrieve
all values in array do next: 1) Enter formula with this function to any cell
(as example B2). 2) Select cells: first cell with inputted formula and some
cells on right hand (as example 2 cells from B2 to C2). 3) Press F2. 4) Press
Ctrl+Shift+Enter. If you want to retrive values in vertical way (as example for
cells from B2 to B3) please use the Excel built-in "TRANSPOSE"
function.
where:
Function
is based upon IAPWS Industrial Formulation 1997 for Thermodynamic Properties of
Water and Steam. The function uses the Newton method to determine the roots.
Since at some stages the function use iterations, to speed up calculations you
may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
Note: In
Mathcad the function have only parameters (r, h) and return an array containing
output (return) parameters in SI units system.
Note: In
Excel the function have only parameters (r, h) and return an array which
contains output (return) parameters in SI units system. By default you will
receive only first output parameter (only one element from array). To retrieve
all values in array do next: 1) Enter formula with this function to any cell
(as example B2). 2) Select cells: first cell with inputted formula and some cells
on right hand (as example 2 cells from B2 to C2). 3) Press F2. 4) Press
Ctrl+Shift+Enter. If you want to retrive values in vertical way (as example for
cells from B2 to B3) please use the Excel built-in "TRANSPOSE"
function.
where:
Function
is used to find parameters in region 2 by Newton method. Since at some stages
the function use iterations, to speed up calculations you may disable precision
mode (functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
Note: In
Mathcad the function have only parameters (h, s) and return an array containing
output (return) parameters in SI units system.
Note: In
Excel the function have only parameters (h, s) and return an array which
contains output (return) parameters in SI units system. By default you will
receive only first output parameter (only one element from array). To retrieve
all values in array do next: 1) Enter formula with this function to any cell
(as example B2). 2) Select cells: first cell with inputted formula and some
cells on right hand (as example 2 cells from B2 to C2). 3) Press F2. 4) Press
Ctrl+Shift+Enter. If you want to retrive values in vertical way (as example for
cells from B2 to B3) please use the Excel built-in "TRANSPOSE"
function.
where:
Function
is based upon IAPWS Industrial Formulation 1997 for Thermodynamic Properties of
Water and Steam. The function uses the Newton method to determine the roots.
Since at some stages the function use iterations, to speed up calculations you
may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
Note: In
Mathcad the function have only parameters (r, h) and return an array containing
output (return) parameters in SI units system.
Note: In
Excel the function have only parameters (r, h) and return an array which
contains output (return) parameters in SI units system. By default you will
receive only first output parameter (only one element from array). To retrieve
all values in array do next: 1) Enter formula with this function to any cell
(as example B2). 2) Select cells: first cell with inputted formula and some cells
on right hand (as example 2 cells from B2 to C2). 3) Press F2. 4) Press
Ctrl+Shift+Enter. If you want to retrive values in vertical way (as example for
cells from B2 to B3) please use the Excel built-in "TRANSPOSE"
function.
where:
Function
is based on function wspRT3HS. After calling wspRT3HS the standard equations
are used to determine the pressure. Since at some stages the function use
iterations, to speed up calculations you may disable precision mode (functions
wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative precision for
internal iterations (functions wspGETTOLERANCE and wspSETTOLERANCE).
Note: In
Mathcad the function have only parameters (h, s) and return an array containing
output (return) parameters in SI units system.
Note: In
Excel the function have only parameters (h, s) and return an array which
contains output (return) parameters in SI units system. By default you will
receive only first output parameter (only one element from array). To retrieve
all values in array do next: 1) Enter formula with this function to any cell
(as example B2). 2) Select cells: first cell with inputted formula and some
cells on right hand (as example 2 cells from B2 to C2). 3) Press F2. 4) Press
Ctrl+Shift+Enter. If you want to retrive values in vertical way (as example for
cells from B2 to B3) please use the Excel built-in "TRANSPOSE"
function.
where:
Function
is used to find parameters in region 5 by Newton method. Since at some stages
the function use iterations, to speed up calculations you may disable precision
mode (functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
Note: In
Mathcad the function have only parameters (h, s) and return an array containing
output (return) parameters in SI units system.
Note: In
Excel the function have only parameters (h, s) and return an array which
contains output (return) parameters in SI units system. By default you will receive
only first output parameter (only one element from array). To retrieve all
values in array do next: 1) Enter formula with this function to any cell (as
example B2). 2) Select cells: first cell with inputted formula and some cells
on right hand (as example 2 cells from B2 to C2). 3) Press F2. 4) Press
Ctrl+Shift+Enter. If you want to retrive values in vertical way (as example for
cells from B2 to B3) please use the Excel built-in "TRANSPOSE"
function.
where:
Function
is based upon IAPWS Industrial Formulation 1997 for Thermodynamic Properties of
Water and Steam. The function uses the Newton method to determine the roots.
Since at some stages the function use iterations, to speed up calculations you
may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
Note: In
Mathcad the function have only parameters (r, h) and return an array containing
output (return) parameters in SI units system.
Note: In
Excel the function have only parameters (r, h) and return an array which
contains output (return) parameters in SI units system. By default you will
receive only first output parameter (only one element from array). To retrieve
all values in array do next: 1) Enter formula with this function to any cell
(as example B2). 2) Select cells: first cell with inputted formula and some
cells on right hand (as example 2 cells from B2 to C2). 3) Press F2. 4) Press
Ctrl+Shift+Enter. If you want to retrive values in vertical way (as example for
cells from B2 to B3) please use the Excel built-in "TRANSPOSE"
function.
235.
Density
in IF-97 region 3 [kg/m3] as function of pressure p [Pa], temperature t [K]:
wspR3PT(p, t)
where:
Function
calculates the density in region 3 by calling the function wspR3PTR0 with the
corresponding initial estimate for density. Used for unification of the
functions in all IF-97 regions. Since at some stages the function use
iterations, to speed up calculations you may disable precision mode (functions
wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative precision for
internal iterations (functions wspGETTOLERANCE and wspSETTOLERANCE).
wspR3PTR0(p, t, r0)
where:
Function
used the Newton method with initial estimate for density to calculate the
density. Used for unification of the functions in all IF-97 regions. Since at
some stages the function use iterations, to speed up calculations you may vary
relative precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
where:
Function
is used to find parameters in region 3 by Newton method. Since at some stages
the function use iterations, to speed up calculations you may disable precision
mode (functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
Note: In
Mathcad the function have only parameters (h, s) and return an array containing
output (return) parameters in SI units system.
Note: In
Excel the function have only parameters (h, s) and return an array which
contains output (return) parameters in SI units system. By default you will
receive only first output parameter (only one element from array). To retrieve
all values in array do next: 1) Enter formula with this function to any cell
(as example B2). 2) Select cells: first cell with inputted formula and some
cells on right hand (as example 2 cells from B2 to C2). 3) Press F2. 4) Press
Ctrl+Shift+Enter. If you want to retrive values in vertical way (as example for
cells from B2 to B3) please use the Excel built-in "TRANSPOSE"
function.
wspS1PT(p, t)
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic
Properties of Water and Steam.
wspS2PT(p, t)
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic
Properties of Water and Steam.
wspS3PT(p, t)
where:
Function
is based upon functions wspR3PT and wspU3RT. Since at some stages the function
use iterations, to speed up calculations you may disable precision mode
(functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
wspS3RT(r, t)
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic
Properties of Water and Steam.
wspS5PT(p, t)
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic
Properties of Water and Steam.
where:
Function
is based upon "Supplementary Release on Backward Equations for Pressure as
a Function of Enthalpy and Entropy p(h,s) to the IAPWS Industrial Formulation
1997 for the Thermodynamic Properties of Water and Steam" (September
2001). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
244.
Temperature
in IF-97 region 1 [K] as function of pressure p [Pa], specific enthalpy h
[J/kg]:
where:
Function
is based upon additional equations of the IAPWS Industrial Formulation 1997 for
Thermodynamic Properties of Water and Steam. Since at some stages the function
use iterations, to speed up calculations you may disable precision mode
(functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
where:
Function
is based upon additional equations of the IAPWS Industrial Formulation 1997 for
Thermodynamic Properties of Water and Steam. Since at some stages the function
use iterations, to speed up calculations you may disable precision mode
(functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
246.
Temperature
at line between areas 2 and 3 [K] as function of pressure p [Pa]:
wspT23P(p)
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for the Thermodynamic
Properties of Water and Steam. Used in function wspWATERSTATEAREA when region
of IF-97 is determined.
247.
Temperature
in IF-97 region 2a [K] as function of pressure p [Pa], specific enthalpy h
[J/kg]:
where:
Function
is based upon additional equations of the IAPWS Industrial Formulation 1997 for
Thermodynamic Properties of Water and Steam. Since at some stages the function
use iterations, to speed up calculations you may disable precision mode
(functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and wspSETTOLERANCE).
where:
Function
is based upon additional equations of the IAPWS Industrial Formulation 1997 for
Thermodynamic Properties of Water and Steam. Since at some stages the function
use iterations, to speed up calculations you may disable precision mode
(functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
249.
Temperature
in IF-97 region 2b [K] as function of pressure p [Pa], specific enthalpy h
[J/kg]:
where:
Function
is based upon additional equations of the IAPWS Industrial Formulation 1997 for
Thermodynamic Properties of Water and Steam. Since at some stages the function
use iterations, to speed up calculations you may disable precision mode
(functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
where:
Function
is based upon additional equations of the IAPWS Industrial Formulation 1997 for
Thermodynamic Properties of Water and Steam. Since at some stages the function
use iterations, to speed up calculations you may disable precision mode
(functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
251.
Temperature
in IF-97 region 2c [K] as function of pressure p [Pa], specific enthalpy h
[J/kg]:
where:
Function
is based upon additional equations of the IAPWS Industrial Formulation 1997 for
Thermodynamic Properties of Water and Steam. Since at some stages the function
use iterations, to speed up calculations you may disable precision mode
(functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
where:
Function
is based upon additional equations of the IAPWS Industrial Formulation 1997 for
Thermodynamic Properties of Water and Steam. Since at some stages the function
use iterations, to speed up calculations you may disable precision mode
(functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
where:
Function
is based upon the "Supplementary Release on Backward Equations for
Pressure as a Function of Enthalpy and Entropy p(h,s) to the IAPWS Industrial
Formulation 1997 for the Thermodynamic Properties of Water and Steam"
(September 2001). Since at some stages the function use iterations, to speed up
calculations you may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations (functions
wspGETTOLERANCE and wspSETTOLERANCE).
254.
Temperature
in IF-97 region 2 [K] as function of pressure p [Pa], specific enthalpy h
[J/kg]:
where:
Function
is based upon functions wspT2APH, wspT2BPH and wspT2CPH. Since at some stages
the function use iterations, to speed up calculations you may disable precision
mode (functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
where:
Function
is based upon functions wspT2APS, wspT2BPS and wspT2CPS. Since at some stages
the function use iterations, to speed up calculations you may disable precision
mode (functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
where:
Function
is based upon "Supplementary Release on Backward Equations for p(h, s) for
Region 3, Equations as a Function of h and s for the Region Boundaries, and a
Equation Tsat(h, s) for Wet Steam of the IAPWS Industrial Formulation 1997 for
the Thermodynamic Properties of Water and Steam" (September 2004). Since
at some stages the function use iterations, to speed up calculations you may
disable precision mode (functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE)
or vary relative precision for internal iterations (functions wspGETTOLERANCE
and wspSETTOLERANCE).
257.
Temperature
in IF-97 region 3 [K] as function of pressure p [Pa], specific enthalpy h
[J/kg]:
where:
Function
is based upon IAPWS Industrial Formulation 1997 for Thermodynamic Properties of
Water and Steam. The function uses the Newton method to determine the roots.
Since at some stages the function use iterations, to speed up calculations you
may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
where:
Function
is based upon IAPWS Industrial Formulation 1997 for Thermodynamic Properties of
Water and Steam. The function uses the Newton method to determine the roots.
Since at some stages the function use iterations, to speed up calculations you
may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
259.
Temperature
in IF-97 region 3 [K] as function of density r [kg/m3], specific enthalpy h
[J/kg]:
where:
Function
is based upon IAPWS Industrial Formulation 1997 for Thermodynamic Properties of
Water and Steam. The function uses the Newton method to determine the roots.
Since at some stages the function use iterations, to speed up calculations you
may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
where:
Function
is used to find the temperature in region 5 by Newton method. Since at some
stages the function use iterations, to speed up calculations you may disable
precision mode (functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary
relative precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
261.
Temperature
in IF-97 region 5 [K] as function of pressure p [Pa], specific enthalpy h
[J/kg]:
where:
Function
is based upon IAPWS Industrial Formulation 1997 for Thermodynamic Properties of
Water and Steam. The function uses the Newton method to determine the roots.
Since at some stages the function use iterations, to speed up calculations you
may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
where:
Function
is based upon IAPWS Industrial Formulation 1997 for Thermodynamic Properties of
Water and Steam. It uses the Newton method to determine the roots of the
function with two arguments. Since at some stages the function use iterations,
to speed up calculations you may disable precision mode (functions
wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative precision for
internal iterations (functions wspGETTOLERANCE and wspSETTOLERANCE).
where:
Function
is based upon "Supplementary Release on Backward Equations for p(h, s) for
Region 3, Equations as a Function of h and s for the Region Boundaries, and a
Equation Tsat(h, s) for Wet Steam of the IAPWS Industrial Formulation 1997 for
the Thermodynamic Properties of Water and Steam" (September 2004).
264.
Thermal
conductivity coefficient [W/(m·K)] as function of density r [kg/m3],
temperature t [K]:
wspTHERMCONDRT(r, t)
where:
Function
is based upon the Revised Release on the IAPS Formulation 1985 for the Thermal
Conductivity of Ordinary Water Substance with correction for ITS-90
(International Temperature Scale). The range of validity is: temperature from
0.01 to 800°C for pressure up to 40 MPa, from 0.01 to 650°C for pressure from
40 to 70 MPa, from 0.01 to 500 °C for pressure from 70 to 100 MPa.
wspU1PT(p, t)
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic
Properties of Water and Steam.
wspU2PT(p, t)
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic
Properties of Water and Steam.
wspU3PT(p, t)
where:
Function
is based upon functions wspR3PT and wspU3RT. Since at some stages the function
use iterations, to speed up calculations you may disable precision mode
(functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative
precision for internal iterations (functions wspGETTOLERANCE and
wspSETTOLERANCE).
wspU3RT(r, t)
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic
Properties of Water and Steam.
wspU5PT(p, t)
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic
Properties of Water and Steam.
270.
Specific
volume in IF-97 region 1 [m3/kg] as function of pressure p [Pa], temperature t
[K]:
wspV1PT(p, t)
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic
Properties of Water and Steam.
271.
Specific
volume in IF-97 region 2 [m3/kg] as function of pressure p [Pa], temperature t
[K]:
wspV2PT(p, t)
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic Properties
of Water and Steam.
where:
Function
is based upon "Supplementary Release on Backward Equations for p(h, s) for
Region 3, Equations as a Function of h and s for the Region Boundaries, and a
Equation Tsat(h, s) for Wet Steam of the IAPWS Industrial Formulation 1997 for
the Thermodynamic Properties of Water and Steam" (September 2004). Since
at some stages the function use iterations, to speed up calculations you may
disable precision mode (functions wspGETTOLERANCEMODE and wspSETTOLERANCEMODE)
or vary relative precision for internal iterations (functions wspGETTOLERANCE
and wspSETTOLERANCE).
where:
Function
is based upon IAPWS Industrial Formulation 1997 for Thermodynamic Properties of
Water and Steam. The function uses the Newton method to determine the roots.
Since at some stages the function use iterations, to speed up calculations you
may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
where:
Function
is based upon IAPWS Industrial Formulation 1997 for Thermodynamic Properties of
Water and Steam. The function uses the Newton method to determine the roots.
Since at some stages the function use iterations, to speed up calculations you
may disable precision mode (functions wspGETTOLERANCEMODE and
wspSETTOLERANCEMODE) or vary relative precision for internal iterations
(functions wspGETTOLERANCE and wspSETTOLERANCE).
275.
Specific
volume in IF-97 region 3 [m3/kg] as function of pressure p [Pa], temperature t
[K]:
wspV3PT(p, t)
where:
Function
is based upon function wspR3PT. Since at some stages the function use
iterations, to speed up calculations you may disable precision mode (functions
wspGETTOLERANCEMODE and wspSETTOLERANCEMODE) or vary relative precision for
internal iterations (functions wspGETTOLERANCE and wspSETTOLERANCE).
276.
Specific
volume in IF-97 region 5 [m3/kg] as function of pressure p [Pa], temperature t
[K]:
wspV5PT(p, t)
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic
Properties of Water and Steam.
wspVUSHCVWDERPT1PT(p, t, *v,
*u, *s, *h, *Cv, *w,
*DVDPt, *DUDPt, *DSDPt, *DHDPt,
*DVDTp, *DUDTp, *DSDTp, *DHDTp)
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic Properties
of Water and Steam and returns the set of properties that speed up calculation
considerably.
Note: In
Mathcad the function have only parameters (p, t) and return an array containing
output (return) parameters in SI units system.
Note: In
Excel the function have only parameters (p, t) and return an array which
contains output (return) parameters in SI units system. By default you will
receive only first output parameter (only one element from array). To retrieve
all values in array do next: 1) Enter formula with this function to any cell
(as example B2). 2) Select cells: first cell with inputted formula and some
cells on right hand (as example 2 cells from B2 to C2). 3) Press F2. 4) Press
Ctrl+Shift+Enter. If you want to retrive values in vertical way (as example for
cells from B2 to B3) please use the Excel built-in "TRANSPOSE"
function.
wspVUSHCVWDERPT2PT(p, t, *v,
*u, *s, *h, *Cv, *w,
*DVDPt, *DUDPt, *DSDPt, *DHDPt,
*DVDTp, *DUDTp, *DSDTp, *DHDTp)
where:
Function
is based upon the IAPWS Industrial Formulation 1997 for Thermodynamic
Properties of Water and Steam and returns the set of properties that speed up
calculation considerably.
Note: In
Mathcad the function have only parameters (p, t) and return an array containing
output (return) parameters in SI units system.
Note: In
Excel the function have only parameters (p, t) and return an array which
contains output (return) parameters in SI units system. By default you will
receive only first output parameter (only one element from array). To retrieve
all values in array do next: 1) Enter formula with this function to any cell
(as example B2). 2) Select cells: first cell with inputted formula and some
cells on right hand (as example 2 cells from B2 to C2). 3) Press F2. 4) Press
Ctrl+Shift+Enter. If you want to retrive values in vertical way (as example for
cells from B2 to B3) please use the Excel built-in "TRANSPOSE"
function.