Tip 76. Units and the function Find

Fig. 76. Solution of a dimension system of the algebraic equations

The feature of the solutions of the problem about sizes of the submarine “Nautilus”, shown in the fig. 74 and fig. 75 is that the units of physical values were used: length, area and volume (see also tip 16, tip 17, tip 21, tip 51, tip 61 and tip 64). The dimension allows, firstly, to control an accuracy of spelling of the formulas (for example, do not sum up area with volume) and, secondly, to increase “readability” of a solution of a problem by a man: not only 1 500, but also 1 500 m³ and etc. ( Tip without number, suggested itself: if a problem has physical values then when you solve the problem in Mathcad it would not be out of place to enable units). In the solutions shown in the fig. 74 and fig. 75, units could be used without any problems as since the arguments of the built-in function Find were the same dimension of length. But the problem about size of “Nautilus” can be expressed another way – for example, to find the length of the submarine and the cross-section area of its bit (crown) core. In this case it is possible to solve this problem with help of the structure Given-Find, for example, only if we reduced all values to non-dimensional ones with help of the method defined in the tip 36. If this was not be done then as rule, the calculation will be interrupted with misinform message that there are not correspondence with units though the reason of the bug was not in it.

All the same it is possible to solve a problem with different dimensions with help of the Given-Find in Mathcad. The solution of such problem is showed in the fig. 76: it turns out that a vector can keep the values with different dimensions but can not give them out to print. In this case separate scalars formed the vector are given out to print.