By Peter Grassmann and H. Sawistowski (Auth.)
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C. Maxwell, 1873): quantity = numerical value x unit. g. g. e. whether h represents the quantity 19*62 m or only the number 19-62. This might at first be thought to be a purely academic question, but in practice a clear distinction must be drawn between the two possibilities, otherwise wrong conclusions could be obtained from correct equations. Naturally such an equation gives a correct result only if—but always when—all the quantities are measured in consistent units of the same system. Thus in our case, on using the SI, h must be expressed in m, t in s, and g in ms -2 .
7 In a fairly airtight chamber with a volume of 30 m 3 , at a temperature of 20°C, as a result of a very rapid combustion process, a quantity of heat amounting to Q kcal is released. What is the maximum size of Q at which the inward-opening door can still be opened despite the pressure rise due to heating of the air? 8. Dimensionally Homogeneous and Dimensional Equations! When the system of units has been decided upon, the quantities can be mea sured by determining, by means of a suitable method, how many times the unit is contained in the quantity being measured.
Then the lines u = const, can be marked in the x-y plane, for u = const. = u(x, y) corresponds to an equation between x and y which is represent ed by a curve in the x-y plane. It should be assumed that one of the curves in the set of curves obtained by successively taking various values for const. passes through both A0 and B0. Then c ( Ü \ = nm \dxjy ~c J*L\- iim A-C^O C0 — A0 \dxJu B ~B ' A-B-*O C 0 — A0 The slope in relation to the length unit of the X-axis differs, depending on whether one proceeds along a line y = const, or a line u = const.
Physical Principles of Chemical Engineering by Peter Grassmann and H. Sawistowski (Auth.)