By Harold A. Simon
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Extra info for A Student's Introduction to Engineering Design
Second, even though the result expressed is universal, so one unique curve of C against Re for a particular body might be expected regardless of the units commonly employed by the experimenter, certain pitfalls must be guarded against. It is common, for example, to define force coefficients as (F/(l/2)pl/ 2 / 2 ), but this is not always true. The factor 1/2 is quite superfluous and merely highlights the need to check the exact definition of such groups. The characteristic length, /, or area, I2, are also liable to vary from one publication to the next.
An experiment may show a variation as in Fig. 2L. The stiffness, K, is defined as the slope of this curve. Although it is clear that K is a function of y, it may be best to assume it a constant. ^ — ——— Actual Approximation Displacement y Fig. 2L Approximation of constant stiffness. Linear behavior leads to the result that the sum of the displacement of the spring under forces Fi and F2 acting separately is the same as the displacement under Fi and F2 acting together. If a differential equation of motion describing a system incorporating such a spring is written down, K will occur in one of the coefficients, a„.
If one wishes to avoid the use of gc because of its nuisance value in physical equations, the pound mass must be consistent with the use of the pound force. 174 lbf sec/ft2 In summary, physical equations must be dimensionally homogeneous if they are correct. When numbers are substituted into the equations to represent the physical quantities, either consistent units must be used or factors such as gc must be introduced to allow for the lack of consistency. It is, however, not recommended that such factors be included in the writing of the equations, which should be true regardless of the choice of units.
A Student's Introduction to Engineering Design by Harold A. Simon