By Bahman Zohuri

This ground-breaking reference offers an summary of key techniques in dimensional research, after which pushes well past conventional functions in fluid mechanics to illustrate how robust this software might be in fixing complicated difficulties throughout many different fields. Of specific curiosity is the book’s assurance of dimensional research and self-similarity tools in nuclear and effort engineering. quite a few useful examples of dimensional difficulties are awarded all through, permitting readers to hyperlink the book’s theoretical factors and step by step mathematical suggestions to sensible implementations.

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**Example text**

A number of choices regarding the repeating variables arise in this case Again, it is true that if one of the repeating variables is changed, it results in a different set of π terms. Therefore, the interesting question is which set of repeating variables is to be chosen, to arrive at the correct set of π terms to describe the problem. The answer to this question lies in the fact that different sets of π terms resulting from the use of different sets of repeating variables are not independent. Thus, anyone of such interdependent sets is meaningful in describing the same physical phenomenon.

3. One error to avoid in choosing the variables is the inclusion of variables whose influence is already implicitly accounted for. In analyzing the dynamics of a liquid flow, for example, one might argue that the liquid temperature is a significant variable. It is important, however, only in its influence on other properties such as viscosity, and should therefore not be included along with them. 4. The Buckingham pi theorem, if applied to the actual number of dimensions being used, tells only that there must be at least a certain number of dimensionless numbers involved.

If ω is a function of (g, l, m), then its dimensions must be a power-law monomial of the dimensions of these quantities. 5 Dimensions, Dimensional Homogeneity, and Independent Dimensions 21 with a, b, and c constants which are determined by comparing the dimensions on both sides of the equation. We see that ⎧ a+b =0 ⎪ ⎨ −2a = −1 ⎪ ⎩ c=0 The solution is then a = 1/2, b = −1/2, c = 0, and we recover Eq. 10. A set of quantities (a1 ,. , ak ) is said to have independent dimensions if none of these quantities have dimensions, which can be represented as a product of powers of the dimensions of the remaining quantities.