By Bahman Zohuri
This ground-breaking reference presents an summary of key thoughts in dimensional research, after which pushes way past conventional purposes in fluid mechanics to illustrate how robust this instrument will be in fixing complicated difficulties throughout many various fields. Of specific curiosity is the book’s insurance of dimensional research and self-similarity equipment in nuclear and effort engineering. a number of useful examples of dimensional difficulties are awarded all through, permitting readers to hyperlink the book’s theoretical factors and step by step mathematical ideas to functional implementations.
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Extra info for Dimensional Analysis and Self-Similarity Methods for Engineers and Scientists
Firstly, one must decide what variables enter the problem. Occasionally a dimensional analysis will show that one of the selected variables should not be present, since it involves a dimension not shared by any of the other variables; but if the wrong variables go in, the wrong dimensionless numbers come out, most of the time. 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.
To apply the Pi theorem to this mixer we choose the blade speed V, its width d, and the butter density ρ as the fundamental variables (k = 3), which we then permute with two remaining variables—the viscosity μ and the drag force FD –to get two dimensionless groups: 1 = V a1 d b1 ρ c 1 μ 2 = V a2 d b2 ρ c 2 F D Expressed in terms of primary dimensions, these groups are: 1 L T a1 = = L T a2 2 M L3 c1 Lb1 M LT M L3 c2 Lb2 ML T2 42 1 Dimensional Analysis Now in order for 1 and 2 to be dimensionless, the exponents for each of the three primary dimensions must vanish.
Presumably, Fanning used the radius of the pipe rather than the diameter as the basis for his analysis. (A copy and description of the Moody diagram should be included here). The Moody chart or Moody diagram is a graph in nondimensional form that relates the Darcy friction factor, Reynolds number and relative roughness for fully developed flow in a circular pipe. It can be used for working out pressure drop or flow rate down such a pipe. A depiction such diagram is presented below Fig. 7; As one final remark, we did not really need to write down the dimension matrix.
Dimensional Analysis and Self-Similarity Methods for Engineers and Scientists by Bahman Zohuri