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    Dimensional Analysis and Similarity

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    Consider flow in a pipe of diameter D through a pipe bend of radius Rb. The pressure loss p through the bend is a function of these two length scales, plus density , viscosity  and average flow velocity V.
    a) Use dimensional analysis to rewrite this function in terms of dimensionless PI groups.
    b) In analyzing data for such pipe-bend losses (Chap.6), the dimensionless loss is often correlated with Dean number:
    De = Red (D/2Rb)^1/2

    Can your dimensional analysis produce a similar group? If not, explain why not.

    See attachment for better formula representation

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    Solution Summary

    This in-depth solution contains step-by-step calculations to rewrite the dimensionless PI groups of the function with dimensional analysis. It also explains if the Dean number can produce a similar group. All workings and formulas are shown with brief explanations.