The pressure drop, p, along a straight pipe of diameter D

Chapter 7, Problem 7.22

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The pressure drop, \(\Delta p\), along a straight pipe of diameter D has been experimentally studied, and it is observed that for laminar flow of a given fluid and pipe, the pressure drop varies directly with the distance, \(\ell\), between pressure taps. Assume that \(\Delta p\) is a function of D and \(\ell\), the velocity, V, and the fluid viscosity, \(\mu\). Use dimensional analysis to deduce how the pressure drop varies with pipe diameter.

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