Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version 8th Edition

Published by Wiley
ISBN 10: 1119080703
ISBN 13: 978-1-11908-070-1

Chapter 1 - Problems - Page 31: 1.13

Answer

constant $ \frac{\pi }{8}$ is dimensionless and yes this equation classify as homogeneous equation

Work Step by Step

$Q=\frac{\pi R^{4} \Delta P}{8 \mu \iota}$ we put dimensions in equation as follows : $Q =L^{3} T^{-1} $ & R = L & $\mu = F L^{-2}T$ & $\Delta P = M L^{-1} T^{-2}$ & $ \iota =L $ $ L^{3} T^{-1} = \frac{\pi}{8} \times \frac{L^{4}\times M L^{-1} T^{-2} }{F L^{-2}T \times L}$ where $F =M L^{-1} T^{-2}$ Delete similar dimensions , $\frac{\pi}{8}$ become dimensionless
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