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: 1.6

Answer

In the $MLT system$, the requested dimensions are: a)$\frac{∂u}{∂t}=LT^{-2}$ b)$\frac{∂^{2}u}{∂x∂t}=T^{-2}$ c)$∫(\frac{∂u}{∂t})dx=L^{2}T^{-2}$

Work Step by Step

Integration and derivative signs are mathematical operators and not physical quantities, so have no dimensions. If $u$ is velocity, $x$ is length, and $t$ is time, then: a)$\frac{∂u}{∂t}=\frac{m/s}{s}=\frac{m}{s^{2}}=LT^{-2}$ b)$\frac{∂^{2}u}{∂x∂t}=\frac{m/s}{m\times s}=\frac{1}{s^{2}}=T^{-2}$ c)$∫(\frac{∂u}{∂t})dx=(\frac{m/s}{s})\times m=\frac{m^{2}}{s^{2}}=L^{2}T^{-2}$
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