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 32: 1.26

Answer

${\frac{V}{\sqrt{g l}}}\,=1.25$

Work Step by Step

In British Uints $\frac{V}{\sqrt{g l}}=\frac{10 \frac{f t}{s}}{\sqrt{\left(32.2 \frac{f t}{s^2}\right)(2 f t)}}=1.25$ In SI units $\begin{aligned} & V=\left(10 \frac{\mathrm{ft}}{\mathrm{s}}\right)\left(0.3048 \frac{\mathrm{m}}{\mathrm{ft}}\right)=3.05 \frac{\mathrm{m}}{\mathrm{s}} \\ & g=9.81 \frac{\mathrm{m}}{\mathrm{s}^2} \\ & l=(2 \mathrm{ft})\left(0.3048 \frac{\mathrm{m}}{\mathrm{ft}}\right)=0.610 \mathrm{~m}\end{aligned}$ $\frac{V}{\sqrt{g l}}=\frac{3.05 \frac{\mathrm{m}}{\mathrm{s}}}{\sqrt{\left(9.81 \frac{\mathrm{m}}{\mathrm{s}^2}\right)(0.610 \mathrm{~m})}}=1.25$ so The value of dimensionless parameter doesn't depend on the unit system
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