Thermodynamics: An Engineering Approach 8th Edition

Published by McGraw-Hill Education
ISBN 10: 0-07339-817-9
ISBN 13: 978-0-07339-817-4

Chapter 17 - Compressible Flow - Problems - Page 890: 17-37

Answer

$Ma= 0.974$

Work Step by Step

The temperature is $$-50+273.15=223.15 \mathrm{~K}.$$ The speed of sound is $$ c=\sqrt{k R T}=\sqrt{(1.4)(0.287 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K})(223.15 \mathrm{~K})\left(\frac{1000 \mathrm{~m}^2 / \mathrm{s}^2}{1 \mathrm{~kJ} / \mathrm{kg}}\right)}\left(\frac{3.6 \mathrm{~km} / \mathrm{h}}{1 \mathrm{~m} / \mathrm{s}}\right)=1077.97 \mathrm{~km} / \mathrm{h} $$ and $$ \mathrm{Ma}=\frac{V}{c}=\frac{1050 \mathrm{~km} / \mathrm{h}}{1077.97 \mathrm{~km} / \mathrm{h}}=0.9741 \mathrm{~km/h} \cong 0.974 \mathrm{~km/h} $$
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