Answer
$\mathcal{V}_{avg}=\frac{2}{R^2}\int_0^R \mathcal{V}(r) rdr$
Work Step by Step
$\dot{m}=\rho\pi R^2\mathcal{V}_{avg}=\int_0^R \rho \mathcal{V}(r)2\pi rdr$
$\mathcal{V}_{avg}=\frac{2}{R^2}\int_0^R \mathcal{V}(r) rdr$
Thermodynamics: An Engineering Approach 8th Edition
by Cengel, Yunus; Boles, Michael
Published by
McGraw-Hill Education
ISBN 10:
0-07339-817-9
ISBN 13:
978-0-07339-817-4
Chapter 5 - Mass and Energy Analysis of Control Volumes - Problems - Page 272: 5-190
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