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: 1.1

Answer

The drag coefficient, Cd, is dimensionless.

Work Step by Step

Find the dimensions of each variable in the initial equation. (F, p, V, A): *Note: l = length and d= distance which have the same units, so l=d $F= m \times a$ = $ m \times (d \times (t^-2)) $ $ p = m\div (l^3) $ = $ m \times (l^-3) $ = $ m \times (d^-3) $ $ V = d \div t $ = $ d \times (t^-1) $ $ A = l \times l $ = $ (l^2) $ = $ (d^2) $ Plug dimensions into initial equation and solve for Cd: $ [(m \times d \times (t^-2)] = (Cd \div 2) \times [ m \times d^-3] \times [d \times t^-1]^2 \times [d^2] $ = $ Cd = 2 [ m^0 \times d^0 \times t^0] $ Therefore, the constant drag coefficient, Cd, is dimensionless.
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