## Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version 8th Edition

Published by Wiley

# 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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