Problem 1/10 Page 14, Engineering Mechanics - Dynamics, Meriam and Kraige, 4th Edition
Given: CD = D / 1/2 r v2 S
D is a force, S is an area, r is a mass density and v is a velocity.
Find: The dimensions of CD.
Dimension of CD = Force / (Mass/Length3) (Length/Time)2 Length2
= Force / { Mass Length / Time2 }
But the units of force are equivalent to the units of mass multiplied by the units of acceleration. The units of acceleration are length/time2. Thus:
Dimensions of CD = Mass Length / Time2 / { Mass Length / Time2 }
CD is dimensionless.