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.
