Question

The force, F, of the wind blowing against a building is given by where V is the wind speed, rho the density of the air, A the cross-sectional area of the building, and CD is a constant termed the drag coefficient. Determine the dimensions of the drag coefficient.

Answer 1

Answer:

dimensions of the drag coefficient is $[M^0 L^0 T^0]$

Drag coefficient is a dimensionless quantity

Explanation:

force is given by$F=\frac{C_{D} \rho V^2 A}{2}$

we get expression for drag coefficient $C_{D} =\frac{2F}{\rho V^2 A}$

By substituting the dimensions  of the F,V,A and density , we get

$C_{D} =\frac{[F]}{[\rho ][V]^2[A]} \\C_{D} =\frac{[MLT^{-2}]}{[ML^{-3} ][L T^{-1}]^2[L^2]} \\C_{D} =\frac{[MLT^{-2}]}{[ML^{-3} ][L^2 T^{-2}][L^2]} \\C_{D} =\frac{[MLT^{-2}]}{[MLT^{-2}]}\\C_{D}=[M^0 L^0 T^0]$

Drag coefficient is a dimensionless