Answer:
dimensions of the drag coefficient is [tex][M^0 L^0 T^0][/tex]
Drag coefficient is a dimensionless quantity
Explanation:
force is given by[tex]F=\frac{C_{D} \rho V^2 A}{2}[/tex]
we get expression for drag coefficient [tex]C_{D} =\frac{2F}{\rho V^2 A}[/tex]
By substituting the dimensions of the F,V,A and density , we get
[tex]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][/tex]
Drag coefficient is a dimensionless
