If area (A) velocity (v) and density (ρ) are base units, then the dimensional formula of force can be represented as
Avρ
Av2ρ
Avρ2
A2vρ
F=kAxvyρz⇒MLT−2=L2xLT−1yML−3z⇒z=1,2x+y−3z=1,−y=−2⇒y=2⇒ x=1 F=kA1v2ρ1=Av2ρ,k=1