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If area (A), velocity (v) and density (ρ) are base units, then the dimensional formula of force can be represented as |
Av$\rho$ $Av^2\rho$ $Av\rho^2$ $A^2v\rho$ |
$Av^2\rho$ |
F = $A^av^b\rho^c$ ⇒ $[MLT^{-2}]$ = $[L^2]^a[LT^{-1}]^b[ML^{-3}]^c$= $[M^cL^{2a+b-3c}T^{-b}]$ Comparing the coefficient on both sides c = 1 -b = -2 ⇒ b = 2 2a+b-3c = 1 ⇒ a = 1 F = $Av^2\rho$ |
