Question

If f v d aretaken as fundamental quantities then derive the dimensional formula for pressure

Answer 1

Answer:

Dimensional formula for pressure is [$ML^{-1}T^{-2}$]

Explanation:

Pressure is defined as force exerted per unit area. That is,

Pressure = $\frac{Force}{Area}$

Force = mass × acceleration, and

acceleration = velocity ÷ time, and

velocity = distance ÷ time

Hence dimensional formula for force is:

[F] = $[M] [LT^{-2} ]$, where M, L, T represent mass, length(distance) and time respectively.

Area = length × length

Hence dimensional formula for area is:

[A] = $[L^{2} ]$

Hence dimensional formula for pressure is:

[P] =  $\frac{[M][LT^{-2}] }{[L^{2}] }$

    = $[ML^{-1}T^{-2}]$