Question

derive the dimensional formula of pressure gradient​

Answer 1

Pressure Gradient = Pressure × [Distance]-1 . . . . (1)

The dimensional formula of distance = [M0 L1 T0] . . . . (2)

⇒ Pressure = Force × [Area]-1 . . . . (3)

Since, Force = mass × acceleration

∴ the dimensions of force = [M] × [L1 T-2] = [M1 L1 T-2] . . . (4)

And, the dimensional formula of area = [M0 L2 T0] . . . (5)

On substituting equation (4) and (5) in equation (3) we get,

Pressure (P) = [M1 L1 T-2] × [M0 L2 T0]-1

Therefore, the dimensional formula of pressure = [M1 L-1 T-2] . . . . (6)

On substituting equation (2) and (6) in equation (1) we get,

Pressure Gradient = Pressure × [Distance]-1

Or, P = [M1 L-1 T-2] × [M0 L1 T0]-1 = [M1 L-2 T-2]

Therefore, the pressure gradient is dimensionally represented as [M1 L-2 T-2].