Question

What is the expression of cretical velocity by using dimensional analysis

Answer 1

hey

Critical velocity is defined as the maximum velocity of a fluid above which a streamline flow changes to turbulent flow. In other words critical velocity the maximum velocity of fluid upto which its flow remains streamline and if the velocity of a fluid increases more than its critical velocity the flow of fluid becomes turbulent.

Mathematically,

Critical velocity (VC) = Re   η /  ρ  r    

where

Re = Reynolds number

η = coefficient of viscosity

ρ = density of fluid

r = radius of tube.

Dimensional Formula of Reynolds number (Re) = M0L0T0

Dimensional Formula of coefficient of viscosity (η) =  M1L-1T-1

Dimensional Formula of Density of fluid (ρ) =M1L-3T0

Dimensional Formula of radius (r) = M0L1T0

Putting these values in above equation we get,

VC = [M0L0T0] [M1L-1T-1] / [M1L-3T0] [M0L1T0]

Dimensional Formula of Critical velocity(VC) = M0L1T-1

SI unit of Critical velocity(VC) is ms-