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-1