What is Dimensional Formula of Critical velocity ?

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 (V_C) = 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,

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

Dimensional Formula of Critical velocity(V_C) = M⁰L¹T^-1
SI unit of Critical velocity(V_C) is ms^-1