# What is Dimensional Formula of Critical velocity ?

Posted in Dimensional Formulae | Email This Post |**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) = M^{0}L^{0}T^{0}

Dimensional Formula of coefficient of viscosity (η) = M^{1}L^{-1}T^{-1}

Dimensional Formula of Density of fluid (ρ) =M^{1}L^{-3}T^{0}

Dimensional Formula of radius (r) = M^{0}L^{1}T^{0}

Putting these values in above equation we get,

**V _{C} = [M^{0}L^{0}T^{0}] [M^{1}L^{-1}T^{-1}] / [M^{1}L^{-3}T^{0}] [M^{0}L^{1}T^{0}]**

**Dimensional Formula of** **Critical velocity**(V_{C}) = **M ^{0}L^{1}T^{-1}**

**SI unit of Critical velocity(V**

_{C}) is ms^{-1}
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