**Critical
Velocity**

**What is
Critical Velocity?**

Critical velocity is the speed and direction at which the flow of a liquid through a tube changes from smooth to turbulent. It is defined as the speed at which falling objects reaches when both gravity and air resistance are equalised on the object.

The critical velocity is that velocity of liquid flow up to which its flow is streamlined and above which its flow becomes turbulent. Reynold’s number is a pure number which determines the nature of flow of liquid through a pipe.

**Formula to
find the Critical Velocity: **Critical Velocity is the ratio of the inertial force per unit
area to the viscous force per unit area for a flowing fluid.

\(Critical\,\,Velocity\,({{V}_{C}})\,\,=\,\,\frac{{{R}_{e}}\eta }{\rho r}\).

Where,

η = Co- efficient Viscosity,

r = Radius,

ρ = Density,

R_{e} = Reynolds number.

**Dimensional
formula of Critical Velocity:**

Dimensional formula of co – efficient of viscosity (η) = M¹L⁻¹T⁻¹

Dimensional formula of Reynolds
number (R_{e}) = M⁰L⁰T⁰

Dimensional formula of Radius (R) = M⁰L¹T⁰

Dimensional formula of density of fluid (ρ) = M¹L⁻³T⁰.

\(Critical\,\,Velocity\left( {{V}_{C}} \right)=\frac{{{R}_{e}}\eta }{\rho r}=\frac{\left( {{M}^{1}}{{L}^{-1}}{{T}^{-1}} \right)\left( {{M}^{0}}{{L}^{0}}{{T}^{0}} \right)}{\left( {{M}^{1}}{{L}^{-3}}{{T}^{0}} \right)\left( {{M}^{0}}{{L}^{1}}{{T}^{0}} \right)}=\left( {{M}^{0}}{{L}^{1}}{{T}^{-1}} \right)\).

∴ Critical Velocity (V_{c}) = (M⁰L¹T⁻¹).