What is Critical Velocity?

Critical Velocity is that velocity at which the movement of a fluid changes from smooth and orderly laminar to chaotic or random turbulent. It is one of the very important concepts in engineering, environmental science and aerodynamics because it predicts the way the fluids are going to behave under different conditions.

How to Calculate Critical Velocity?

The formula to determine the critical velocity of liquid flowing through a tube ,

where,

•  Vc is the critical velocity

•  K is the Reynold's number

•   is coefficient of the viscosity of the liquid

•  r is the radius of the tube through which the liquid flows

•  ρ is the density of the liquid

Depending upon the value of Reynold's number, the type of flow can be determined as follows:

• If K lies between 0 to 2000 then the flow remains laminar or streamlined

• K between 2000 to 3000 then remains flow is turbulent or unstable

• And at K above 3000 then the flow becomes highly unstable.

Solved Problems

Problem 1: Water is flowing in a pipe. The dynamic viscosity is 0.001 Pa·s, density is 1000 kg/m³, and the radius of the pipe is 0.05 m. If K is 0.5 for a pipe that is circular in cross section, what is the critical velocity (Vc) of the water in the pipe?

Solution: 

Given,

Dynamics viscosity of water (η) = 0.001 Pa·s

Density of water (ρ) = 1000 kg/m³

Radius of the pipe (r) = 0.05 m

Assuming K = 0.5 for pipe circular in shape.

Formula for critical velocity is given as,

Substituting the values in equation:

Therefore, The critical velocity for water in this pipe is 1 10-5 .The critical velocity for water in this pipe i m/s. If the velocity of water exceeds that value, the flow becomes turbulent.

 

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