Critical Velocity and Reynolds’s Number

Critical Velocity

When the velocity of flow is less than a certain value, called critical velocity, the flow remains streamlined. But when the velocity of flow exceeds the critical velocity, the flow becomes turbulent.

The value of critical velocity of any liquid depends on the

  • nature of the liquid i.e. coefficient of viscosity (η) of the liquid
  • diameter of the tube (d) through which the liquid flows
  • density of the liquid (ρ)

Experiments show that

vc ∝ η

vc ∝ 1/ρ

vc ∝ 1/d

Hence,

vc = R.η/ρ d

where R is constant of proportionality and is called Reynolds’s Number. It has no dimensions.

Reynolds Number

Reynolds number is a dimensionless number, whose value gives one an approximate idea whether the flow would be turbulent.

R = ρvd/η

Experiments show that if R is below 1000, the flow is streamline or laminar. The flow becomes unsteady when R is between 1000 and 2000 and the flow becomes turbulent for R greater than 2000.