Critical Velocity Formula

Critical velocity is the speed and direction at which the flow of a liquid through a tube changes from smooth to turbulent. Determining the critical velocity depends on multiple variables, but it is the Reynolds number that characterizes the flow of the liquid through a tube as either turbulent or laminar. The Reynolds number is a dimensionless variable, which means that it has no units attached to it. In this article, we shall be discussing the critical velocity formula.

How to Calculate Critical Velocity?

The formula to calculate the critical velocity of a liquid flowing through a tube is given by

\(V_c=\frac{k_\eta}{r_\rho }\)

where, Vc is the critical velocity

K is the Reynold’s number

\(\eta\) is the coefficient of the viscosity of the liquid

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

\(\rho\( is the density of the liquid

Depending on the value of Reynold’s number, the flow type can be decided as follows:

  • If K is between 0 to 2000, the flow is laminar or streamlined.
  • If K is between 2000 to 3000, the flow is turbulent or unstable
  • If K is above 3000, the flow is highly unstable

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Practise This Question

A ball is connected to a rope and swung around in uniform circular motion. The tension in the rope is measured at 10 N and the radius of the circle is 1 m. How much work is done in one revolution around the circle?