Critical Velocity Formula

Critical Velocity Formula

Critical velocity is defined as the speed at which a falling item achieves equilibrium between gravity and air resistance.

The third way to define critical velocity is the rate and direction at which a fluid may flow through a conduit without becoming turbulent. Turbulent flow is described as fluid flow that is erratic and changes amplitude and direction on a continual basis. It is the polar opposite of laminar flow, which is defined as fluid movement in parallel layers with no layer disturbance.

Formula of Critical Velocity

The critical velocity of a free-falling object is the speed at which gravity and air resistance are equalised. It is the speed at which the flow of a fluid changes from streamlined to turbulent. A liquid’s critical velocity is determined by a variety of parameters, including its Reynolds number, viscosity coefficient, tube radius, and fluid density. It is represented by the symbol Vc. Its unit of measurement is m/s, and the dimensional formula is given as [M⁰L¹T^-1].

V_c = R_eη / ρr

Where,

V_c is the critical velocity,

R_e is the ratio of inertial force to viscous force, that is, Reynolds number,

η is the coefficient of viscosity,

ρ is the density of the fluid,

r is the radius of tube.

Critical Velocity Types

Lower Critical Velocity: The rate at which laminar flow ceases or switches to the transition phase. There is a temporal difference between laminar and turbulent flow. Experiments have shown that when a laminar flow transitions to turbulence, the transition is gradual. There is, however, a transition period between the two types of fluxes. In 1883, Prof. Reynolds Osborne pioneered this experiment.

Upper Critical Velocity: The Critical Velocity at which a flow switches from a transition phase to a turbulent flow is referred to as the “greater or higher Critical velocity.”

The Critical Velocity Formula is the speed and direction at which a liquid’s flow in a tube transitions from smooth to turbulent. The critical velocity is determined by a variety of variables, but the Reynolds number characterises the flow of liquid through a tube as turbulent or laminar. The Reynolds number is a dimensionless variable, meaning it has no units associated with it. The Critical Velocity Formula will be discussed in the Critical Velocity Formula.

How to Calculate Critical Velocity?

The speed at which gravity and air resistance on a falling object are equalised is known as the Critical Velocity Formula of the object. The alternate method of elucidating Critical Velocity is to determine the speed and direction at which a fluid will flow through a conduit without becoming turbulent. Turbulent flow is described as an unpredictable fluid flow that changes amplitude and direction continually.

The quantity of gas necessary to maintain fluids entrained in the gas stream and raised to the surface is described as “critical velocity.” The higher the line pressure, the higher the needed flow rate. The bigger the pipe or tube, the greater the needed flow rate. Reynolds demonstrated experimentally that if the average velocity of the flow of a certain liquid is less than a specific value, the motion is streamlined, and if it is more than this value, the flow becomes turbulent.

Solved Problems on Critical Angle

Problem 1: Determine the critical velocity of a fluid flowing through a 5 m radius tube. The fluid’s density and coefficient of viscosity are 2.5 kg/m³ and 2 kg/ms, respectively. The Reynolds number is 2500.

Solution:

We have,

R_e = 2500

η = 2

ρ = 2.5

r = 5

Using the formula we get,

V_c = R_eη / ρr

= (2500) (2)/ (2.5) (5)

= 2000/5

= 400 m/s