Understanding the Free and Forced Vortex Flow -->

Understanding the Free and Forced Vortex Flow

Vortex flow tornado


What is Vortex Flow in fluid mechanics?

Vortex flow definition: It is a type of flow that occurs in fluids where the flow rotates around a central axis, creating a swirling motion. Simply it is a flow of rotating mass of fluid or flow of fluid along curved path. This type of flow can be observed in tornadoes, whirlpools, and other phenomena where fluid is rotating in a confined area.

Types of Vortex Flow

There are two vortex types
1. Free vortex flow
2. Forced vortex flow

Free Vortex Flow

In a free vortex flow, the fluid is rotating due to the conservation of angular momentum, without any external forces. This type of vortex flow is commonly observed in natural systems, such as tornadoes and whirlpools. In a free vortex motion, the flow velocity is inversely proportional to the radius. Example of free vortex flow includes a whirlpool in a river, water flowing out of a bathtub or a sink, flow in a centrifugal pump casing and flow around the circular bend in a pipe.

Forced Vortex Flow

In a forced vortex flow, an external force is applied to the fluid, such as a rotating impeller in a pump or a spinning rotor in a turbine, to generate the rotational motion. This type of vortex flow is commonly found in man-made systems, such as hydraulic turbines and mixing tanks. In a forced vortex motion the velocity of flow is directly proportional to the radius. Other examples for forced vortex flow is rotating a vessel containing a liquid with constant angular velocity, flow inside the centrifugal pump.

The main difference between free and forced vortex flow lies in the origin of the rotational motion. Free vortex flow is driven by the conservation of angular momentum, and forced vortex flow is driven by an external force.

Free Vortex Flow Equation

Free and forced vortex flow- Velocity profile
Free and forced vortex flow - Velocity profile

  • No external torque or energy required. The fluid rotating under certain energy previously given to them. In a free vortex mechanics, overall energy flow remains constant. There is no energy interaction between an external source and a flow or any dissipation of mechanical energy in the flow.
  • Fluid mass rotates due to conservation of angular momentum.
  • Velocity inversely proportional to the radius.

For a free vortex flow

Free vortex flow - Velocity equation
At the center (r = 0) of rotation velocity approaches to infinite, that point is called singular point.

Forced Vortex Flow Equation

  • To maintain a forced vortex flow, it required a continuous supply of energy or external torque.
  • All fluid particles rotate at the constant angular velocity ω as a solid body. Therefore, a flow of forced vortex is called as a solid body rotation.
  • Tangential velocity is directly proportional to the radius.

                  v = r ω          
                  ω = Angular velocity.
                  r = Radius of fluid particle from the axis of rotation.

  • The surface profile of vortex flow is parabolic.

Forced vortexForced vortex - Height equation

  • In forced vortex total energy per unit weight increases with an increase in radius.
  • Forced vortex is not irrotational; rather it is a rotational flow with constant vorticity 2ω.

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