# Free And Forced Vortex Flow

Vortex flow: flow of rotating mass of fluid or flow of fluid along curved path.

### Free vortex flow

• 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

At the center (r = 0) of rotation velocity approaches to infinite, that point is called singular point.

• The free vortex flow is irrotational, and therefore, also known as the irrotational vortex.
• In free vortex flow, Bernoulli’s equation can be applied.
Examples include a whirlpool in a river, water flows out of a bathtub or a sink, flow in centrifugal pump casing and flow around the circular bend in a pipe.

### Forced vortex flow

• 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.
• 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.
Examples for forced vortex flow is rotating a vessel containing a liquid with constant angular velocity, flow inside the centrifugal pump.

1. 