Question

Which of the following examples are representing Free Vortex Flow?

(i) Flow of liquid inside the impeller of a centrifugal pump

(ii) A whirlpool in a river

(iii) Flow of fluid in a centrifugal pump casing

(iv) Flow of liquid through a hole provided at the bottom of a container

(ii) and (iv) only

(ii), (iii) and (iv)

(i), (ii) and (iv)

(ii) and (iii) only

Answer ( Option B)

(ii), (iii) and (iv)

Solution

Vortex Flow

Vortex flow is defined as the flow of a fluid along a curved path or the flow of a rotating mass of fluid is known a 'Vortex Flow'. The vortex flow is of two types namely :

1. Forced vortex flow, and

2. Free vortex flow.

Forced Vortex Flow:

Forced vortex flow is defined as that type of vortex flow, in which some external torque is required to rotate the fluid mass. The fluid mass in this type of flow, rotates at constant angular velocity, . The tangential velocity of any fluid particle is given by

v = ω × r

Where, r = Radius of fluid particle from the axis of rotation.

Examples of forced vortex are :

1. A vertival cylinder containing liquid which is rotated about its central axis with a constant angular volocity ω , as shown in fig above.

2. Flow of liquid inside the impeller of a centrifugal pump.

3. Flow of water through the runner of a turbine.

Free Vortex Flow:

When no external torque is required to rotate the fluid mass, that type of flow is called free vortex flow. Thus the liquid in case of free vortex is rotating due to the rotation which is imparted to the fluid previously. Examples of the free vortex flow are:

1. Flow of liquid through a hole provided at the bottom of a container.

2. Flow of liquid around a circular bend in a pipe.

3. A whirlpool in a river.

4. Flow of fluid in a centrifugal pump casing.

The relation between velocity and radius, in free vortex is obtained by putting the value of external torque equal to zero, or the time rate of change of angular momentum, i.e., moment of momentum must be zero. Consider a fluid particle of mass 'm' at a radial distance r from the axis of rotation, having a tangential velocity v.

Then,

Angular momentum = Mass × Velocity = m × v

Moment of momentum = Momentum × r = m×v×r