ψ Exists for __________

Question

Question

This question was previously asked in

JKSSB JE CE 2021 Official Paper Shift 2 (Held on 29 Oct 2021)

Answer 1

Explanation:

Velocity potential exists for irrotational flows only.
Velocity and stream function can exist in both rotational and irrotational flows.

Stream Function:

It is the scalar function of space and time.
The partial derivative of stream function with respect to any direction gives the velocity component perpendicular to that direction. Hence it remains constant for a streamline
Stream function defines only for the two-dimensional flow which is steady and incompressible..

Properties of stream function:

If ψ exists, it follows continuity equation and the flow may be rotational or irrotational.
If ψ satisfies the Laplace equation, then the flow is irrotational.

Velocity Potential function:

This function is defined as a function of space and time in a flow such that the negative derivation of this function with respect to any direction gives the velocity of fluid in that direction.

Properties of Velocity Potential function:

If velocity potential (ϕ) exist, there will be a flow.
Velocity potential function exists for flow then the flow must be irrotational.
If velocity potential (ϕ) satisfies the Laplace equation, it represents the possible steady incompressible irrotational flow.