Question

If velocity potential (ϕ) exists in a fluid flow, then the flow is said to be:
1. turbulent
2. irrotational
3. rotational
4. laminar

Answer 1

Correct Answer - Option 2 : irrotational

Explanation:

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 the fluid in that direction.

Properties of Velocity Potential function:

• If velocity potential (ϕ) exists, 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.

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:

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