Velocity potential function exist only when

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MPPSC AE Civil Engineering 2021 Official Paper
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  1. flow is laminar
  2. flow is turbulent
  3. flow is irrotational
  4. flow is rotational

Answer (Detailed Solution Below)

Option 3 : flow is irrotational
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Detailed Solution

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Explanation:

Velocity Potential Function:

It is defined as the scalar function of space and time, such that its negative derivative with respect to any direction gives the velocity in that direction.

It is denoted by ϕ and defined for two-dimensional as well as three-dimensional flow.

Properties of Stream function:

  • If velocity potential function exists, the flow should be irrotational
  • If the velocity potential function satisfies the Laplace equation i.e. , it is a case of steady incompressible irrotational flow

Additional Information

Stream Function:

It is defined as the scalar function of space and time, such that its partial derivative with respect to any direction gives the velocity component at right angles to that direction.

It is denoted by ψ and defined only for two-dimensional flow.

Properties of Stream function:

  • If stream function exists, it is a possible case of fluid flow (satisfies continuity equation) which may be rotational or irrotational
  • If the stream function satisfies the Laplace equation i.e. , it is a case of irrotational flow

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