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Consider the following statements about velocity potential : 1. Velocity potential is a vector function similar to stream function. 2. It is a fully three dimensional function and not limited to two coordinates. 3. Velocity potential does not exist at stagnation points. 4. Velocity potential exists only if the flow is Irrotational. Which of these statements are correct?

Consider the following statements about velocity potential : 1. Velocity potential is a vector function similar to stream function. 2. It is a fully three dimensional function and not limited to two coordinates. 3. Velocity potential does not exist at stagnation points. 4. Velocity potential exists only if the flow is Irrotational. Which of these statements are correct? Correct Answer 2, 3 and 4

Explanation:

Velocity potential function (ϕ) :

  • It is defined as a scalar smooth function of space and time such that its negative derivative w.r.t any direction gives the fluid velocity in the direction.
  • It is defined for 1D, 2D and 3D flow.
  • It is defined only for incompressible and irrotational flow
  • It has to satisfy Laplace equation to be possible flow field.

Stream function(ψ) :

  • It is defined as the scalar function of space and time, such that its derivative w.r.t. and direction gives the velocity component at right angles to that direction.
  • It is defined only for 2D flow.
  • Defined both for rotational and irrotational incompressible flow.
  • It also satisfy Laplace equation for a possible 2D flow.
From the above definition, statement (1) is wrong. All other statements except (1) is correct.

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