Potential function is applicable only for __________ flow.

ANS:A - irrotational

The potential function is applicable only for irrotational flow.

Explanation:

1. Irrotational Flow: Irrotational flow refers to flow where the fluid particles do not rotate about their own axes as they move. Mathematically, this means the curl of the velocity vector field V\mathbf{V}V is zero, i.e., ∇×V=0\nabla \times \mathbf{V} = 0∇×V=0.
   • In irrotational flow, there exists a scalar function called the potential function ϕ\phiϕ such that V=∇ϕ\mathbf{V} = \nabla \phiV=∇ϕ.
   • This potential function ϕ\phiϕ satisfies Laplace's equation ∇2ϕ=0\nabla^2 \phi = 0∇2ϕ=0, and it provides a straightforward way to express the velocity field.
2. Turbulent Flow: Turbulent flow involves chaotic, irregular fluctuations in velocity and pressure. It is characterized by eddies and vortices, indicating significant rotational components in the flow. Therefore, a potential function cannot describe turbulent flow due to the presence of vorticity.
3. Steady Flow: Steady flow refers to flow where the velocity field does not change with time at any point in the flow field. While potential functions are applicable to steady flow, steady flow alone does not ensure the applicability of a potential function; the flow must also be irrotational.
4. None of These: This option is incorrect because potential functions are specifically applicable to irrotational flow and not to turbulent flow or steady flow alone.

Conclusion: