Question

What is a velocity potential?

(a) ∇ × ϕ

(b) ∇ϕ

(c) – ∇ × V

(d) (∇ × V)ϕ

I had been asked this question in class test.

I would like to ask this question from Irrotational Flow topic in chapter Velocity Potential Equation of Aerodynamics

Answer 1

The correct option is (b) ∇ϕ

To elaborate: The irrotational flow is given by the curl of velocity vector. If we take a gradient of the scalar function, we get zero as a result.

∇ × (∇ϕ) = 0

Thus the velocity potential is described as the scalar function ∇ϕ. It satisfies the Laplace equations as well.