Question

For an irrotational flow, what is the relation for the velocity potential?

(a) V = ∇ × ϕ

(b) V = ∇ϕ

(c) V = -∇ × V

(d) V = (∇ × V)ϕ

This question was addressed to me in an interview for job.

This interesting question is from The Velocity Potential Equation in division Velocity Potential Equation of Aerodynamics

Answer 1

Right option is (b) V = ∇ϕ

The explanation is: 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 describing as the scalar function ∇ϕ.