Question

For a steady flow, the velocity potential function for velocity V can be given by _______

(a) u = -δϕ/δx, v = δϕ/δy, w = δϕ/δx

(b) u = δϕ/δx, v = δϕ/δy, w = δϕ/δx

(c) u = -δϕ/δx, v = -δϕ/δy, w = δϕ/δ

(d) u = -δϕ/δx, v = -δϕ/δy, w = -δϕ/δx

I had been asked this question by my college director while I was bunking the class.

My question comes from Source Flow topic in chapter Inviscid & Incompressible Flow of Aerodynamics

Answer 1

The correct answer is (d) u = -δϕ/δx, v = -δϕ/δy, w = -δϕ/δx

Explanation: Velocity potential function is scalar function of space and time and its negative derivative with respect to any direction gives the fluid velocity in that direction. Mathematically, it is ϕ = f(x,y,z) such that,

u = -ϕδ/xδ,

v = -ϕδ/δy,

w = -ϕδ/δx.