Question

Which of these assumptions is invalid for the linearized velocity potential equation?

(a) \(\frac {u^{‘}}{V_∞}\) << 1

(b) \(\frac {v^{‘}}{V_∞}\) << 1

(c) \(\frac {w^{‘}}{V_∞}\) >> 1

(d) \(\frac {w^{‘}}{V_∞}\) << 1

The question was asked in an internship interview.

This is a very interesting question from Linearized Velocity Potential Equation in portion Linearized and Conical Flows of Aerodynamics

Answer 1

The correct option is (c) \(\frac {w^{‘}}{V_∞}\) >> 1

Easy explanation: The perturbation velocity potential equation is given by:

(a^2 – (V∞ + ϕx)^2) ϕxx + (a^2 – ϕy^2) ϕyy + (a^2 – ϕz^2) ϕzz – (2(V∞ + ϕx) ϕy) ϕxy – (2(V∞ + ϕx) ϕz) ϕxz – (2ϕy ϕz) ϕyz

This relation is non – linear in nature and in order to reduce to the linear form, an assumption is made i.e. the perturbations in uniform flow is very small. This results in u^‘, v^‘, w^‘ << V∞.