Question

Which of these is linearized velocity potential equation?

(a) (1 – M\(_∞^2\))ϕxx + ϕyy + ϕzz = 0

(b) ϕxx + (1 – M\(_∞^2\))ϕyy + ϕzz = 0

(c) ϕxx + ϕyy + (1 – M\(_∞^2\))ϕzz = 0

(d) (1 – M\(_∞^2\))[ϕxx + ϕyy + ϕzz] = 0

The question was asked at a job interview.

This intriguing question originated from Linearized Velocity Potential Equation topic in chapter Linearized and Conical Flows of Aerodynamics

Answer 1

The correct option is (a) (1 – M\(_∞^2\))ϕxx + ϕyy + ϕzz = 0

To explain I would say: When the assumptions of small perturbations and transonic, hypersonic conditions are excluded, the linearized velocity potential equation is found out as follows:

(1 – M\(_∞^2\))ϕxx + ϕyy + ϕzz = 0

Where, ϕxx = \(\frac {∂^2 ϕ}{∂x^2}\), ϕyy = \(\frac {∂^2 ϕ}{∂y^2}\), ϕzz = \(\frac {∂^2 ϕ}{∂z^2}\)