Question

Which equation is satisfied when the Mach number approaches to zero in linearized velocity potential equation?

(a) Laplace equation

(b) Momentum equation

(c) Energy equation

(d) Euler’s equation

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

Query is from Linearized Velocity Potential Equation topic in section Linearized and Conical Flows of Aerodynamics

Answer 1

The correct option is (a) Laplace equation

The best explanation: The linearized velocity potential equation is given by (1 – M\(_∞^2\))ϕxx + ϕyy + ϕzz = 0. When the Mach number approaches to zero, the equation takes the form ϕxx + ϕyy + ϕzz = 0 which is a form of Laplace equation ∇^2ϕ = 0 and the flow becomes incompressible.