Question

Prandtl – Glauert compressibility correction is based on which of the following methods?

(a) Velocity potential equation

(b) Energy equation

(c) Momentum equation

(d) Continuity equation

The question was posed to me in quiz.

The query is from Prandtl-Glauert Compressibility topic in section Subsonic Compressible Flow over Airfoils : Linear Theory, Linearized Supersonic Flow of Aerodynamics

Answer 1

The correct option is (a) Velocity potential equation

The best explanation: Prandtl – Glauert compressibility correction is based on the linearized perturbation velocity potential equation which is given by:

(1 – M\(_∞^2\))\(\frac {∂^2 \hat {ϕ}}{∂x^2} + \frac {∂^2 \hat {ϕ}}{∂y^2}\) = 0

Where, ϕ is the velocity potential. It is a combination of continuity, momentum and energy equation. The above equation is only applicable for thin bodies

\(\hat {ϕ}\) is perturbation velocity potential which is a non linear equation.