Question

Linearized velocity potential equation is applicable to hypersonic flow.

(a) True

(b) False

I got this question in homework.

I'd like to ask this question from Linearized Velocity Potential Equation topic in portion Linearized and Conical Flows of Aerodynamics

Answer 1

The correct choice is (b) False

The best I can explain: Linearized velocity potential equation is not applicable for hypersonic flows with Mach number greater than 5 as in the non – linear velocity potential equation, there is an assumption made that the magnitude of M\(_∞^2 \big [ \)(γ – 1) \(\frac {u^{‘}}{V_∞} + (\frac {γ + 1}{2}) \frac {u^{‘^2}}{V_{∞}^{2}} + (\frac {γ – 1}{2})(\frac {w^{‘{^2}} + u^{‘^{2}}}{V_∞^2}) \big ] \frac {∂v^{‘}}{∂x}\) is small compared to the left hand side thus is neglected to arrive at the linearized velocity potential equation.