# Aerodynamics Questions and Answers – Prandtl-Glauert Compressibility

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This set of Aerodynamics Multiple Choice Questions & Answers (MCQs) focuses on “Prandtl-Glauert Compressibility”.

1. Prandtl – Glauert compressibility correction is applied for finding airfoil properties at low speed.
a) True
b) False

Explanation: After the World War 2 period when high speed aircrafts came into being, the aerodynamic theory over thin airfoils for incompressible flow was not applicable. The assumption of incompressible flow could not be used and hence Prandtl – Glauert compressibility correction came into being. This correction makes use of the data for incompressible flow applicable for high speed aircraft in a compressible flow.

2. For which of thee flows is Prandtl – Glauert compressibility correction is effective?
a) Subsonic flow
b) Sonic flow
c) Supersonic flow
d) Hypersonic flow

Explanation: Prandtl – Glauert compressibility correction is a theory that is purely applicable for subsonic flow i.e. flow with Mach number less than 1. As the Mach number reaches 0.7, the results obtained are inaccurate.

3. 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

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.

4. For which of these conditions is Prandtl – Glauert compressibility equation valid?
a) Thick airfoil, small angle of attack
b) Thick airfoil, large angle of attack
c) Thin airfoil, large angle of attack
d) Thin airfoil, small angle of attack

Explanation: The Prandtl – Glauert compressibility equation is more or less accurate for small perturbations which occur for thin airfoils kept at small angle of attack. One added condition is that this equation is inaccurate for transonic and hypersonic flows.

5. What is the relation between linearized pressure coefficient for compressible Cp and incompressible flow Cp,0?
a) Cp = βCp,0
b) Cp = $$\frac {C_{p.0}}{β}$$
c) Cp = $$\frac {β}{C_{p.0}}$$
d) Cp = β2Cp,0

Explanation: Linearized pressure coefficient for compressible flow Cp is derived using the Prandtl – Glauert compressibility equation. It is given by:
Cp = –$$\frac {2\hat {u}}{V_∞}$$
Where, $$\hat {u} = \frac {∂\hat {ϕ}}{∂x}$$ is the velocity perturbation
Cp = –$$\frac {2}{V_∞} \frac {∂\hat {ϕ}}{∂x}$$
$$\frac {∂\hat {ϕ}}{∂x} = -\frac {1}{β} \frac {∂\bar {ϕ}}{∂ξ}$$
Where, $$\bar {ϕ}$$ is the perturbation velocity for incompressible flow
β = $$\sqrt {1 – M_∞^2}$$
Cp = –$$\frac {2}{V_∞} \frac {1}{β} \frac {∂\bar {ϕ}}{∂ξ} = \frac {C_{p.0}}{β}$$
This relation helps in finding out the coefficient of pressure for a compressible flow using the incompressible pressure coefficient value.

6. If the lift coefficient for an aircraft at low speed is 0.45, then what is the value of the coefficient of drag at Mach number 0.7?
a) 0.51
b) 0.49
c) 0.63
d) 0.71

Explanation: Given, cl,0 = 0.45, M = 0.7
The coefficient of lift for compressible and incompressible flow are related by the following relation:
cl = $$\frac {c_{l.0}}{β} = \frac {c_{l.0}}{\sqrt {1 – M_∞^2}} = \frac {0.45}{\sqrt {1 – 0.7^2}}$$
cl = $$\frac {0.45}{\sqrt {0.51}}$$ = 0.63

Sanfoundry Global Education & Learning Series – Aerodynamics.

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