Aerodynamics Questions and Answers – Linearized Subsonic Flow

This set of Aerodynamics Multiple Choice Questions & Answers (MCQs) focuses on “Linearized Subsonic Flow”.

1. What is the surface boundary condition for a thin airfoil at a subsonic flow? (Where shape of the airfoil is represented as y = f(x))
a) \(\frac {∂ϕ}{∂x}\) = V \(\frac {df}{dx}\)
b) \(\frac {∂ϕ}{∂y} = \frac {df}{dy}\)
c) \(\frac {∂ϕ}{∂x}\) = – V\(_∞^2 \frac {df}{dx}\)
d) \(\frac {∂ϕ}{∂x} = \frac {dV_∞}{dx}\)
View Answer

Answer: a
Explanation: For an airfoil with x – component of velocity as V + u and y – component of the velocity as v, the surface boundary condition is
\(\frac {df}{dx} = \frac {v^{‘}}{V_∞ + u^{‘}}\) = tanθ
Since it is a thin airfoil, the perturbation vector u is very small in comparison to the freestream velocity V, resulting in \(\frac {df}{dx} = \frac {v^{‘}}{V_∞}\) = θ (Where tanθ ~ θ for small angles). Expressing the perturbation v in terms of velocity potential we get
v = \(\frac {∂ϕ}{∂x}\)
Substituting this in the above equation:
\(\frac {df}{dx} = \frac {\frac {∂ϕ}{∂x}}{V_∞}\) = θ
\(\frac {∂ϕ}{∂x}\) = V \(\frac {df}{dx}\)

2. Which of these is the linearized perturbation velocity potential equation over a thin airfoil in a subsonic compressible flow?
a) β2xx + ϕyy) = 0
b) ϕxx + ϕyy = 0
c) β2ϕxx + ϕyy = 0
d) β2ϕxx + ϕxy = 0
View Answer

Answer: c
Explanation: For a compressible subsonic flow over a thin airfoil, the two dimensional linearized perturbation velocity potential equation is given by
β2ϕxx + ϕyy = 0
In this equation the perturbations are assumed to be small with the value of β = \(\sqrt {1 – M_∞^{2}} \).

3. Which of the equations governs the linearized incompressible flow over an airfoil at subsonic velocity using transformed coordinate system?
a) Laplace’s equation
b) Euler’s equation
c) Navier – Stokes equation
d) Cauchy’s equation
View Answer

Answer: a
Explanation: The compressible linearized perturbation velocity potential equation is transformed into incompressible using a transformed coordinate system (ξ, η). The equation is given by
ϕξξ + ϕηη = 0
This is the Laplace equation representing the incompressible flow in a linearized form.

4. The shape of the airfoil in both (x, y) and transformed (ξ, η) space are different.
a) True
b) False
View Answer

Answer: b
Explanation: The shape of the airfoil in (x, y) space is given by y = f(x) and in (ξ, η) space is given by η = q(ξ). Since \(\frac {df}{dx} = \frac {dq}{dξ}\) hence the shape of the airfoil in both the spaces irrespective of the transformation remains same.

5. What does the Prandtl – Glauert rule relate?
a) Shape of airfoil in transformed spaces
b) Incompressible flow to the compressible flow for same airfoil
c) Coefficient of lift to coefficient of pressure
d) Coefficient of drag to coefficient of pressure
View Answer

Answer: b
Explanation: The Prandtl – Glauert equation is given by:
Cp = \(\frac {C_{p0}}{\sqrt {1 – M_∞^{2}}}\), Cl = \(\frac {C_{l0}}{\sqrt {1 – M_∞^{2}}}\), Cd = \(\frac {C_{d0}}{\sqrt {1 – M_∞^{2}}}\)
This equation relates the pressure/lift/drag coefficient in incompressible flow Cp0 to the pressure/lift/drag coefficient in compressible flow (Cp) for a two – dimensional airfoil with the same profile.
Note: Join free Sanfoundry classes at Telegram or Youtube

6. Linearized theory is applicable for transonic regions as well.
a) True
b) False
View Answer

Answer: b
Explanation: According to the Prandtl – Glauert rule, as the limit of Mach number is increased to one, the aerodynamic forces – lift and drag becomes infinity which is practically impossible. Thus, this rule is only applicable for subsonic and supersonic regimes.
Cl = \(\frac {C_{l0}}{\sqrt {1 – M_∞^{2}}}\), Cd = \(\frac {C_{d0}}{\sqrt {1 – M_∞^{2}}}\)

7. For a subsonic flow, how does the coefficient of pressure vary with increasing Mach number?
a) Increases
b) Decreases
c) Remains same
d) First increases, then decreases
View Answer

Answer: a
Explanation: For a subsonic flow, the linearized coefficient of pressure is given by the equation below according to which when the Mach number is increased, the coefficient of pressure increases. Although, one thing to note is that as this Mach number is increased to unity, the coefficient of pressure reaches infinity and thus, for transonic regions, this equation fails.
Cp ∝ \(\frac {1}{\sqrt {1 – M_∞^{2}}}\)

8. Up to which Mach number is Prandtl – Glauert rule applicable for subsonic flow?
a) 1
b) 0.5
c) 0.8
d) 0.65
View Answer

Answer: c
Explanation: For an increasing Mach number in a subsonic flow over a body, the coefficient of pressure also increases as a result of Prandtl – Glauert rule. But, after Mach number 0.8 the equation fails because the flow enters transonic regime where coefficient of pressure tends to infinity as Mach number tends to unity.

Sanfoundry Global Education & Learning Series – Aerodynamics.


To practice all areas of Aerodynamics, here is complete set of 1000+ Multiple Choice Questions and Answers.

Subscribe to our Newsletters (Subject-wise). Participate in the Sanfoundry Certification contest to get free Certificate of Merit. Join our social networks below and stay updated with latest contests, videos, internships and jobs!

Youtube | Telegram | LinkedIn | Instagram | Facebook | Twitter | Pinterest
Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

Subscribe to his free Masterclasses at Youtube & discussions at Telegram SanfoundryClasses.