# Gas Dynamics Questions and Answers – Supersonic Flow over a Wedge

This set of Gas Dynamics Multiple Choice Questions & Answers (MCQs) focuses on “Supersonic Flow over a Wedge”.

1. Which of the following does not describe the properties of a weak oblique shock correctly?
a) The flow downstream of the weak shock is supersonic
b) Weak oblique shocks occur at small deflection angles
c) Weak oblique shocks can compress the flow with an infinitesimal increase in entropy
d) Weak oblique shocks are considered as Mach waves with same shock angle

Explanation: Weak shock angle is not equal to Mach angle, also they differ by a finite amount. Mach waves compress the supersonic flow without increasing entropy, whereas in weak oblique shock there is a small increase in entropy to compress the supersonic flow.

2. Find the shock strength of a weak oblique shock with flow Mach number of 2 and a small deflection angle of 1°. Assume that the flow is isentropic and shock angle is almost equal to the Mach angle. Take heat capacity ratio (ɣ) of gas as 1.4.
a) 0.0564
b) 0.0356
c) 4.5
d) 3.5

Explanation: Weak shock strength is given by, $$\frac {p_2 – p_1}{p_1} = \frac {ɣM_1^2 \theta }{\sqrt {(M_1^2 – 1)}} = \frac {1.4 \times 2^2 \times 0.0174}{\sqrt {3}}$$ = 0.0564. We can see that; the shock strength of a weak shock is directly proportional to the small deflection angle.

3. What properties are directly proportional to the small deflection angle in a weak shock?
a) Stagnation pressure and temperature are directly proportional to the small deflection angle in a weak shock
b) Total temperature and pressure are directly proportional to the small deflection angle in a weak shock
c) Change in entropy is directly proportional to the small deflection angle in a weak shock
d) Static density and temperature are directly proportional to the small deflection angle in a weak shock

Explanation: For very small deflection angle, static pressure, temperature, and density are directly proportional to the deflection angle. Change in entropy is proportional to the third power of the deflection angle. Stagnation properties are constant since the flow is isentropic in nature.

4. If ε is the difference between the shock angle and wave angle, then what is the upstream Mach number normal to the oblique shock wave? Assume ε to be very small.
a) 1 – ε(M$$_1^2$$ – 1)
b) 1 + ε(M$$_1^2$$ – 1)
c) 1 – ε$$(\sqrt {M_1^2 – 1} )$$
d) 1 + ε$$(\sqrt {M_1^2 – 1} )$$

Explanation: Given that β = μ + ε, where ε << μ. Therefore, sin⁡β = sin⁡(μ + ε) = sin⁡μ sin⁡ε + cos⁡ε cos⁡μ = sin⁡μ + ε cos⁡μ. We know sin⁡μ = $$\frac {1}{M_1}$$ and cos⁡μ = $$\frac {\sqrt {(M_1^2 – 1) }}{M_1}$$. So, sin⁡β = $$\frac {1}{M_1} + \frac {\epsilon \sqrt {(M_1^2 – 1) }}{M_1}$$. Now, the Mach number of the upstream flow normal to the shock wave is M1 sin⁡β = 1 + ε$$(\sqrt {M_1^2 – 1})$$.

5. What is true for smooth supersonic compression through weak shocks?
a) Increase in entropy by a number of weak shocks is greater than the increase by one single shock for a given deflection
b) Mach lines formed due to small deflection are divergent
c) Change in flow velocity is achieved in a shorter distance when closer to the wall than further away
d) Velocity downstream of the smooth supersonic compression is subsonic

Explanation: Increase in entropy by a number of weak shocks is smaller than a single shock for a given deflection angle. Reduction in entropy is of factor $$\frac {1}{n^2}$$, for ‘n’ weak shock waves. Also, the Mach lines are convergent in nature and hence, the change in flow velocity is achieved in a shorter distance when further away from the wall than closer to it. The deflection angle is taken to be small for smooth supersonic compression to obtain supersonic flow downstream.

6. What is the approximate percentage change in flow velocity across a weak shock, for a small deflection of 0.1° and upstream flow Mach number (M1) of 2?
a) 5.7%
b) 57%
c) 11%
d) 45%

Explanation: Change in the velocity of the flow is given by, $$\frac {Δw}{w} = -\frac {\theta }{\sqrt {(M_1^2 – 1)}} = -\frac {0.1}{\sqrt 3}$$ = -0.057. Hence the percentage change in flow velocity is 5.7%. The negative sign depicts that the flow velocity is reducing across the shock wave.

7. There is a strong oblique shock formation just close to the wall with a small deflection due to a combination of weak shocks.
a) True
b) False

Explanation: There is a combination of Mach lines for a small deflection. These Mach lines then converge at a point further away from the wall. Above the convergence point, there is a strong oblique shock formation.

8. When the wall deflection is convex in nature, what is the flow velocity upstream and downstream of the Mach wave?
a) The upstream velocity component parallel to the first Mach wave is not equal to the downstream velocity component parallel to the last Mach wave
b) The upstream velocity component normal to the first Mach wave is greater than the downstream velocity component normal to the last Mach wave
c) The upstream velocity component normal to the first Mach wave is smaller than the downstream velocity component normal to the last Mach wave
d) The two velocity components normal to the first and last Mach waves are equal

Explanation: During a supersonic expansion at a convex corner, the velocity components parallel to the Mach waves are equal. Since expansion follows an isentropic process, the normal component of the velocity downstream is greater than upstream normal velocity component.

9. What happens to the flow properties when the flow is turned away from itself?
a) There is an entropy decrease across the flow
b) Static properties are instantly increased across the flow
c) Pressure, temperature, and density decreases gradually throughout the flow
d) Flow velocity reduces across the flow

Explanation: When flow turns away from itself, expansion waves are created which follows an isentropic process. Pressure, density, and temperature are gradually decreased through a series of waves.

10. Which of the following is true for the Mach lines in a centered expansion wave?
a) Mach lines diverge from the point where the deflection corner starts
b) The first Mach line created at the corner is called the Prandtl – Meyer expansion fan
c) The last Mach line created at the corner is called the Prandtl – Meyer expansion fan
d) The Mach lines in a centered expansion wave are curved

Explanation: In a centered expansion fan, Mach lines diverge from the corner. There is a fan of straight Mach lines from the corner which makes up the Prandtl – Meyer expansion fan.

Sanfoundry Global Education & Learning Series – Gas Dynamics.

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