# Gas Dynamics Questions and Answers – Detached Shocks

This set of Gas Dynamics Multiple Choice Questions & Answers (MCQs) focuses on “Detached Shocks”.

1. Which of the statements correctly describe the behavior of supersonic flow when exiting from a supersonic nozzle?
a) An imaginary free boundary preserves the atmospheric pressure along its length
b) Supersonic flow diffuses into the atmosphere without any shock interaction
c) Like reflection takes place in a free boundary of the supersonic flow
d) Unlike reflection takes place in the solid boundary of the exhaust nozzle

Explanation: When supersonic flow exits from the nozzle, an imaginary free boundary is created so as to preserve the atmospheric surrounding pressure along its length. From this free jet boundary, unlike reflections take place whereas from a solid boundary like reflections takes place.

2. Consider a 2-dimensional nozzle with perfect gas and uniform conditions p1 = 1 atm and M1 = 2.0. What is the exit pressure of the nozzle if exit Mach number is lesser than the entry Mach number and the flow is turned by 10°? Assume flow is isentropic and γ = 1.4.
a) 0.544 atm
b) 1.7 atm
c) 1.715 atm
d) 1 atm

Explanation: Given that M2 < M1 and s1 = s2. From Prandtl-Meyer functions table for M1 = 2, ν1 = 26.38°. We have ν2 = ν1 – θ = 16.5°. Again referring to the table, we get M2 = 1.655. From isentropic tables we have, $$\frac {p_1}{p_0}$$ = 0.1278 and $$\frac {p_2}{p_0}$$ = 0.2168. So p2 = 1.7 p1 = 1.7 atm.

3. In a 2-dimensional nozzle with perfect gas and uniform conditions p1 = 1 atm and M1 = 2.0. What is the exit pressure of the nozzle if exit Mach number is greater than the entry Mach number and the flow is turned by 10°? Assume flow is isentropic and γ = 1.4.
a) 0.544 atm
b) 1.7 atm
c) 1.715 atm
d) 1 atm

Explanation: Given that M1 < M2 and s1 = s2. From Prandtl-Meyer functions table for M1 = 2, ν1 = 26.38°. We have ν2 = ν1 + θ = 36.38°. Again referring to the table, we get M2 = 2.387. From isentropic tables we have, $$\frac {p_1}{p_0}$$ = 0.1278 and $$\frac {p_2}{p_0}$$ = 0.06948. So p2 = 0.544 p1 = 0.544 atm.

4. A steady supersonic flow expands from Mach number 2 and pressure p1 to pressure p2 = $$\frac {p_1}{2}$$ from a centered rarefaction. What is the final flow deflection angle?
a) 26.38°
b) 37.81°
c) 11.43°
d) 10°

Explanation: From Prandtl-Meyer functions table for M1 = 2, ν1 = 26.38°. From isentropic tables we have, $$\frac {p_1}{p_0}$$ = 0.1278. Given that $$\frac {p_2}{p_1}$$ = 0.5, we get $$\frac {p_2}{p_0}$$ = 0.5 × 0.1278 = 0.0639. So from isentropic table and Prandtl-Meyer functions table, we get M2 = 2.444 and ν2 = 37.81°. We have, ν2 – ν1 = θ = 11.43°, the flow deflection angle.

5. A uniform supersonic flow at Mach number 2 expands through two convex corners of 10° each. What is the angle of the second expansion fan?
a) 36.38°
b) 26.38°
c) 46.38°
d) 14.16°

Explanation: From Prandtl-Meyer functions table for M1 = 2, ν1 = 26.38°. We have ν2 = ν1 + θ = 36.38°. Again referring to the table, we get M2 = 2.38. The Prandtl-Meyer function after the second fan is ν3 = ν2 + θ = 46.38° and corresponding Mach number M3 = 2.83. The Mach angles are μ1 = 30, μ2 = 24.84, μ3 = 20.69. The angle of the second fan is μ23 = θ + μ2 – μ3 = 14.16°.

6. Which of the following statements correctly describes the shock waves when flow deflection angle is, θ > θmax?
a) The normal shock wave is formed attached to the nose
b) Detached curved shock is formed ahead of the nose
c) Normal shock is formed over the nose and around and later the shock gets curved and detached
d) Attached shock waves are formed when Mach number is low

Explanation: When the flow deflection angle, θ > θmax, then curved and detached shock wave is formed ahead of the nose as there is no solution for a straight oblique shock. Even for a streamlined body, the shock wave is detached for any Mach number.

7. Which of the following is true in case of detached shock waves?
a) For a given wedge angle, when Mach number increases, the detachment point gets away from the nose
b) When wedge angle is equal to maximum flow deflection angle, the shock gets detached but it is straight
c) When wedge angle is equal to maximum flow deflection angle, the shock is attached but it is curved
d) For a given wedge angle, when Mach number decreases, the detachment point gets away from the nose

Explanation: For a given wedge angle, when the Mach number decreases, the shock angle increases and the detachment point gets away from the nose. When wedge angle is equal to maximum flow deflection angle, the shock is attached but it is curved, which represents the region between the lines the M1 = 1 and θ = θmax in θ-β-M graph.

8. What is the type of reflection called when shock waves reflect from a boundary and give rise to expansion waves?
a) Like reflections
b) Unlike reflections
c) Opposite reflections
d) Solid boundary reflections

Explanation: When shock waves reflect from a boundary and give rise to expansion waves, it is called as, unlike reflections. Unlike reflections take place from the free boundary and like reflections from the solid boundary.

Sanfoundry Global Education & Learning Series – Gas Dynamics.