This set of Gas Dynamics Multiple Choice Questions & Answers (MCQs) focuses on “The Prandtl-Meyer Expansion”.

1. What are the values of expansion angle and deflection angle, when the radial component of the flow is zero and the expansion angle is maximum? Assume heat capacity ratio = 1.4.

a) Expansion angle = 220.5° and Deflection angle = 130.5°

b) Expansion angle = 180° and deflection angle = 90°

c) Expansion angle = 130.5° and deflection angle = 220.5°

d) Expansion angle = 120° and deflection angle = 90°

View Answer

Explanation: When radial velocity is zero and expansion is maximum, the static pressure drops down to zero. Maximum expansion angle is given by, ∅

_{max}= \(\frac {π}{2}(\sqrt {\frac {γ+1}{γ-1}})\). For heat capacity ratio, γ = 1.4, ∅

_{max}= μ = \(\frac {π}{2}(\sqrt {\frac {1.4+1}{1.4-1}})\) = 220.5° and deflection angle is θ = μ – \(\frac {π}{2}\) = 130.5°.

2. If the polar components of the expansion flow are V_{r} and V_{∅} then what is true about the properties of these polar components?

a) The radial component of the flow is constant and flow the properties are only dependent upon the ∅ component

b) The ∅ component of the flow is constant and flow the properties are only dependent upon the r component

c) At the beginning of the expansion fan, the r component of the velocity is equal to the sonic velocity

d) V_{r} is maximum at the beginning of the expansion fan and becomes zero for maximum expansion

View Answer

Explanation: Flow properties do not change along any radial line and vary with ∅ only. At the beginning of the fac, the ∅ component of velocity is equal to the local speed of sound. V

_{r}is maximum at the end of the expansion fan where the expansion angle is maximum.

3. A uniform flow of Mach number 2 passes over an expansion corner with wall deflection angle as 10°. What is the Mach number of the flow downstream of the expansion fan? Assume ɣ = 1.4.

a) 2

b) 1.652

c) 2.386

d) 3.258

View Answer

Explanation: From the Prandtl-Meyer function table, for M

_{1}= 2, ϑ

_{1}= 26.38°. Now ϑ

_{2}= θ + ϑ

_{1}= 26.38 + 10 = 36.38°. Again from the table, we get, M

_{2}= 2.386.

4. A uniform flow of Mach number 2 passes over a compression corner with wall deflection angle as 10°. What is the Mach number of the flow downstream of the oblique shock? Assume ɣ = 1.4.

a) 2

b) 1.652

c) 2.386

d) 3.258

View Answer

Explanation: From the Prandtl-Meyer function table, for M

_{1}= 2, ϑ

_{1}= 26.38°. Now ϑ

_{2}= ϑ

_{1}– θ = 26.38 – 10 = 16.38°. Again from the table, we get, M

_{2}= 1,652.

5. A uniform flow with Mach number 2, flows over a compound wall with two successive turns with 20° and 6° expansion angle. What is the Mach number of the flow downstream of the 2^{nd} turn? Assume ɣ=1.4.

a) 2.83

b) 2.38

c) 3.14

d) 3.38

View Answer

Explanation: From the Prandtl-Meyer function table, for M

_{1}= 2, ϑ

_{1}= 26.38°. We can find, ϑ

_{2}from equation, ϑ

_{2}= θ + ϑ

_{1}= 20 + 26.38 = 46.38°. Again, referring the table for, ϑ

_{2}= 46.38°, we get M

_{2}= 2.83. Again for ϑ

_{3}, we use ϑ

_{3}= θ + ϑ

_{2}= 6 + 46.38 = 52.38°. From the table, we finally get, M

_{3}= 3.14.

6. What does the Prandtl-Meyer function physically represent in a turning flow?

a) The inclination angle of the wave with respect to the Mach line corresponding to Mach 1

b) The flow inclination of the wave with respect to the horizontal axis parallel to the upstream flow

c) The wall deflection angle measured from the vertical axis perpendicular to the upstream flow

d) Mach wave angle of the centered expansion fan wave

View Answer

Explanation: The Prandtl-Meyer function denoted by ν(M) is a function of the Mach number of the flow. Physically it represents the flow inclination angle of the wave corresponding to the line with zero turning angle (∅ = 0). When Mach number is equal to 1 the function becomes zero and hence the angle is measured with respect to this line.

7. When is the motion known to be self-similar?

a) When the motion preserves its geometry in space

b) When the motion preserves its geometry in space or time

c) When the motion preserves its geometry in space or time or both

d) When the motion is described by two variables

View Answer

Explanation: When the motion preserves its geometry in space or time or both, it is known to be self-similar. Prandtl-Meyer is a self-similar motion, and Prandtl-Meyer function is a similarity variable.

8. What is the relation between Prandtl-Meyer function and flow turning angle in a supersonic compression?

a) ν_{n} = ν_{n-1} + |θ_{n} – θ_{n-1}|

b) ν_{n} = ν_{n-1} – |θ_{n} – θ_{n-1}|

c) ν_{n} = ν_{n-1} + |θ_{n} + θ_{n-1}|

d) ν_{n} = ν_{n-1} – |θ_{n} + θ_{n-1}|

View Answer

Explanation: When the flow is compressed in a supersonic regime, the flow is no more isentropic for large deflection angles. For θ < 5°, the flow is assumed to be isentropic. The flow is turning towards itself and the deflection angle becomes negative but equal to the deflection in an expansion turn. Hence the relation is, ν

_{n}= ν

_{n-1}– |θ

_{n}– θ

_{n-1}|.

9. What is the range for the Prandtl-Meyer function (ν)?

a) 0 < ν < ν_{max}

b) ν_{min} < ν < ν_{max}

c) ν_{min} < ν < ∞

d) 0 < ν < ∞

View Answer

Explanation: Prandtl-Meyer function varies from Mach number 1 to infinity which corresponds to 0 and ν

_{max}values. The maximum value of the function is given by, ν

_{max}= \(\frac {π}{2} (\sqrt {\frac {γ+1}{γ-1}}-1)\). Its value is not defined for Mach number less than unity.

10. When is a non-simple region created in a flow?

a) When two simple waves of opposite family (+ or -) interact

b) When a simple wave is reflected by a wall

c) When two simple waves of the same family (+ only or – only) interact

d) When the flow is isentropic in nature there is a single relation between Prandtl-Meyer function and flow deflection

View Answer

Explanation: A non-simple is created when two simple waves of a different family (+ or -) interact. The relation between ν and θ is not simple anymore and calculation for such regions is done through methods of characteristics.

**Sanfoundry Global Education & Learning Series – Gas Dynamics.**

To practice all areas of Gas Dynamics, __ here is complete set of Multiple Choice Questions and Answers__.