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# Aerodynamics – Flow Compressible

1 - Question

The definition of flow being compressible is______

a) M > 0.3

b) M > 0.5

c) Depends on precision required

d) Another name for supersonic flows

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Answer: aExplanation: For the subsonic flows, it depends on the matter of accuracy whether to treat a flow as compressible or not. For supersonic flows it is always compressible. In general, M > 0.3 can be regarded as compressible flow.

2 - Question

Incompressible flow is a myth actually.

a) True

b) False

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Answer: aExplanation: Strictly speaking, all flows are compressible i.e. incompressible flow is a myth actually. But for all practical applications, flow with Mach number < 0.3 can be assumed incompressible since the density variation is less than 5%.

3 - Question

Prandtl relation for normal shock waves is_______

a) a2=u1u2

b) a*2=u1u2

c) a*a0=u1u2

d) a20=u1u2

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Answer: bExplanation: The Prandtl relation for the normal shock waves taking into account combined form of mass and moment equation and alternate forms of the energy equation. The final equation comes out in the form of a*2=u1u2, where u1, u2 are velocities before and after the normal shock.

4 - Question

Prandtl relation can also be expressed in terms of characteristic Mach number as 1=M∗1M∗2.

a) True

b) False

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Answer: aExplanation: The Prandtl relation is given as a*2=u1u2 while the characteristic Mach number is given as M*=ua∗. So, putting this into the Prandtl relation we get the equation 1=M∗1M∗2 where M∗1 and M∗2 are the characteristic Mach number upstream and downstream of the normal shock.

5 - Question

For a particular gas, Mach number behind the shock wave is a function of which all parameters ahead of the shock wave. Choose the correct option.

a) Mach number, pressure

b) Mach number only

c) Mach number, temperature

d) Mach number, temperature, pressure

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Answer: bExplanation: The remarkable result for the normal shock wave is that for a given gas (given gamma), the Mach number ahead of the normal shock wave is a function of the Mach number ahead of the normal shock wave only, irrespective of pressure, density, temperature etc. The values are tabulated and found in gas tables for reference.

6 - Question

Which of the following is incorrect for a normal shock wave?

a) M1=1 then M2=1

b) M1 > then M2 > 1

c) M∗1=1→M∗2=1

d) M1→∞ then M2=finite value

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Answer: bExplanation: For a normal shock wave, the upstream and downstream Mach numbers are related irrespective of the other parameters for a particular flow. According to the relation, M1=1 then M2=1 and M1 > then M2 < 1, since normal shock wave compresses the flow. Also, by Prandtl relation when M∗1=1→M∗2=1 and when M1→∞ then M2 takes a finite value.

7 - Question

Select the correct statement for a Mach wave.

a) M > 1

b) P2P1=0.528

c) T2T1=1

d) ρ2ρ1=∞

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Answer: cExplanation: A Mach wave is a normal shock wave of diminishing strength. It occurs for M=1 upstream. Then downstream M=1 also. And all the ratios are equal to 1, i.e P2P1=1, T2T1=1, ρ2ρ1=1. This can be found by calculation when we put m=1. The properties across Mach wave do not change.

8 - Question

Shock waves can occur both in subsonic and supersonic medium since the concerning equations are not concerned with whether M > 1 or M < 1.

a) False

b) True

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Answer: aExplanation: Equations of mass, momentum, energy are valid in both super and subsonic mediums and hence shock wave can occur in both mediums. But, thermodynamics delete the possibility of shockwaves occurring in subsonic medium. Entropy change is negative if the upstream medium is subsonic and hence no shock waves occur in subsonic medium, else second law is violated.

9 - Question

Select the false statement for the normal shock wave.

a) Entropy increases across normal shock wave

b) Normal shock wave has velocity and pressure gradients

c) Shock wave is pretty thick

d) Thermal and frictional dissipation there

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Answer: cExplanation: The shock waves are a very thin region and have entropy increase across them. The normal shock wave has large velocity and temperature gradients across it and hence the irreversibility. The thermal conduction and frictional effect lead to increase in entropy.

10 - Question

Specifying the temperature ratio across the normal shock wave will yield which of the following across the normal shock wave?

a) Upstream flow velocity

b) Upstream Mach number

c) Downstream temperature

d) Downstream flow velocity

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Answer: bExplanation: Specifying a dimensionless quantity across the normal shock wave will specify all the other ratios and both the upstream and downstream Mach numbers. But for finding the velocity, temperature also needs to be specified and vice versa.

11 - Question

A normal shock wave can be specified with a single velocity.

a) True

b) False

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Answer: bExplanation: When the single velocity is given, either upstream or downstream, a host of various temperatures will give a set of various Mach numbers, and hence different normal shock waves. But if the temperature is given along with the velocity, both either upstream or downstream, it specifies the normal shock wave.

12 - Question

The total temperature across the normal shock wave is constant. Which statement gives the wrong reason for this?

a) Adiabatic flow across normal shock wave

b) Normal shock wave has an isentropic flow

c) Calorifically perfect gas

d) Thermal dissipation there

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Answer: dExplanation: The flow across the normal shock wave is isentropic i.e. it is adiabatic also. Since, we are concerned with calorically perfect gases in an adiabatic, inviscid, steady flow the total temperature remains constant. Thermal dissipation is not a reason for total temperature being constant.

13 - Question

Select the false statement for the normal shock wave.

a) Entropy increases across normal shock wave

b) The total pressure remains constant

c) The total temperature remains constant

d) Normal shock wave is a compression wave

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Answer: bExplanation: Across the normal shock wave, the entropy increases, by second law of thermodynamics. It is a compression wave and the total pressure also changes. It is related to the entropy change inversely. Also, being an adiabatic flow, total temperature remains constant.