Aerodynamics - Unsteady Wave Motion Quiz(MCQ)
A)
Time
B)
Direction
C)
Both Time and Direction
D)
Temperature

Correct Answer :   Both Time and Direction

Explanation : Moving shock wave is an example of unsteady flow which means that all its flow properties such as density, velocity, temperature are a function of both the direction (x) and time (t). Although stationary shock wave are steady flow, thus the flow properties are only a function of direction (x).

A)
True
B)
False
C)
Can Not Say
D)
None of the above

Correct Answer :   False

Explanation : Shock tube makes use of unsteady wave motion. It is a closed tube at both ends having a diaphragm which separates high pressure region known as the driver section and low pressure region known as the driven section.

3 .
How is total enthalpy related in a stationary shock wave?
A)
Constant
B)
h2 > h1
C)
h2 < h1
D)
h02 < h01

Correct Answer :   Constant

Explaination : For a stationary shock wave, the total enthalpy remains constant across the shock wave which means that h02 = h01. Although, in case of moving shock wave, this is not the case. The enthalpy does not remain constant across the shock.

A)
Becomes sonic
B)
Velocity increases
C)
Velocity decreases
D)
Appears stationary

Correct Answer :   Appears stationary

Explanation : Usually shock waves propagate with subsonic or supersonic speed but when the shockwave propagates in a flow that moves as well, and it is in the opposite direction with the same velocity as the flow, then it appears to be stationary known as ‘standing shock wave’.

A)
Induces gas behind it
B)
Induces gas ahead of it
C)
Leaves a small area of vacuum behind it
D)
Leaves a small area of vacuum ahead of it

Correct Answer :   Induces gas behind it

Explanation : When the normal shock wave is not opposed to the flow velocity, it propagates with some velocity W into the laboratory facility. This leads to the induction of gas behind it to move in the wave direction.

A)
1.43
B)
2.37
C)
3.82
D)
4.21

Correct Answer :   2.37

Explanation :

A)
Density
B)
Velocity ratio
C)
Pressure ratio
D)
Mach number

Correct Answer :   Pressure ratio

Explanation : In a stationary wave, changes across the shock wave is governed by the Mach number. But, in a moving shock wave it is dependent majorly on the pressure ratio as seen in the formula below which shows the equation for density and pressure ratio across a moving shock wave.

8 .
What is the continuity equation for a moving shock wave?

A)
ρ1W = ρ2(W – up)
B)
ρ1W = ρ2up
C)
ρ1W = ρ2(W + up)
D)
ρ1(W + up) = ρ2up

Correct Answer :   ρ1W = ρ2(W – up)

Explaination : Continuity equation across a shock wave is given by the formula
ρ1u1 = ρ2u2
Where, subscripts 1 and 2 are the sections behind and ahead of the shock wave. The above formula is valid only for stationary wave. For a moving wave, there is a induced gas formation behind the shock wave resulting in (W – up) being the velocity behind the shock wave which is relative to the wave, and W is the velocity of the gas ahead of the shock wave. Thus, the continuity equation becomes:
ρ1W = ρ2(W – up)
up is the velocity of induced mass motion due to the gas
W is the velocity of the normal shock wave.

9 .
If the Mach number of the moving shock wave relative to the laboratory Ms = 1.25 then what is the Mach number of the reflected shock wave in a calorically perfect gas?
A)
1.1102
B)
1.2331
C)
1.4821
D)
1.5671

Correct Answer :   1.2331

Explaination :

10 .
What is the continuity equation for a reflected shock wave?

A)
ρ1W = ρ5up
B)
ρ1W = ρ2(W – up)
C)
ρ1W = ρ5(W + up)
D)
ρ2(WR + up) = ρ5WR

Correct Answer :   ρ2(WR + up) = ρ5WR

Explaination : Continuity equation across a shock wave is given by the formula
ρ1u1 = ρ2u2
Where, subscripts 1 and 2 are the sections behind and ahead of the shock wave. This above formula is valid only for stationary wave. For a reflected unsteady shock wave, the velocity ahead of the shock relative to wave is WR + up and the velocity behind the shock relative to the wave is WR. Thus, the continuity equation becomes:
ρ2(WR + up) = ρ5WR

A)
Zero
B)
Equal to the wave velocity
C)
Less than the wave velocity
D)
More than the wave velocity

Correct Answer :   Zero

Explanation : The intensity of this reflected shock (WR) is such that with velocity up, the originally induced mass motion is stopped dead at the wall. The mass motion behind the shock wave that is reflected must be zero. Therefore, the reflected shock wave maintains the zero – velocity boundary state.

A)
Plot of wave motion between x and t
B)
Diagram of shock creation inside shock tube
C)
Plot of wave motion between t and x
D)
Plot of reflected wave motion between t and x

Correct Answer :   Plot of wave motion between t and x

Explanation : When unsteady wave motion i.e. moving shock wave is studied, wave diagram is often constructed. It is a sketch of the wave diagram plot on a graph with x – axis representing distance and y – axis representing the time. The diagram shows where the incident, reflected shock occurs after applying the boundary conditions.

A)
Weak waves
B)
Sound waves
C)
Waves with large perturbations
D)
Waves with small temperature fluctuations

Correct Answer :   Waves with large perturbations

Explanation : The traveling waves have small perturbations in ambient conditions having small changes in pressure, density etc. Such waves are weak waves but finite waves have large perturbations at ambient conditions.

A)
True
B)
False
C)
Can Not Say
D)
None of the above

Correct Answer :   True

Explanation : Finite waves which propagate in some direction x have properties such as temperature, pressure, density, velocity a function of distance x for time t at an instant. The flow is supposed to be isentropic.

A)
Wave shape changes
B)
Linear equations are used to govern the flow variables
C)
The perturbations are large
D)
Wave propagates with added local speed and speed of sound

Correct Answer :   Linear equations are used to govern the flow variables

Explanation : Finite waves unlike the sound waves have high perturbation of density, velocity, temperature etc. They are known to propagate at speed which is an addition of local speed of mass velocity and speed of sound. The shape of the finite wave does not remain constant like the sound waves and the flow variables are governed by the nonlinear equations.

A)
Linearized region
B)
Expansion region
C)
Propagating region
D)
Compression region

Correct Answer :   Compression region

Explanation : The density of the finite wave varies along the distance of its propagation. The region where the density increases is known as the finite compression region, and the portion where the density decreases is known as the finite expansion region.

17 .
What is the slope for C characteristic line?
A)
ua
B)
u + a
C)
u – a
D)
u/a

Correct Answer :   u – a

Explaination : At a point (x,y) in an x – y plane there exists paths through this point known as C+ and C characteristic lines. They represent the path of sound waves which are left and right running. The slope for a C characteristic line is given by u – a and for C+ characteristic is u + a.