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Correct answer is (c) EXIT pressure < Inlet pressure

The best I can explain: The air in the nozzle will NEVER flow by itself considering that the area ratio between the inlet and the throat is very high. There needs to be a pressure difference created for the air to MOVE. This happens only when the exit pressure is less than the the inlet pressure (PE < p0).

Right choice is (c) 2.36

To explain: Given M = 2.7

If we assume that there’s a normal SHOCK PRESENT at the entrance of the diffuser, then using the GAS table we can find the ratio of total pressures \(\frac {p_{01}}{p_{02}}\).

For M = 2.7, \(\frac {p_{02}}{p_{01}}\) = 0.4236

Using the relation beween the throat areas and total pressure we get

\(\frac {A_{t2}}{A_{T1}} = \frac {p_{01}}{p_{02}} = \frac {1}{0.4236}\) = 2.36

Correct option is (c) s1 < s2

To elaborate: When the flow INTERACTS with the oblique shock waves inside the supersonic diffuser, the flow diffuses to a slower velocity. This results in a normal shock wave at the end of the diffuser. Thus the EXIT ENTROPY is HIGHER than the entropy at the inlet section.

Correct option is (a) PRESENCE of shock WAVES

For explanation: Due to the presence of OBLIQUE shock waves on the convergent portion, the ideal supersonic diffuser is far from achievable. This contributes to the breaking of the isentropic FLOW characteristics according to which the entropy in the diffuser is constant. In fact, the flow in reality is viscous and there is an INCREASE in entropy near the boundary layer.

Correct option is (b) False

Best explanation: The goal of the diffuser is to reduce the flow velocity with small total pressure loss. If we reduce the INCOMING supersonic flow through a series of oblique shock followed by a WEAK normal shock WAVE, LEADS to lower total pressure loss compared to reducing the incoming supersonic flow to subsonic using one strong normal shock.

The correct option is (d) Exit pressure is same as the inlet pressure

Best EXPLANATION: Choked FLOW is a condition where the exit pressure is lower than inlet pressure to a POINT where the flow after throat section BECOMES frozen. After this, DESPITE lowering the value of exit pressure, inlet pressure has no effect. The mass flow remains constant despite reducing the exit pressure.

Correct answer is (a) 2

The EXPLANATION is: Supersonic WIND tunnel is broadly classified into two CATEGORIES – Intermittent wind tunnel and CONTINUOUS wind tunnel. Out of these two, the intermittent wind tunnel is more commonly used due to simpler design, faster START and more power available to start the wind tunnel.

Right ANSWER is (a) Isentropic

Easy explanation: In an ideal supersonic diffuser, the air is SLOWED to subsonic speed and then expended to the atmosphere. This is done by isentropic COMPRESSION as ideally there should be no loss in TOTAL pressure.

Correct choice is (a) Higher total PRESSURE loss

Explanation: In real scenario FAR from hypothetical nature of the diffuser, the oblique shock WAVES interact with the viscous boundary layer of the diffuser wall. This leads to the separation of the boundary layer thereby increasing the total pressure LOSSES. One thing to remember is that the aim of the diffuser is to reduce the flow velocity by low total pressure losses, but the boundary layer separation prevents that from happening.

Correct answer is (d) Test model

Easy explanation: SUPERSONIC wind tunnel mainly COMPRISES of three components – convergent – divergent nozzle, test section which is CONSTANT AREA duct and a diffuser to further slow down the speed to low subsonic speed. Test model is not a part of the wind tunnel and is inserted INSIDE to take measurements such as lift, drag.

Right choice is (a) 2

Easiest explanation: The area – Mach relation which is the ratio of local area to throat area as a FUNCTION of Mach number yields two SOLUTIONS for a given Mach number. One is a subsonic value and the other is the CORRESPONDING SUPERSONIC value.

Correct CHOICE is (b) False

Explanation: If we CONSIDER the nozzle throat area as section 1, then the mass flow RATE through the section is \(\dot {m_1}\) = ρ1u1A1t. The mass flow rate through th diffuser throat area is \(\dot {m_2}\) = ρ2u2A2t. Since there’s steady flow in side the wind tunnel, thus the mass flow rate remains same.

\(\dot {m_1} = \dot {m_2}\)

ρ1u1A1t = ρ2 u2A1t

But due to the PRESENCE of shock waves inside the diffuser, the DENSITY and the flow velocity are not same. (ρ1≠ρ2, u1≠u2). This means that the throat areas are also not same.

Correct option is (a) ηD = \(\FRAC {(\frac {p_{d_0}}{p_0})_{ACTUAL }}{(\frac {p_{0_2}}{p_{01}})_{normal \, shock \, at \, M_e}}\)

The explanation is: The EFFICIENCY of diffuser is measured by the ratio of actual total PRESSURE ratio \(\frac {p_{d_0}}{p_0}\)to the total pressure ratio across hypothetical normal shock wave at test section MACH number \(\frac {p_{0_2}}{p_{01}}\).

Correct option is (a) True

Best explanation: The goal of the diffuser is to reduce the FLOW velocity with small total pressure loss. If we reduce the incoming SUPERSONIC flow through a series of oblique shock followed by a WEAK normal shock wave, leads to lower total pressure loss compared to REDUCING the incoming supersonic flow to subsonic using one strong normal shock.

Correct OPTION is (b) At2 > At1

Explanation: There are two throats in the SUPERSONIC wind TUNNEL. The first is that of the nozzle and the second is that of the DIFFUSER. The nozzle’s throat region is equal to A * (sonic area) and the diffuser’s throat area is GREATER than the nozzle’s throat area because of the rise in entropy within the diffuser.

The correct option is (c) Convergent – DIVERGENT

Easy EXPLANATION: Supersonic WIND tunnel produces flow of Mach number above 1. This is achieved using convergent – divergent nozzle. This selection is based on area – VELOCITY relation, according to which the subsonic flow accelerates in the convergent section to SONIC speed after which the speed is further accelerated in the divergent section.

Right option is (b) Adiabatic expansion

Explanation: The process of slowing down the incoming flow inside the diffuser is DONE USING adiabatic expansion. The pressure is constant throughout, if this was not the case then reduced TOTAL pressure in front of the COMPRESSOR would yield less flow velocity.

Correct option is (b) 2

The EXPLANATION is: In case of supersonic wind tunnels, there are two throats present. One is the nozzle THROAT where the sonic SPEED is achieved and the SECOND throat is the diffuser throat where supersonic incoming flow is isentropically compressed to Mach 1.

Right answer is (a) Ideal isentropic diffuser

To explain: In case of ideal isentropic diffuser the total pressure remains constant. Thus from the relation between the throat area and total pressure we see that P01 = P02 = constant. Hence the throat AREAS AT2 = At1. It is important to note that ideal isentropic diffuser is a hypothetical case and is not possible to achieve in real life.

\(\frac {A_{T2}}{A_{t1}} = \frac {p_{01}}{p_{02}}\)

Right answer is (b) Shock WAVE interaction with walls

The explanation is: In real life, oblique shock DIFFUSERS have viscous flow. The presence of shock waves inside the diffuser leads to interaction with the viscous boundary layer of the diffuser walls which leads to additional pressure losses. There’s also friction involved which makes oblique shock diffusers far from the IDEAL diffusers which have no total pressure losses.

The correct option is (a) Subsonic flow

Explanation: The AREA – VELOCITY relation is given by:

\(\frac {dA}{A}\) = (M^2 – 1)\(\frac {du}{u}\)

ACCORDING to this FORMULA, for subsonic flows the value of M^2 – 1 becomes NEGATIVE since 0 < M < 1. Thus, with decreasing cross – sectional area, the velocity increases. Decreasing area is achieved by convergent duct.

Correct ANSWER is (d) Shock waves

For explanation I would say: In case of actual SUPERSONIC DIFFUSER, there’s a series of oblique shock formations. It’s present in the convergent and the test section of the wind tunnel. The interaction between the viscous flow and the shock waves RESULTING in SLOWING down the flow velocity.

The correct choice is (a) Cross – SECTIONAL area

Best explanation: One – DIMENSIONAL FLOWS are those flows that have a constant crossectional area and only the flow variables i.e. pressure, VELOCITY, density, temperature etc vary wrt X. What separates Quasi one – dimensional flow from this is the variable cross – sectional area wrt x.

Right choice is (a) pB = pe

For explanation I would say: Back PRESSURE, which is the pressure downstream the nozzle’s EXIT is equal to the exit pressure when the FLOW at the exit is subsonic. This is because of a DISCREPANCY between maintaining a steady subsonic flow in case of pressure difference.

Correct option is (B) False

To explain I would say: In the case of subsonic flow, convergent nozzle leads of increased velocity using the area – velocity relation. Similarly, for supersonic flow the DIVERGENT nozzle leads to increased flow velocity. THUS, in order to OBTAIN the supersonic flow we make use of convergent – divergent nozzle.