# Rocket Propulsion Questions and Answers – Real Nozzles

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This set of Rocket Propulsion Multiple Choice Questions & Answers (MCQs) focuses on “Real Nozzles”.

1. For an asymmetric nozzle section of diameter 12 cm, determine the average value of flow velocity if the velocity distribution is of the form v2 = (2r – 3r2) x 104 m/s, where r denotes the radial location in the cross-section plane.
a) 1104.4 m/s
b) 765.4 m/s
c) 891.4 m/s
d) 404 m/s

Explanation: V2av = (2π/A2)∫v2rdr integrating over 0 to r2.
A2 = πd22/4
= 0.011 m2
∫v2rdr = ∫ (2r2 – 3r3)x 104 dr
= {(2/3)r23 – (3/4)r24} x 104
r2 = d2/2 = 0.06 m
so V2av = (2π/0.011) x 1.34
= 765.4 m/s.

2. In a boundary layer flow along with the nozzle, why is the layer closest to the wall cooler?
a) Flow velocity is minimum; Low energy flow leads to less temperature
b) Heat transfer to the walls
c) Radial heat propagation from the nozzle axis is a very slow process
d) Mass flow rate closer to the nozzle axis is maximum

Explanation: Because of heat transfer to the wall, the fluid layer closer to the wall will be cooler. But the boundary layer as a whole will have a higher temperature than the free stream flow because as the flow is slowed down in a boundary layer, it will lead to the conversion of flow kinetic energy to heat energy by viscous friction.

3. In which of the following cases is the effect of the boundary layer more pronounced?
a) Longer nozzles with high area ratios
b) Shorter nozzles with high area ratios
c) Longer nozzles with low area ratios
d) Shorter nozzles with low area ratios

Explanation: In longer nozzles with high area ratios, a relatively higher proportion of mass flow is found to be lying within the low-velocity region of the boundary layer. When that happens, the boundary layer plays a significant role in reducing the performance of the rocket engine.

4. What happens to the solid particles in multiphase flow at the nozzle exit when the size of the particles increases?
a) Lower momentum and lower thermal energy
b) Higher momentum and lower thermal energy
c) Lower momentum and higher thermal energy
d) Higher momentum and higher thermal energy

Explanation: As the particle size increases, its mass increases as a function of the cube of the diameter, but the drag force on them increases only as a function of the square of its diameter. So larger particles do not move as fast as smaller ones and when they reach the nozzle exit, their temperature is higher because they give away less thermal energy.

5. Which of the following is the correct expression for particle fraction β? Given: Total mass = mT, mass of the particles = mp.
a) mT/mp + mT
b) mp/mp + mT
c) mp/mT
d) mT/mp

Explanation: Particle fraction is defined as the ratio of the mass of the particle to the total mass. Enthalpy (h), gas constant (R), specific volume (V), etc can be specified as a function of particle fraction in a multiphase flow.

6. How do the characteristic velocity (c) and the specific impulse (Isp) vary as particle fraction β is increased?
a) Both Isp and c decreases
b) Both Isp and c increases
c) Isp decreases, c increases
d) Isp increases, c decreases

Explanation: Both specific impulse and characteristic velocity decrease as the particle fraction is increased. The loss of specific impulse is about 2% if the particle fraction is small (less than 6%). For larger values of particle fraction, the theory is not helpful and the losses can be as high as 10 to 20%.

7. Which of the following is not correct for transient periods when compared to steady periods of rocket operation?
a) Lower average thrust
b) Higher chamber pressure
c) Lower specific impulse
d) Higher velocity variations

Explanation: Transient period happens during the start or end of the operation, i.e. when the process hasn’t achieved a steady state yet. In that period, the chamber pressure, average thrust and specific impulse values are lower than its steady-state values and the velocity variations are significant.

8. Which of the following terms denote the ratio of kinetic energy per unit flow of the actual jet leaving the nozzle to that of a hypothetical ideal one with the same working substance, initial state and exit pressure as that of the actual exhaust jet?
a) Velocity correction factor (ζv)
b) Discharge correction factor (ζd)
c) Thrust correlation factor (ζF)
d) Energy efficiency factor (e)

Explanation: Energy efficiency factor (e) compares the kinetic energy of actual jet leaving the nozzle to that of a jet leaving an ideal nozzle while assuming the same working fluids, initial states, and exit pressure. e = v2a2/v2i2 = v2a2/{v1a2 + Cp(T1-T2)}.

9. Determine the velocity correction factor (ζv) if the energy conversion efficiency is 0.94.
a) 0.97
b) 0.85
c) 0.92
d) 0.99

Explanation: ζv = $$\sqrt{e}$$, where e is the energy conversion efficiency.
So ζv = $$\sqrt{0.94}$$ = 0.97 is the final answer.

10. Find the actual mass flow rate for a discharge correction factor (ζd) of 1.15. For an ideal nozzle of same design and initial state, the following information is given: Volume flow rate (Q) = 0.53 m3/s; static temperature (T) = 590 K; static pressure (P) = 0.15 MPa; R = 287 J/kg/K.
a) 0.47
b) 0.88
c) 0.28
d) 0.54