Home Back
Chapter 8: Variable Area Flow
This chapter contains 48 unsolved problems.
# Short Problem Description Manual solution
Inactive links
Computer solution
Inactive links
1
Flow rate. Pressure and temperature at nozzle exit.
q01.pdf q01.py
2
Normal shock in nozzle, Supersonic flow at the exit plane, Minimum reservoir pressure for choking.
q02.pdf q02.py
3
Maximum back-pressure to choke the nozzle, Normal shock in the nozzle, Back-pressure for perfectly expanded nozzle, Supersonic flow at the nozzle exit plane.
q03.pdf q03.py
4
Throat and exit areas of the nozzle, Design back-pressure and temperature, Lowest back-pressure with no supersonic flow, Back-pressure with no shock waves.
q04.pdf q04.py
5
Maximum back-pressure for choking, Back-pressures for shock in the nozzle, Design back-pressure, Back-pressures for supersonic flow at nozzle exit.
q05.pdf q05.py
6
Flow rate under design conditions, Exit area of the nozzle, Design back-pressure and the temperature, Lowest back-pressure for which there is only subsonic flow, Back-pressure for normal shock wave on the exit plane, Back-pressure for no shock waves in the nozzle, Back-pressures for oblique shock waves, Back-pressures for expansion waves, Back-pressures at which a normal shock wave in divergent section.
q06.pdf q06.py
7
Variable area diffuser.
q07.pdf q07.py
8
Exit area of the nozzle, Mass flow rate at design conditions, Back-pressure when normal shock wave at exit, Back-pressures for expansion waves.
q08.pdf q08.py
9
Rocket nozzle thrust at sea level versus space.
q09.pdf q09.py
10
Throat area, exit area and exit velocity.
q10.pdf q10.py
11
Mass flow rate through CD passage, Mach number at the minimum area section, Velocity and pressure at the exit section.
q11.pdf q11.py
12
Nozzle throat area, Mach numbers before and after the shock, Nozzle area where the shock occurs, Nozzle area at exit, Density at exit of the nozzle.
q12.pdf q12.py
13
Mach number and the temperature at nozzle exit, Nozzle area where the normal shock wave occurs.
q13.pdf q13.py
14
Pressure, temperature, and Mach number at the nozzle exit.
q14.pdf q14.py
15
Nozzle area where the shock occurs, Mach number and pressure just before and just after the shock wave.
q15.pdf q15.py
16
Inlet and exit Mach numbers, Increase in entropy, Area where the shock occurs, Stagnation pressure at the exit.
q16.pdf q16.py
17
Exit area, Exit temperature, Exit Mach number, Area where the shock wave occurs, Pressure ratio across the shock.
q17.pdf q17.py
18
Pressure in the reservoir for normal shock at nozzle exit.
q18.pdf q18.py
19
Nozzle area at which the normal shock wave is located, Increase in entropy across the shock, Back-pressure when shock wave is located at nozzle exit.
q19.pdf q19.py
20
Nozzle throat area, Nozzle exit area, Temperatures upstream and downstream of the shock wave, Change in entropy through the nozzle.
q20.pdf q20.py
21
Mass flow rate at design conditions, Exit pressure when normal shock wave occurs in the divergent section.
q21.pdf q21.py
22
Mach number at exit of the nozzle.
q22.pdf q22.py
23
Minimum supply stagnation pressure for choking the nozzle, Mass flow rate through the nozzle, Supply stagnation pressure when normal shock wave occurs in the divergent portion.
q23.pdf q23.py
24
Mach numbers on each side of this shock wave, Back-pressure required to maintain the shock at a location.
q24.pdf q24.py
25
Throat areas of the nozzle and diffuser.
q25.pdf q25.py
26
Mach number, Stagnation temperature and pressure, Mass flow rate through the nozzle, Exit area, pressure, and temperature.
q26.pdf q26.py
27
Mass flow rate of carbon dioxide using venturimeter.
q27.pdf q27.py
28
Large rocket engine designed to propel a satellite launcher, Throat and exit diameters of the nozzle.
q28.pdf q28.py
29
Mach number, temperature, and velocity of the air at the discharge.
q29.pdf q29.py
30
A small jet aircraft designed to cruise at Mach 1.5, Ideal area ratio for this diffuser, Mach number to which the aircraft must be taken to swallow the normal shock wave.
q30.pdf q30.py
31
Fixed supersonic convergent-divergent diffuser, Mach number to swallow the shock during startup.
q31.pdf q31.py
32
Variable-area diffuser, Percentage reduction in diffuser throat area.
q32.pdf q32.py
33
Diffuser with a variable area ratio, Throat area at cruise / throat area at given Mach.
q33.pdf q33.py
34
Percentage increase in throat area.
q34.pdf q34.py
35
Wind tunnel test section with a variable area diffuser, Idea diffuser throat area / Starting throat area.
q35.pdf q35.py
36
Rate of air discharge from a tank.
q36.pdf q36.py
37
Transonic wind tunnel testing.
q37.pdf q37.py
38
Pressures and Mach numbers at given cross-sectional area.
q38.pdf q38.py
39
Moving piston, Air velocity at exit, Piston velocity, Flow rate of discharged air.
q39.pdf q39.py
40
Pressure in the second reservoir.
q40.pdf q40.py
41
Angle of flow at discharge.
q41.pdf q41.py
42
Meteorite punching hole in the skin of an orbiting space laboratory.
q42.pdf q42.py
43
Jet engine is running on a test bed.
q43.pdf q43.py
44
Back-pressures for constant mass flow rate.
q44.pdf q44.py
45
Nozzle area at which the shock wave occurs.
q45.pdf q45.py
46
Exit area of the nozzle, Mass flow rate at design conditions, Back-pressure when normal shock wave on the exit plane, Back-pressures when normal shock wave in the nozzle, Back-pressures when oblique shock waves will occur, Back-pressures when expansion waves will occur.
q46.pdf q46.py
47
Mach number and flow direction just downstream of oblique shock waves.
q47.pdf q47.py
48
Flow direction just downstream of expansion waves, Effect of expansion waves on thrust.
q48.pdf q48.py

For further details, please contact me at:
mail.spbhat@gmail.com
If you observe any error or want to provide me with feedback, please don't hesitate to contact me.

Thanks,
Sourabh Bhat