Chapter 8: Variable Area Flow
This chapter contains 48 unsolved problems.
# Short Problem Description Manual solution
Computer solution
1
Flow rate. Pressure and temperature at nozzle exit.
2
Normal shock in nozzle, Supersonic flow at the exit plane, Minimum reservoir pressure for choking.
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.
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.
5
Maximum back-pressure for choking, Back-pressures for shock in the nozzle, Design back-pressure, Back-pressures for supersonic flow at nozzle exit.
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.
7
Variable area diffuser.
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.
9
Rocket nozzle thrust at sea level versus space.
10
Throat area, exit area and exit velocity.
11
Mass flow rate through CD passage, Mach number at the minimum area section, Velocity and pressure at the exit section.
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.
13
Mach number and the temperature at nozzle exit, Nozzle area where the normal shock wave occurs.
14
Pressure, temperature, and Mach number at the nozzle exit.
15
Nozzle area where the shock occurs, Mach number and pressure just before and just after the shock wave.
16
Inlet and exit Mach numbers, Increase in entropy, Area where the shock occurs, Stagnation pressure at the exit.
17
Exit area, Exit temperature, Exit Mach number, Area where the shock wave occurs, Pressure ratio across the shock.
18
Pressure in the reservoir for normal shock at nozzle exit.
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.
20
Nozzle throat area, Nozzle exit area, Temperatures upstream and downstream of the shock wave, Change in entropy through the nozzle.
21
Mass flow rate at design conditions, Exit pressure when normal shock wave occurs in the divergent section.
22
Mach number at exit of the nozzle.
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.
24
Mach numbers on each side of this shock wave, Back-pressure required to maintain the shock at a location.
25
Throat areas of the nozzle and diffuser.
26
Mach number, Stagnation temperature and pressure, Mass flow rate through the nozzle, Exit area, pressure, and temperature.
27
Mass flow rate of carbon dioxide using venturimeter.
28
Large rocket engine designed to propel a satellite launcher, Throat and exit diameters of the nozzle.
29
Mach number, temperature, and velocity of the air at the discharge.
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.
31
Fixed supersonic convergent-divergent diffuser, Mach number to swallow the shock during startup.
32
Variable-area diffuser, Percentage reduction in diffuser throat area.
33
Diffuser with a variable area ratio, Throat area at cruise / throat area at given Mach.
34
Percentage increase in throat area.
35
Wind tunnel test section with a variable area diffuser, Idea diffuser throat area / Starting throat area.
36
Rate of air discharge from a tank.
37
Transonic wind tunnel testing.
38
Pressures and Mach numbers at given cross-sectional area.
39
Moving piston, Air velocity at exit, Piston velocity, Flow rate of discharged air.
40
Pressure in the second reservoir.
41
Angle of flow at discharge.
42
Meteorite punching hole in the skin of an orbiting space laboratory.
43
Jet engine is running on a test bed.
44
Back-pressures for constant mass flow rate.
45
Nozzle area at which the shock wave occurs.
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.
47
Mach number and flow direction just downstream of oblique shock waves.
48
Flow direction just downstream of expansion waves, Effect of expansion waves on thrust.