Arab Academy for Science, Technology and Maritime Transport (AASTMT)

College of Engineering & Technology Lecturer: Assoc. Prof. Dr. Eng. Khairy Elsayed

Course title: Thermodynamics II Course code: ME 333

Sheet 6: Compressible Flow in Nozzles

Stagnation Properties
1. Air flows through a device such that the stagnation pressure is 0.6 MPa, the stagnation temperature is
400 ◦ C , and the velocity is 570 m/s. Determine the static pressure and temperature of the air at this state.

2. Calculate the stagnation temperature and pressure for the following substances flowing through a duct: (a)
helium at 0.25 MPa, 50 ◦ C , and 240 m/s; (b) nitrogen at 0.15 MPa, 50 ◦ C , and 300 m/s; and (c) steam at
0.1 MPa, 350 ◦ C , and 480 m/s.

3. Air enters a compressor with a stagnation pressure of 100 kPa and a stagnation temperature of 35 ◦ C , and
it is compressed to a stagnation pressure of 900 kPa. Assuming the compression process to be isentropic,
determine the power input to the compressor for a mass flow rate of 0.04 kg/s.

4. Products of combustion enter a gas turbine with a stagnation pressure of 0.75 MPa and a stagnation
temperature of 690 ◦ C , and they expand to a stagnation pressure of 100 kPa. Taking k = 1.33 and R
= 0.287 kJ/kg K for the products of combustion, and assuming the expansion process to be isentropic,
determine the power output of the turbine per unit mass flow.

One-Dimensional Isentropic Flow

5. Helium enters a convergingdiverging nozzle at 0.7 MPa, 800 K, and 100 m/s. What are the lowest temperature
and pressure that can be obtained at the throat of the nozzle?

6. Air enters a convergingdiverging nozzle at a pressure of 1200 kPa with negligible velocity. What is the lowest
pressure that can be obtained at the throat of the nozzle?

Isentropic Flow through Nozzles

7. Nitrogen enters a convergingdiverging nozzle at 700 kPa and 400 K with a negligible velocity. Determine the
critical velocity, pressure, temperature, and density in the nozzle.

8. Air enters a convergingdiverging nozzle at 1.2 MPa with a negligible velocity. Approximating the flow as
isentropic, determine the back pressure that would result in an exit Mach number of 1.8.

9. An ideal gas with k = 1.4 is flowing through a nozzle such that the Mach number is 1.8 where the flow area
is 36 cm2 . Approximating the flow as isentropic, determine the flow area at the location where the Mach
number is 0.9.

Shock Waves and Expansion Waves

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10. Air enters a normal shock at 26 kPa, 230 K, and 815 m/s. Calculate the stagnation pressure and Mach
number upstream of the shock, as well as pressure, temperature, velocity, Mach number, and stagnation
pressure downstream of the shock.

11. Air enters a converging-diverging nozzle with low velocity at 2.0 MPa and 100 ◦ C . If the exit area of the
nozzle is 3.5 times the throat area, what must the back pressure be to produce a normal shock at the exit
plane of the nozzle?

12. Air enters a convergingdiverging nozzle of a supersonic wind tunnel at 1 MPa and 300 K with a low velocity. If
a normal shock wave occurs at the exit plane of the nozzle at Ma = 2.4, determine the pressure, temperature,
Mach number, velocity, and stagnation pressure after the shock wave.

13. Air flowing at 32 kPa, 240 K, and Ma1 = 3.6 is forced to undergo an expansion turn of 158. Determine the
Mach number, pressure, and temperature of air after the expansion.

14. Consider the supersonic flow of air at upstream conditions of 70 kPa and 260 K and a Mach number of 2.4
over a two-dimensional wedge of half-angle 10◦ . If the axis of the wedge is tilted 25◦ with respect to the
upstream air flow, determine the downstream Mach number, pressure, and temperature above the wedge.

Steam Nozzles
15. Steam enters a converging nozzle at 5.0 MPa and 400 ◦ C with a negligible velocity, and it exits at 3.0 MPa.
For a nozzle exit area of 60 cm2 , determine the exit velocity, mass flow rate, and exit Mach number if the
nozzle (a) is isentropic and (b) has an efficiency of 94 percent.

16. Steam enters a convergingdiverging nozzle at 1 MPa and 500 ◦ C with a negligible velocity at a mass flow
rate of 2.5 kg/s, and it exits at a pressure of 200 kPa. Assuming the flow through the nozzle to be isentropic,
determine the exit area and the exit Mach number.

Problems from Previous Exams

17. The thrust developed by the engine of a Boeing 777 is about 380 kN. Assuming choked flow in the nozzles,
determine the mass flow rate of air through the nozzle. Take the ambient conditions to be 220 K and 40 kPa.

18. A stationary temperature probe inserted into a duct where air is flowing at 190 m/s reads 85 ◦ C . What is the
actual temperature of the air?

19. A subsonic airplane is flying at a 5000-m altitude where the atmospheric conditions are 54 kPa and 256
K. A Pitot static probe measures the difference between the static and stagnation pressures to be 16 kPa.
Calculate the speed of the airplane and the flight Mach number.

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20. Nitrogen enters a converging-diverging nozzle at 620 kPa and 310 K with a negligible velocity, and it
experiences a normal shock at a location where the Mach number is Ma = 3.0. Calculate the pressure,
temperature, velocity, Mach number, and stagnation pressure downstream of the shock. Compare these
results to those of air undergoing a normal shock at the same conditions.

21. Saturated steam enters a convergingdiverging nozzle at 1.75 MPa, 10 percent moisture, and negligible
velocity, and it exits at 1.2 MPa. For a nozzle exit area of 25 cm2 , determine the throat area, exit velocity,
mass flow rate, and exit Mach number if the nozzle (a) is isentropic and (b) has an efficiency of 92 percent.