Modern Engineering Thermodynamics

Problems 687
Problems (* indicates problems in SI units)
1. Explain the difference between T o and T os .
2. Explain why we use both symbols T o and T os but use only p os
and do not refer to p o at all.
3. The absolute maximum exit velocity from any type of nozzle
can be obtained by multiplying Eq. (16.2) by T and setting
p
T = 0 R. Then, ðV exit Þ max
=
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p
2g c c p T o = ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2g c c p T os : Determine the
absolute maximum exit velocity for the nozzle in Example 16.6,
and determine the percentage of this value achieved by the
actual exit velocity.
4.* Saturated water vapor at 150.°C enters an isentropic converging
nozzle with a negligible velocity and exits at 0.300 MPa.
Determine the exit quality, temperature, and velocity. Do not
assume ideal gas behavior.
5. Air flows in a circular tube with a velocity of 275 ft/s at a
temperature of 103°F and a pressure of 175 psig. Determine its
stagnation pressure and temperature.
6. Calculate the isentropic stagnation temperature and pressure
on your hand as you hold it outside the window of an
automobile traveling at 55.0 mph on a day when the static
temperature and pressure are 70.0°F and 14.7 psia.
7. Steam at 600.°F and 200. psia is traveling at 1500. ft/s. Determine
the isentropic stagnation temperature and pressure of the steam by
a. Assuming steam to be an ideal gas.
b. Using the steam tables (or Mollier diagram or computer
program).
8.* A steam jet with a static pressure and temperature of 10.0 MPa
and 400.°C has a velocity of 750. m/s. Determine the isentropic
stagnation pressure and temperature of the jet. Do not assume
ideal gas behavior.
9. Using Eq. (16.9), show that the speed of sound is infinite in an
incompressible substance.
10.* If the speed of sound in saturated liquid water at 90.0°C is
1530 m/s, determine the isentropic compressibility α of the water,
where
α = − 1
∂v
v ∂p
11.* Determine the Mach number of a meteor traveling at 5000. m/s
through still air at 0.00°C.
12. Determine the Mach number of a bullet traveling at 3000. ft/s
through still air at 70.0°F.
13. The rotor of an axial flow air compressor has a diameter of
2.30 ft. What is the maximum rpm of the rotor such that its
blade tips do not exceed the local sonic velocity when the air in
the compressor is at 150.°F?
14.* Determine the stagnation temperature and Mach number of
carbon dioxide gas flowing in a 1.00 × 10 –2 m diameter circular
tube at a rate of 0.100 kg/s. The temperature and pressure are
30.0°C and 0.500 MPa.
15.* The isentropic stagnation–static property formula given in Eqs.
(16.12) to (16.14) and (16.18) to (16.20) are valid only for ideal
gases. In Chapter 11, the conditions under which steam behaves as
an ideal gas are discussed (steam gas). Suppose steam at 4.00 MPa,
400.°C is to be expanded through a converging nozzle under
choked flow conditions. Use Eq. (16.18) to calculate T* and use the
steam tables (or Mollier diagram or computer program) with this
value of T*ands* = s os to find p*andρ* = 1/v*. Then compare
these values with the ones calculated from Eqs. (16.19) and (16.20).
s
16. A nozzle is to be designed to accelerate the flow of air from a
Mach number of 0.100 to 1.00. Determine the inlet to exit area
ratio of the nozzle assuming isentropic flow.
17. A diffuser is to be designed to reduce the Mach number of air
from 0.90 to 0.10. Assuming isentropic flow, determine the exit
to inlet area ratio of the diffuser.
18.* Argon escapes into the atmosphere at 0.101325 MPa from a
1.00 m 3 storage tank initially at 5.00 MPa and 25.0°C through a
converging-diverging nozzle with a throat area of 1.00 × 10 –3 m 2 .
a. Is the flow through the nozzle initially choked?
b. If so, at what tank pressure does it unchoke?
c. How long does it take to unchoke if the tank is maintained
at 25.0°C?
19. Air at 100. psia and 70.0°F enters a converging nozzle with a
negligible velocity and is expanded isentropically until the exit
temperature is 32.0°F. Determine the exit Mach number and
pressure.
20.* Air at 150. kPa 100.°C enters a converging nozzle with a
negligible velocity and is expanded isentropically until the exit
pressure reaches 101 kPa. Determine the exit Mach number and
temperature.
21.* 1.86 kg/s of air flows through a converging-diverging supersonic
wind tunnel whose reservoir isentropic stagnation conditions are
18.0 atm at 300. K and whose exit Mach number is 4.80. If the
reservoir isentropic stagnation pressure is raised to 20.0 atm at
the same temperature, find the new mass flow rate and exit
Mach number if the exit pressure remains constant.
22.* Air enters a converging-diverging isentropic nozzle at 10.0 MPa
and 500. K with a negligible velocity and is accelerated to a
Mach number of 4.50. Determine the static temperature,
pressure, and density at (a) the throat, and (b) the exit. (c) Find
the exit to throat area ratio.
23. Low-velocity helium enters a converging-diverging isentropic
nozzle at 250. psia and 120.°F. It is accelerated to a Mach
number of 2.0. at the exit. Determine the static temperature,
pressure, and density at (a) the throat, and (b) the exit. (c) Find
the exit to throat area ratio.
24.* A converging-diverging nozzle is attached to a compressed air
reservoir at 1.00 MPa and 27.0°C. There are two positions in the
nozzle where A/A* = 2.00, one is in the converging section and
the other is in the diverging section. Determine the Mach
number, pressure, temperature, density, and velocity at each
section.
25.* Air at 0.500 MPa and 21.0°C enters an isentropic convergingdiverging
nozzle with a negligible velocity. The exit to throat
area ratio of the nozzle is 1.34. If the throat velocity is sonic,
determine the exit static pressure, temperature, and Mach
number, if (a) the exit is subsonic and (b) the exit is supersonic.
26. A supersonic converging-diverging nozzle is to be designed to be
attached to a standard machine shop air supply having
isentropic stagnation conditions of 100. psia and 70.0°F. The
throat of the nozzle is to have a diameter of 0.250 in, and the
nozzle exhausts into the atmosphere at 14.7 psia. For an
isentropic nozzle, determine
a. The exit Mach number.
b. The exit temperature.
c. The mass flow rate of air through the nozzle.
d. The exit diameter of the diverging section.