Chapter 17 | 87917–115E Steam enters a converging nozzle at 450 psia and
900°F with a negligible velocity, and it exits at 275 psia. For
a nozzle exit area of 3.75 in^2 , determine the exit velocity,
mass flow rate, and exit Mach number if the nozzle (a) is
isentropic and (b) has an efficiency of 90 percent. Answers:
(a) 1847 ft/s, 18.7 lbm/s, 0.900, (b) 1752 ft/s, 17.5 lbm/s, 0.849
17–116 Steam enters a converging–diverging 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. Answers:31.5 cm^2 , 1.738
17–117 Repeat Prob. 17–116 for a nozzle efficiency of 95
percent.Review Problems
17–118 Air in an automobile tire is maintained at a pres-
sure of 220 kPa (gauge) in an environment where the atmo-
spheric pressure is 94 kPa. The air in the tire is at the
ambient temperature of 25°C. Now a 4-mm-diameter leak
develops in the tire as a result of an accident. Assuming isen-
tropic flow, determine the initial mass flow rate of air through
the leak. Answer:0.554 kg/min
17–119 The thrust developed by the engine of a Boeing 777
is about 380 kN. Assuming choked flow in the nozzles, deter-
mine the mass flow rate of air through the nozzle. Take the
ambient conditions to be 265 K and 85 kPa.
17–120 A stationary temperature probe inserted into a duct
where air is flowing at 250 m/s reads 85°C. What is the
actual temperature of air? Answer:53.9°C
17–121 Nitrogen enters a steady-flow heat exchanger at
150 kPa, 10°C, and 100 m/s, and it receives heat in the
amount of 125 kJ/kg as it flows through it. The nitrogen
leaves the heat exchanger at 100 kPa with a velocity of 180
m/s. Determine the stagnation pressure and temperature of
the nitrogen at the inlet and exit states.
17–122 Derive an expression for the speed of sound based
on van der Waals’ equation of state PRT(vb) a/v^2.
Using this relation, determine the speed of sound in carbon
dioxide at 50°C and 200 kPa, and compare your result to that
obtained by assuming ideal-gas behavior. The van der Waals
constants for carbon dioxide are a364.3 kPa ·m^6 /kmol^2
and b0.0427 m^3 /kmol.
17–123 Obtain Eq. 17–10 by starting with Eq. 17–9 and
using the cyclic rule and the thermodynamic property relations17–124 For ideal gases undergoing isentropic flows, obtain
expressions for P/P*,T/T*, and r/r* as functions of kand Ma.
17–125 Using Eqs. 17–4, 17–13, and 17–14, verify that for
the steady flow of ideal gases dT 0 /TdA/A(1 Ma^2 )cp
Ta0 s
0 Tb
Pandcv
Ta0 s
0 Tb
v.dV/V. Explain the effect of heating and area changes on the
velocity of an ideal gas in steady flow for (a) subsonic flow
and (b) supersonic flow.
17–126 A subsonic airplane is flying at a 3000-m altitude
where the atmospheric conditions are 70.109 kPa and 268.65 K.
A Pitot static probe measures the difference between the static
and stagnation pressures to be 35 kPa. Calculate the speed of
the airplane and the flight Mach number. Answers:257 m/s,
0.783
17–127 Plot the mass flow parameter m.
/(AP 0 ) versus
the Mach number for k1.2, 1.4, and 1.6 in the range of 0
Ma 1.
17–128 Helium enters a nozzle at 0.8 MPa, 500 K, and
a velocity of 120 m/s. Assuming isentropic flow, deter-
mine the pressure and temperature of helium at a location
where the velocity equals the speed of sound. What is the
ratio of the area at this location to the entrance area?
17–129 Repeat Prob. 17–128 assuming the entrance veloc-
ity is negligible.
17–130 Air at 0.9 MPa and 400 K enters a converging
nozzle with a velocity of 180 m/s. The throat
area is 10 cm^2. Assuming isentropic flow, calculate and plot
the mass flow rate through the nozzle, the exit velocity, the
exit Mach number, and the exit pressure–stagnation pressure
ratio versus the back pressure–stagnation pressure ratio for a
back pressure range of 0.9 Pb0.1 MPa.
17–131 Steam at 6.0 MPa and 700 K enters a con-
verging nozzle with a negligible velocity. The
nozzle throat area is 8 cm^2. Assuming isentropic flow, plot
the exit pressure, the exit velocity, and the mass flow rate
through the nozzle versus the back pressure Pbfor 6.0 Pb
3.0 MPa. Treat the steam as an ideal gas with k1.3,cp
1.872 kJ/kg ·K, and R0.462 kJ/kg ·K.
17–132 Find the expression for the ratio of the stagnation
pressure after a shock wave to the static pressure before the
shock wave as a function of kand the Mach number upstream
of the shock wave Ma 1.
17–133 Nitrogen enters a converging–diverging nozzle at 700
kPa and 300 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 num-
ber, and stagnation pressure downstream of the shock. Com-
pare these results to those of air undergoing a normal shock
at the same conditions.
17–134 An aircraft flies with a Mach number Ma 1 0.8 at
an altitude of 7000 m where the pressure is 41.1 kPa and the
temperature is 242.7 K. The diffuser at the engine inlet has
an exit Mach number of Ma 2 0.3. For a mass flow rate of
65 kg/s, determine the static pressure rise across the diffuser
and the exit area.1 RT 0cen84959_ch17.qxd 4/21/05 11:08 AM Page 879