Homework 5 Due Monday, March
24, 2008
1.
Steam at 5 MPa and 500 ºC
enters a nozzle steadily with a velocity of 80 m/s, and it leaves at 2 MPa and 400 ºC. The inlet area of the nozzle is 50 cm2,
and heat is being lost at a rate of 90 kJ/s. Determine (a) the mass flow rate of the
steam, (b) the exit velocity of the steam, and (c) the exit area of the
nozzle. (C&B)
T1 = 500 ºC, T2
= 400 ºC, Q2-dot = 90 kJ s-1; x2-dot = 589.9 m s-1 and A2 = 15 cm2
2.
Air at 600 kPa and 127 ºC
enters an adiabatic diffuser steadily at a rate of 6000 kg/h and leaves at 100 kPa. The velocity of
the air stream is decreased from 230 to 30 m/s as it passes through the
diffuser. Find (a) the exit temperature
of the air and (b) the exit area of the diffuser. (C&B)
T2
= 427
K and A2 = 6.8 x 10-2 m2
3.
Refrigerant-134a enters a diffuser steadily as saturated vapor at 700 kPa with a velocity of 140 m/s, and it leaves at 800 kPa and 40 ºC. The refrigerant is gaining heat at a rate of 3 kJ/s as it passes through the diffuser. If the exit area is 80 percent greater than
the inlet area, determine (a) the exit velocity and (b) the mass flow rate of
the refrigerant. (C&B) v2 = 71.7
m/s, m-dot = 0.655 kg/s
4.
Air enters a compressor of a gas-turbine plant at ambient conditions of 100 kPa and 25 ºC with a low
velocity and exits at 1 MPa and 347 ºC with a velocity of 90 m/s.
The compressor is cooled at a rate of 1500 kJ/min, and the power input
to the compressor is 250 kW. Determine
the mass flow rate of air through the compressor. (C&B)
5.
A well-insulated valve is used to throttle steam from 8 MPa
and 500 ºC to 6 MPa. Determine the final temperature of the
steam. (C&B) 490.1 ºC
6.
A stream of refrigerant-134a at 1 MPa and 12 ºC is mixed with another stream at 1 MPa
and 60 C. If the mass flow rate of the
cold stream is twice that of the hot one, determine the temperature and the
quality of the exit stream. (C&B) T
= 39.39 ºC
and x = 0.221
7.
A long roll of 2-m-wide and 0.5-cm-thick 1-Mn manganese steel plate (ρ = 7854 kg/m3 and Cp
= 0.434 kJ/kg· ºC) coming off a furnace at 820 ºC is to be quenched in an oil bath at 45 ºC to a temperature of 51.1 ºC. If the metal sheet is moving at a steady
velocity of 10 m/min, determine the required rate of heat removal from the oil
to keep its temperature constant at 45 ºC. (C&B)
Q-dot = 4368 kW
8.
Steam enters a long, horizontal pipe with an inlet diameter of D1 =
12 cm at 1 MPa and 250 ºC
with a velocity of 2 m/s. Further
downstream, the conditions are 800 kPa and 200 ºC, and the diameter is D2 = 10 cm. Determine (a) the mass flow rate of the steam
and (b) the rate of heat transfer.
(C&B) m-dot
= 0.0972 kg/s and Q-dot = 10.04 kJ/s
9.
An insulated, vertical piston-cylinder device initially contains 10 kg of
water, 8 kg of which is in the vapor phase.
The mass of the piston is such that it maintains a constant pressure of
300 kPa inside the cylinder. Now steam at 0.5 MPa
and 350 ºC is allowed to enter the
cylinder from a supply line until all the liquid in the cylinder has
vaporized. Determine (a) the final
temperature in the cylinder and (b) the mass of the steam that has entered. (C&B) Tf
= 133.6 ºC
and m = 9.78 kg
10.
Two rigid tanks are connected by a valve. Tank A contains 0.2 m3 of water at
400 kPa and 80 percent quality. Tank B contains 0.5
m3 of water at 200 kPa and 250 ºC. The valve is now opened, and the two tanks
eventually come to the same state. Determine the pressure and the amount of
heat transfer when the system reaches thermal equilibrium with the surroundings
at 25 ºC. (C&B) Qout
= 2171 kJ and P = 3.169 kPa
"(C&A)"
indicates a problem taken from Y. A. çengel and M. A. Boles, "Thermodynamics – An
Engineering Approach," fifth edition.