HW 6 - Due Monday, March 2

ME 200 Homework #06 - Spring 2015
Homework Due: Monday, March 2, 2015
HW06(1)
A homeowner has devised a humidifier that is shown
at right. Water is taken from the faucet and fed to a
reservoir that incorporates an electric resistance heater.
The reservoir is shaped like a nozzle so that vapor will
be ejected at a high speed and distributed to the room.
Water enters the reservoir through a hose having a
diameter of 5 mm and has a temperature of 20 oC, a
pressure of 100 kPa, and a volume flow rate of 1 liter
per hour. Saturated water vapor at 100 kPa leaves the
top of the device through a 20 mm diameter circular
opening.
Saturated Vapor
100 kPa
Water
1 liter/shr
20 C, 100 kPa
(a) Estimate the electrical power input required to
operate the device. (Answer: -0.718 kW)
(b) Calculate the ratio of the change in the fluid’s kinetic energy to its change in enthalpy. On
this basis, state whether or not it is reasonable to neglect kinetic energy differences.
You can assume steady state and steady flow (SSF), neglect heat transfer between the reservoir
and the room, and neglect differences in potential energy.
HW06(2)
A very long cylindrical steel rod (=500 lbm/ft3, Cp=0.111 Btu/lbmoR) of 4-inch diameter is heat
treated by drawing it at a velocity of 10 ft/min through an oven maintained at 1700 oF. If the rod
enters the oven at 90 oF and leaves at 1300 oF, determine the rate of heat transfer (in Btu/h) to the
rod in the oven. (Hint: treat the moving rod as a “steel flow”) (Answer: 4.15×106 Btu/h)
1700 oF
10 ft/min
90 oF
1300 oF
Steel rod
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HW06(3)
The right figure provides steady-state data
for water vapor flowing through a piping
configuration. At each exit, the volumetric
flow rate, pressure, and temperature are
equal. Determine the mass flow rate at the
inlet and exits, each in lbm/s. (Answer:
for 1, 23.36 lbm/s, for 2 and 3, 11.68 lbm/s)
HW06(4)
Air enters a nozzle steadily at 50 psia, 140 oF, and 150 ft/s, it leaves at 14.7 psia and 900 ft/s. The
heat loss from the nozzle is estimated to be 6.5 Btu/lbm of air flowing. The inlet area of the
nozzle is 0.1 ft2. Determine:
(a) The exit temperature of air. (Answer: 47 oF)
(b) The exit area of the nozzle. (Answer: 0.048 ft2)
HW6(5)
Refrigerant-134a at 700 kPa and 100 oC enters an adiabatic nozzle steadily with a velocity of 20
m/s and leaves at 300 kPa and 30 oC. Determine:
(a) The exit velocity. (Answer: 356.9m/s)
(b) The ratio of the inlet to exit area A1/A2.
HW6(6)
Air enters a diffuser operating at steady state at 300 K, 1 bar, with a velocity of 180 m/s, and
exits with a velocity of 18 m/s. The ratio of the exit area to the inlet area is 8. Assuming the ideal
gas model for the air and ignoring heat transfer, determine the temperature in K, and pressure, in
kPa, at exit. (Answer: T2 = 316.1 K, p2 = 131.7 kPa)
HW6(7)
Steam at 12 MPa and 600 oC enters a turbine
operating at steady state. As shown in the figure, 20%
of the entering mass flow is extracted at 4.0 MPa and
280 oC. The rest of the steam exits as a saturated
vapor at 0.06 bar. The turbine produces 2000 kW of
power. Heat transfer from the turbine to the
surrounding occurs at a rate of 15 kW. Neglecting
kinetic and potential energy effects, determine the
mass flow rate of the steam entering the turbine, in
kg/s. (Answer: 2.07 kg/s)
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HW06(8)
Air is compressed from 14.7 psia and 60 oF to a pressure of 150 psia while being cooled at a rate
of 10 Btu/lbm by circulating water through the compressor. The volume flow rate of the air at the
inlet is 5000 ft3/min, and the power input to the compressor is 700 hp. Determine:
(a) The mass flow rate of the air. (Answer: 6.36 lbm/s)
(b) The temperature at the compressor exit. (Answer: 341 oF)
HW06(9)
A pump is used to circulate water in a home heating system. Water enters the well-insulated
pump (operating at steady state) at a rate of 1.5 liter/min. The inlet pressure and temperature are
1 bar and 80 oC, respectively. At the exit, the pressure is 8 bar. The pump requires 20 W of
power input. Water can be modeled as an incompressible substance with constant density of 970
kg/m3 and constant specific heat of 4.2 kJ/kg▪K. Neglecting kinetic and potential energy effects,
determine the temperature change, in K, as the water flows through the pump. Comment on this
change. (Answer: 0.0245 K)
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