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Homework #8 MEMS 0051 – Introduction to Thermodynamics solved

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Starting with the Conservation of Energy equation:
d E
dt = Q˙ − W˙ +
X
N
i=1
m˙ i

hi +
V
2
i
2
+ gzi


X
M
j=1
m˙ j

hj +
V
2
j
2
+ gzj

,
and the Continuity equation:
d m
dt =
X
N
i=1
m˙ i −
X
M
j=1
m˙ j ,
Solve the following:
Problem #1
Steam enters a turbine through a pipe with a diameter of 0.2 [m]. The steam enters with a velocity of 100
[m/s], a pressure of 14,000 [kPa] and a temperature of 600 ◦C. The steam is exhausted through a pipe with
a diameter of 0.8 [m], a pressure of 500 [kPa] and a temperature of 180 ◦C. Determine:
a) the exit velocity of the steam;
b) the mass flow rate of the steam.
Problem #2
A device has one inlet with a cross-sectional flow area of 0.6 [m2
] in which steam enters with a velocity of
50 [m/s], a pressure of 1,000 [kPa] and a temperature of 400 ◦C. There are two outlets. One outlet has
saturated liquid exiting through a 0.018 [m2
] pipe with a mass flow rate of 50 [kg/s] at a pressure of 150
[kPa]. Determine:
a) the mass flow rate at the inlet;
b) the mass flow rate of the second outlet.
Problem #3
Air enters a device at 1,000 [kPa] and 580 [K] and leaves with a volumetric flow rate of 1.8 [m3/s] at 100
[kPa] and 500 [K]. Heat is transferred from the device to the surroundings at 347 [kJ] per kilogram of air
entering the device. Determine:
a) the power developed by the device;
b) the the volumetric flow rate at the inlet.
Problem #4
Air flows through a diffuser with a mass flow rate of 0.5 [kg/s] from an inlet condition of 300 [kPa], 290 [K]
and 400 [m/s] to an exit condition of 1,4000 [kPa] and 40 [m/s]. Determine:
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a) the exit temperature of the air;
b) the inlet cross-sectional flow area.
Problem #5
A turbine with sufficient insulation accepts steam at the rate of 85 [m3/min] at 3,000 [kPa] and 400 ◦C. A
portion of the steam is siphoned from the turbine at a pressure of 500 [kPa], a temperature of 180 ◦C at
a velocity of 20 [m/s]. The remainder of the steam, with a mass flow rate of 40,000 [kg/hr] expands to a
pressure of 6 [kPa] with a quality of 90%. Determine:
a) the power developed by the turbine;
b) the diameter of the siphon.
Problem #6
An open feedwater heater (OFWH) accepts liquid water at 1,000 [kPa] and a temperature of 50 ◦C. The
OFWH also accepts water with a mass flow rate per that of inlet one, i.e. ˙m2/ ˙m1=0.22. Saturated liquid
water exits the OFWH. Determine:
a) the temperature of the second incoming stream, if superheated;
b) the quality of the second incoming stream, if saturated.
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