FINAL EXAMINATION
THERMO I
5/15/2004
OPEN BOOK PORTION
1.)
A pump takes 20 kg/sec of water at 25°C, 1 atm, through an inlet pipe of
10 cm diameter, and raises it to a final pressure of 1 MPa. The outlet pipe
diameter is 1 cm.
The pump efficiency is 90 percent.
Find:
a)
The velocity of the water in the inlet pipe.
b)
The velocity of the water in the outlet pipe.
c)
The power required to drive the pump (kW).
Conservation of mass:
m
in
= m
out
First law:
2
2
IN
IN
IN
c
OUT
OUT
c
W
+ m(h
+
/2g )
= m(h
+
/2g )
v
v
&
&
&
(a):
IN
in
m=
A
/v
v
&
;
From Table 10s,
v
in
= v
l,sat
(T
in
) = v
out
= 0.001003 m
3
/kg
so
IN
IN
=mv/A
v
&
=
0.001003(m
3
/kg)x20(kg/s)/(
π
x0.1
2
/4)(m
2
)
= 2.55 m/s
(b):
v
out
=
v
in
(A
in
/A
out
) = 2.55 x (10/1)
2
= 255 m/s
(c):
For an incompressible fluid,
isentropic
process, Eq. (6.58) gives
(h
out
 h
in
)
s
= v
L
(P
out
 P
in
) = 0.001003x(1000101.3) = 0.9014 kJ/kg, and
first law becomes
IN,S
W
&
=
m
&
[0.9014 + (1/2g
c
)(
v
2
out

v
2
in
)]
= 20(kg/s)[0.9014 (kJ/kg) + (1/2x1000 (J/kJ))(255
2
2.55
2
)]
= 20x(0.9014+32.51) = 668.2 kW
IN,A
W
&
=
IN,S
W
&
/
η
P
= 668.2/0.9 = 742.4 kW
Note the Table or Figure number for all data used in your solution
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2.)
A Rankine cycle operates at a boiler pressure of 800 kPa, and the
superheater brings the exit temperature of the steam entering the turbine
to 500°C.
The condenser operates at 8 kPa.
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 Spring '08
 DEINERT
 Thermodynamics, kPa, figure number

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