Homework SourseA flash chamber fitted with an inlet valve produces saturate
A flash chamber fitted with an inlet valve produces saturated vapor and saturated liquid streams from a single entering stream of liquid water. Operation is steady-state. Stray heat transfer and the effects of motion and gravity are negligible. Determine (a) the mass flow rate of saturated vapor, in kg/s and (b) the total rate of exergy destruction in kW. Let T0 = 298K, p0 = 1 bar. M=10kg/s T1=150C P1=6Bar P2=P3=2Bar
Solution
U
cv
dt
5
m
cv
c
dT dt
With Eq. 3.20b the enthalpy term of the energy rate balance can be expressed as
h
1
2
h
2
5
c
1
T
1
2
T
2
2
1
y
1
p
1
2
p
20
2
where the pressure term is dropped by assumption 4. Since the water is well mixed, the temperature at the exitequals the temperature of the overall quantity of liquid in the tank, so
h
1
2
h
2
5
c
1
T
1
2
T
2
where
T
represents the uniform water temperature at time
t
. With the foregoing considerations the energy rate balance becomes
m
cv
cdT dt
5
Q
#
cv
2
W
#
cv
1
m
#
c
1
T
1
2
T
2
As can be verified by direct substitution, the solution of this first-order, ordinary differential equation is
T
5
C
1
exp
a
2
m
#
m
cv
t
b
1
a
Q
#
cv
2
W
#
cv
m
#
c
b
1
T
1
The constant
C
1
is evaluated using the initial condition: at
t
= 0,
T
5
T
1
. Finally
T
5
T
1
1
a
Q
#
cv
2
W
#
cv
m
#
c
bc
1
2
exp
a
2
m
#
m
cv
t
bd
Substituting given numerical values together with the specific heat
c
for liquid water from Table A-19
T
5
318 K
1
£ 3
2
7.6
2
1
2
0.6
24
kJ
/
s
a
2703600 kg
s
ba
4.2kJkg
?
K
b § c
1
2
exp
a
2
270 kg
/
h45 kg
t
bd
5
318
2
22
3
1
2
exp
1
2
6
t
24
where
t
is in hours. Using this expression, we construct the accompanying plotshowing the variation of temperature with time.
In this case idealizations are made about the state of the mass containedwithin the system and the states of the liquid entering and exiting. Theseidealizations make the transient analysis manageable.
Abi l i t y t o…
apply the time-dependent mass and ener g y r ate bal-ances
