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Chapter 4
Energy Transfer by Heat, Work, and Mass
Flow Work and Energy Transfer by Mass
457C
Energy can be transferred to or from a control volume as heat, various forms of work, and by mass.
458C
Flow energy or flow work is the energy needed to push a fluid into or out of a control volume.
Fluids at rest do not possess any flow energy.
459C
Flowing fluids possess flow energy in addition to the forms of energy a fluid at rest possesses. The
total energy of a fluid at rest consists of internal, kinetic, and potential energies. The total energy of a
flowing fluid consists of internal, kinetic, potential, and flow energies.
460E
Steam is leaving a pressure cooker at a specified pressure. The velocity, flow rate, the total and flow
energies, and the rate of energy transfer by mass are to be determined.
Assumptions
1
The flow is steady, and the initial startup period is disregarded.
2
The kinetic and potential
energies are negligible, and thus they are not considered.
3
Saturation conditions exist within the cooker at
all times so that steam leaves the cooker as a saturated vapor at 30 psia.
Properties
The properties of saturated liquid water and water vapor at 30 psia are
v
f
= 0.017004 ft
3
/lbm,
v
g
= 13.748 ft
3
/lbm,
u
g
= 1088.0 Btu/lbm, and
h
g
= 1164.3 Btu/lbm (Table A5E).
Analysis
(
a
) Saturation conditions exist in a pressure cooker at all times after the steady operating
conditions are established. Therefore, the liquid has the properties of saturated liquid and the exiting steam
has the properties of saturated vapor at the operating pressure. The amount of liquid that has evaporated,
the mass flow rate of the exiting steam, and the exit velocity are
ft/s
15.4
V
lbm/s
10
1.165
3

=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
×
=
=
=
×
=
=
=
Δ
=
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
Δ
=
2
2
2
3
3

3
3
liquid
ft
1
in
144
in
0.15
/lbm)
ft
748
lbm/s)(13.
10
(1.165
lbm/min
0699
.
0
min
45
lbm
145
.
3
lbm
145
.
3
gal
1
ft
13368
.
0
/lbm
ft
0.017004
gal
0.4
c
g
c
g
f
A
v
m
A
m
t
m
m
v
V
m
&
&
&
ρ
H
2
O
Sat. vapor
P = 30 psia
Q
(
b
) Noting that
h
=
u
+
Pv
and that the kinetic and potential energies are disregarded, the flow and total
energies of the exiting steam are
Btu/lbm
1164.3
Btu/lbm
76.3
=
≅
+
+
=
=
−
=
−
=
=
h
pe
ke
h
u
h
Pv
e
θ
0
.
1088
3
.
1164
flow
Note that the kinetic energy in this case is ke =
V
2
/2 = (15.4 ft/s)
2
= 237 ft
2
/s
2
= 0.0095 Btu/lbm, which is
very small compared to enthalpy.
(
c
) The rate at which energy is leaving the cooker by mass is simply the product of the mass flow rate and
the total energy of the exiting steam per unit mass,
Btu/s
1.356
=
×
=
=
−
Btu/lbm)
4.3
lbm/s)(116
10
165
.
1
(
3
mass
m
E
&
&
Discussion
The numerical value of the energy leaving the cooker with steam alone does not mean much
since this value depends on the reference point selected for enthalpy (it could even be negative). The
significant quantity is the difference between the enthalpies of the exiting vapor and the liquid inside
(which is
h
fg
) since it relates directly to the amount of energy supplied to the cooker.
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 Spring '07
 Dr.Kinne

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