Modern Engineering Thermodynamics

332 CHAPTER 10: Availability Analysis
and the associated availability transport rate for the incremental mass dm is
ðdA/dtÞ mass
flow
= _A mass
flow
= aðdm/dtÞ = a _m = ½u − u 0 + p 0 ðv − v 0 Þ − T 0 ðs − s 0 Þ + V 2 /2g c + gZ/g c Šð _m Þ
Figure 6.1 in Chapter 6 indicates that the amount of incremental “flow work” associated with moving the mass
dm across the system boundary is
and the corresponding flow work rate is
ðdWÞ mass
flow
dW
mass
dt flow
= pvðdmÞ
= pv dm
= _mpv
dt
If we assume that the incremental mass dm does not undergo any heat transfer or change in kinetic or potential
energy as it moves through the incremental distance dΡ required to cross the system boundary, then Eq. (10.11)
gives the incremental work mode availability transport as
ðdWÞ mass − p 0 ðdVÞ = ðdWÞ mass − p 0 ðvdmÞ
flow
flow
where dV is the volume of the incremental mass dm. Then,
ðdAÞ mass
flow
and the work mode net availability transport rate is
= a W dm = pvdm − p 0 vdm = vðp − p 0 Þdm
ð _AÞ mass
flow
= a W _m = vðp − p 0 Þ _m
Combining these equations with the nonwork mass flow availability transport gives the total flow availability
transport, a f dm, as
or
or
adm + a W dm = ða + a W Þdm = a f dm
a f = a + a w = u − u 0 + p 0 ðv − v 0 Þ − T 0 ðs − s 0 Þ + pv − pv 0 + V 2
+ gZ
2g c g c
= ðu + pvÞ − ðu 0 + p 0 v 0 Þ − T 0 ðs − s 0 Þ + V2 + gZ
2g c g c
The specific flow availability of a flow stream
a f = h − h 0 − T 0 ðs − s 0 Þ + V2
2g c
+ gZ
g c
(10.20)
where a f is the specific flow availability of the mass crossing the system boundary, and the total flow availability of
the mass crossing the system boundary is
_A f = _mða f Þ = _m h− h 0 − T 0 ðs − s 0 Þ + V2 + gZ
2g c g c
The concept of flow availability is illustrated in the following example.
EXAMPLE 10.6
Compute the specific flow availability at the exit of a garden hose used to fill a child’s wading pool. The hose is held
horizontally 4.00 ft above the ground and the water exits the hose at 3.00 ft/s at 50.0°F. Take the local environment (ground
state) to be atmospheric temperature and pressure of 70.0°F and 14.7 psia.