Modern Engineering Thermodynamics

s − s 0 = c ln T T 0
10.8 Flow Availability 333
Solution
First, draw a sketch of the system (Figure 10.11).
3.00 ft/s
T = 50.0°F
4.00 ft
Ground state:
T 0 = 70.0°F
p 0 = 14.7 psia
FIGURE 10.11
Example 10.6.
The unknown is the specific flow availability at the exit of a garden hose. The material is water, and the system is open.
The specific flow availability is defined by Eq. (10.16) as
a f = h − h 0 − T 0 ðs − s 0 Þ + V2
2g c
+ gZ
g c
The liquid water exiting the garden hose fits our definition of an incompressible fluid, so Eqs. (3.62) and (7.33) can be used
to compute
and
h − h 0 = cðT − T 0 Þ + vðp − p 0 Þ
Using the subscript w for the water, we can write the specific flow availability of the stream of water exiting the garden
hose as
ða f Þ w = c w ðT w − T 0 Þ + v w ðp w − p 0 Þ − c w T 0 ln T w
+ V2 w
+ gZ w
T 0 2g c g c
where T 0 = T air = 70.0°F and p 0 = p air = 14.7 psia. The liquid water is a slightly compressed liquid; however, the amount of
compression is only a few psia (p actual − p sat (50.0°F) = 14.7 − 0.1780 = 14.52 psia), and the effect of this small amount of
compression is negligible. Thus, for the specific volume v we use the value of saturated liquid at the actual temperature of
the water, or v = v sat (50.0°F) = 0.01602 ft 3 /lbm. Substituting in all the appropriate numerical values into the specific flow
availability equation, we get
a f = ð1:00 Btu/lbmÞð50:0 − 70:0RÞ + 0:01602 ft 3 /lbmÞð14:7 − 14:7 lbf/in 2 144 lbf/in 2
Þ
778:16 ft .lbf/Btu
− ð70:0 + 459:67 RÞ ln
50:0 + 459:67
ð3:00 ft/s 2 Þ 2
+
70:0 + 459:67 2ð32:174 lbm.ft/lbf .s 2 Þð778:16 ft .lbf/BtuÞ
ð32:174 ft/s 2 Þð4:00 ftÞ
+
ð32:174 lbm.ft/lbfgs 2 Þð778:16 ft .lbf/BtuÞ = 0:393Btu/lbm
Exercises
16. Determine the value of the flow availability in Example 10.6 when the garden hose is lying on the ground. Assume that
the other variables remain unchanged. Answer: (a f ) w = 0.388 Btu/lbm.
17. Suppose you put a nozzle on the end of the garden hose in Example 10.6 and increase the velocity of the water leaving the
hose from 3.00 ft/s to 15.0 ft/s. Determine the new flow availability, assuming all the other variables remain unchanged.
Answer: (a f ) w = 0.397 Btu/lbm.
18. While you are spraying the garden hose in Example 10.6, a weather front comes through and lowers the atmospheric
temperature from 70.0°F to50.0°F. Determine the new flow availability assuming all the other variables remain unchanged.
Answer: (a f ) w = 0.00500 Btu/lbm.