Modern Engineering Thermodynamics

170 CHAPTER 6: First Law Open System Applications
EXAMPLE 6.1
Determine the mass flow energy transport rate of steam at 100. psia, 500.°F leaving a system through a 6.00-inch inside diameter
pipe at a velocity of 300. ft/s at a height of 15.0 ft above the floor (the zero height potential).
Solution
First, draw a sketch of the system (Figure 6.2).
6.00 inch ID pipe with
steam at 100. psia
and 500.°F
15.0 ft
300. ft/s
FIGURE 6.2
Example 6.1.
This is an open system, and the unknown is _E mass : The material is steam.
flow
From the superheated steam table, Table C.3a in Thermodynamic Tables to accompany Modern Engineering Thermodynamics, we
find that, at 100. psia and 500.°F,
v = 5:587 ft 3 /lbm
h = 1279:1 Btu/lbm
Now, since ρ =1/v, we can find _m from Eq. (6.1):
Then,
_m = ρAV = AV v
2
π 3 12 ft
2
ð300: ft/sÞ
=
5:587 ft 3 = 10:5 lbm/s
/lbm
and
ke = V2
2g c
=
ð300:Þ 2 ft 2 /s 2
2 32:174 lbm = 1398
.ft
ft .lbf
lbm
lbf .s 2
= 1398 ft
.lbf 1 Btu
lbm 778:16 ft.lbf
= 1:80 Btu
lbm
pe = gZ
g c
In this problem, we have only one flow stream, so
= ð32:174 ft/s2 Þð15:0ftÞ
32:174 lbm .ft
lbf .s 2
= 15:0 ft .lbf
lbm
_E mass
flow
1 Btu
778:16 ft.lbf
= − ½ _m ðh + ke + peÞŠ out
= 15:0 ft .lbf
lbm
= 0:019 Btu/lbm
= − ð10:5 lbm/sÞ½ð1279:1 + 1:80 + 0:019Þ Btu/lbmŠ
= − 1:35 × 10 4 Btu/s
Exercises
1. Determine the percentage contribution to the mass flow energy transport rate in Example 6.1 of each of the following
terms: (a) enthalpy, (b) kinetic energy, and (c) potential energy. Answers: (a) 99.86%, (b) 0.14%, and (c) 0.0015%.
2. Determine the percent error incurred in the answer to Example 6.1 if the kinetic and potential energy terms are
neglected. Answer: Percent error = 0.142%.
3. Suppose the fluid leaving the system through the 6.00-inch pipe in Example 6.1 were saturated liquid water at 50.0°F,
and determine the percentage error incurred in neglecting the kinetic and potential energies of the flow stream. Answer:
Percent error = 9.14%.