fluid_mechanics

430 Chapter 8 ■ Viscous Flow in Pipes
COMMENT Note that for this pressure drop, the amount due
to elevation change 1the hydrostatic effect2 is g1z 2 z 1 2 8.67 psi
and the amount due to the increase in kinetic energy is
r1V 2 2 V 2 122 2.07 psi.
(b) If the only losses included are the major losses, the head
loss is
From Table 8.1 the roughness for a 0.75-in.-diameter copper
pipe 1drawn tubing2 is e 0.000005 ft so that eD 8 10 5 .
With this eD and the calculated Reynolds number 1Re
45,0002, the value of f is obtained from the Moody chart as
f 0.0215. Note that the Colebrook equation 1Eq. 8.352 would
give the same value of f. Hence, with the total length of the pipe
as / 115 5 10 10 202 ft 60 ft and the elevation
and kinetic energy portions the same as for part 1a2, Eq. 1 gives
or
(Ans)
COMMENT Of this pressure drop, the amount due to pipe
friction is approximately 121.3 10.72 psi 10.6 psi.
(c)
or
If major and minor losses are included, Eq. 1 becomes
where the 21.3 psi contribution is due to elevation change, kinetic
energy change, and major losses [part 1b2], and the last term represents
the sum of all of the minor losses. The loss coefficients of
the components 1K L 1.5 for each elbow and K L 10 for the
wide-open globe valve2 are given in Table 8.2 1except for the loss
coefficient of the faucet, which is given in Fig. E8.8a as K L 22.
Thus,
or
p 1 gz 2 1 2 r1V 2 2 V 2 12 rf / D
11248 2992 lbft 2
h L f / D 2g
11.94 slugsft 3 60 ft
210.02152 a
0.0625 ft b 18.70 ft s2 2
2
11248 299 15152 lbft 2 3062 lbft 2
p 1 21.3 psi
p 1 gz 2 1 2 r1V 2 2 V 2 12 fg / D
p 1 21.3 psi a rK L V 2
a rK V 2
L
2 11.94 slugs 18.70
ft 3 ft22
2 310 411.52 24
2
1321 lbft 2
Note that we did not include an entrance or exit loss because points
112 and 122 are located within the fluid streams, not within an ata
rK V 2
L 9.17 psi
2
V 2 1
2g a rK V 2
L
2
V 1
2
V 2 1
2
2
(2)
(3)
taching reservoir where the kinetic energy is zero. Thus, by combining
Eqs. 2 and 3 we obtain the entire pressure drop as
p 1 121.3 9.172 psi 30.5 psi
(Ans)
This pressure drop calculated by including all losses should be the
most realistic answer of the three cases considered.
COMMENTS More detailed calculations will show that the
pressure distribution along the pipe is as illustrated in Fig. E8.8b
for cases 1a2 and 1c2—neglecting all losses or including all losses.
Note that not all of the pressure drop, p 1 p 2 , is a “pressure
loss.” The pressure change due to the elevation and velocity
changes is completely reversible. The portion due to the major
and minor losses is irreversible.
This flow can be illustrated in terms of the energy line and hydraulic
grade line concepts introduced in Section 3.7. As is shown
in Fig. E8.8c, for case 1a2 there are no losses and the energy line
1EL2 is horizontal, one velocity head 1V 2 2g2 above the hydraulic
grade line 1HGL2, which is one pressure head 1gz2 above the pipe
itself. For cases 1b2 or 1c2 the energy line is not horizontal. Each bit
of friction in the pipe or loss in a component reduces the available
H, elevation to energy line, ft
p, psi
F I G U R E E8.8b
80
60
40
20
30
20
10
30.5 psi
27.1 27.8
(a) No losses
(c) Including all
losses
Pressure
loss
20.2 21.0
18.5 19.3
10.7
Elevation
and
kinetic
energy
10.7
0
0 10 20 30 40 50 60
Slope due to pipe friction
Sharp drop due to component loss
Energy line including all
losses, case (c)
Energy line with no losses, case (a)
0 0 10 20 30 40 50 60
Distance along pipe from point (1), ft
F I G U R E E8.8c
11.7
12.4
Distance along pipe from point (1), ft
9.93
6.37
3.09
6.37
4.84
2.07
2.07 p 2 = 0
Location: (1) (3) (4) (5) (6) (7)(8) (2)