fluid_mechanics

234 Chapter 5 ■ Finite Control Volume Analysis
H out
h L
h s
h s + h L
h s
h s – h L
H in
h L = 0, h s = 0
h L > 0, h s = 0
h L = 0, h s > 0
h L > 0, h s > 0
h L = 0,
h s < 0
h L > 0,
h s < 0
F I G U R E 5.8
fluid flows.
Total-head change in
Some important possible values of H out in comparison to H in are shown in Fig. 5.8. Note that h L
(head loss) always reduces the value of H out , except in the ideal case when it is zero. Note also that
h L lessens the effect of shaft work that can be extracted from a fluid. When h L 0 (ideal condition)
the shaft work head, h s , and the change in total head are the same. This head change is sometimes
called “ideal head change.” The corresponding ideal shaft work head is the minimum required
to achieve a desired effect. For work out, it is the maximum possible. Designers usually strive to
minimize loss. In Chapter 12 we learn of one instance when minimum loss is sacrificed for survivability
of fish coursing through a turbine rotor.
E XAMPLE 5.25
Energy—Head Loss and Power Loss
GIVEN The pump shown in Fig. E5.25a adds 10 horsepower
to the water as it pumps water from the lower lake to the upper
lake. The elevation difference between the lake surfaces is 30 ft
and the head loss is 15 ft.
FIND Determine
(a) the flowrate and
(b) the power loss associated with this flow.
SOLUTION
Section (2)
Control volume
Flow
Pump
Section (1)
30 ft
(a)
The energy equation (Eq. 5.84) for this flow is
where points 2 and 1 (corresponding to “out” and “in” in Eq.
5.84) are located on the lake surfaces. Thus, p 2 p 1 0 and
V 2 V 1 0 so that Eq. 1 becomes
h s h L z 2 z 1
(2)
where z 2 30 ft, z 1 0, and h L 15 ft. The pump head is obtained
from Eq. 5.85 as
where
h s
p 2
g V 2 2
2g z 2 p 1
g V 2 1
2g z 1 h s h L
h s W # shaft net in Q
110 hp21550 ft#lbshp2162.4 lbft 3 2 Q
88.1Q
is in ft when Q is in ft 3 /s.
(1)
or
Flow
F I G U R E E5.25a
Hence, from Eq. 2,
88.1Q 15 ft 30 ft
Q 1.96 ft 3 /s
(Ans)
COMMENT Note that in this example the purpose of the
pump is to lift the water (a 30-ft head) and overcome the head loss
(a 15-ft head); it does not, overall, alter the water’s pressure or
velocity.