ε/D = 6.7 105.
on the basis of pipe diameter, fluid speed, and
roughness:
Using the relative roughness and Reynolds num-
Pipe diameter: 0.154 m (6-in. Schedule 40 pipe)
ber to find the Darcy friction factor from a Moody
Pipe cross-sectional area: 0.02 m2
friction factor chart, we find that
v = fluid speed = Q/A
(A12)
f ≈ 0.014.
Q = 0.106 m3/s (system requirement)
Plugging these values into eq A14 results in a
∴ v = 0.106/0.02 = 5.7 m/s.
head of 0.85 m. Finally, the vapor pressure head at
16C is 0.18 m. Filling in the values derived for eq
Entrance loss is calculated on the basis of fluid
velocity and an entrance loss coefficient, Ke. In
A11, we get
this case, Ke is 0.5, based on a flush, square-edged
entrance (Lindeburg 1984, p. 324).
NPSHA = 10.33 + 0.49 0.85 0.18
v2
NPSHA = 9.8 m (32.2 ft).
he = Ke
(A13)
2 gc
Using a set of pump curves from the manufactur-
(opening is 1.56 times larger than hose).
er (not shown), a net positive suction head re-
quired of approximately 4.6 m is necessary at 106
he ≈ 0.3 m.
L/s (15 ft @ 1685 gpm). For higher flow rates,
which occur with lower outlet line resistances
Equivalent lengths of the various components are
(shorter lines), the NPSHA drops quickly. At 142
taken from standard tables:
L/s, the NPSHA becomes 7.3 m, and at 190 L/s,
which we were approaching with only 76 m of
Short 90 (eye inlet): 2.75 m
hose attached to the dredge, we are at or slightly
Intake hose (6 in.): 2.44 m
above the NPSHR. However, for our operations,
the 356-mm (14-in.) impeller operating near 1500
Entrance loss (see above): 0.3 m.
rpm should work well.
Total equivalent length is therefore 5.5 m. To cal-
With the slurry pump hydraulic system pres-
culate the suction friction loss, the Darcy equa-
sure relief valve set to 33 MPa (4800 psi), the
tion is used:
pump tests were rerun. The data, as shown in
Table A2, are as expected from the calculations
f (L)(v)2
above.
hf =
.
(A14)
2Dgc
Table A2. Final pump performance
Using cold, clear water,
test results.
ν = 1.11 cS (≈ 16C).
Control
Slurry pump
Outlet
setting
Outlet
Hyd.
flow
Plugging into the formula for the Reynolds num-
(%)
(kPa)
(MPa)
(visual)
ber,
100
108.9
33
Full pipe
Dv
95
108.9
33
Full pipe
= e
(A15)
NRe
ν
90
108.9
33
Full pipe
85
108.9
33
Full pipe
results in a Reynolds number of
80
108.9
33
Full pipe
75
108.9
33
Full pipe
(0.15)(5.7)
70
108.9
33
Full pipe
NRe =
1.11 10-6
65
104.8
31
Full pipe
60
95.1
27
Near full pipe
NRe = 7.8 105
55
85.5
23
Near full pipe
50
75.8
20
Near full pipe
7/8 pipe
45
64.1
6
which is in the turbulent region. To determine the
3/4 pipe
40
54.5
12
Darcy friction factor f, the relative roughness
ratio, ε/D, must be estimated. Using 0.15 m for
5/8 pipe
35
47.6
10
1/ to 1/ pipe
30
42.7
6.2
the hose diameter and a specific roughness ε = 1
3
2
25
37.9
4.8
Trickle
105 (Lindeburg 1984),
24
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