Example Problem – Matching a Pump to a Piping System
Given
: Water (
ρ
= 1000 kg/m
3
,
µ
= 1.00
×
10
3
kg/m
⋅
s) is pumped from one large reservoir to another
large reservoir that is at a higher elevation. The free surfaces of both reservoirs are exposed to
atmospheric pressure, as sketched. The dimensions and minor loss coefficients are provided in the
figure. The pipe is 2.2 cm I.D. cast iron pipe. The total pipe length is 150.0 m. The entrance and exit
are sharp. There are three regular threaded 90degree elbows, and one fully open threaded globe valve.
The pump’s performance (supply curve) is approximated by the expression
2
available
pump, u supply
0
H
h
H
=
=
−
±
aV
where shutoff head
H
0
= 20.0 m of water column, coefficient
a
= 0.072 m/Lpm
2
, available pump head
H
available
is in units of meters of water column, and volume flow rate
V
±
is in units of liters per minute
(Lpm).
Valve
z
1
Reservoir
z
2
Pump
1
z
2
–
z
1
V
1
≈
0
Reservoir
2
V
2
≈
0
D
z
2
–
z
1
=
8.0 m (elevation difference)
D
=
2.2 cm (pipe diameter)
K
L
, Entrance
=
0.50 (sharp pipe entrance)
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 Fall '05
 CIMBALA
 volume flow rate, total pipe length

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