Brochure

H [m]
10
8
12
6
4
2
0
0 1.0 1.5
2.0
Q [m
3
/h]
Water at 20
o
C
10.2 m
1 bar
998.2 kg /m
3
1 bar = 10.2 m
H [m]
50
40
30
20
10
0
0 10 20 30 40 50 60 70
Q [m
3
/h]
3434
2.4 Head
The dierent performance curves are introduced on the following pages.
A QH curve or pump curve shows the head (H) as a function of the flow (Q). The
flow (Q) is the rate of fluid going through the pump. The flow is generally stated
in cubic metre per hour [m
3
/h] but at insertion into formulas cubic metre per
second [m
3
/s] is used. Figure 2.5 shows a typical QH curve.
The QH curve for a given pump can be determined using the setup shown in
figure 2.6.
The pump is started and runs with constant speed. Q equals 0 and H reaches
its highest value when the valve is completely closed. The valve is gradually
opened and as Q increases H decreases. H is the height of the fluid column in the
open pipe after the pump. The QH curve is a series of coherent values of Q and H
represented by the curve shown in figure 2.5.
In most cases the dierential pressure across the pump Dp
tot
is measured and
the head H is calculated by the following formula:
[ ]
Pa
ppp
dyn
(2.1)
(2.2)
(2.5)
(2.6)
(2.7)
stattot
+ =
[ ]
PaV
2
1
2
1
2
1
p
2
dyn
⋅ ⋅ = ρ
[ ]
Papppp
geodynstattot
∆ + ∆ + ∆
p∆
p∆
∆ =
[ ]
Papp
stat, instat, outstat
− =
[ ]
PaVV
2
in
2
outdyn
⋅⋅−⋅ ⋅ = ρ ρ
(2.8)
2
1
[
]
Pa
D
1
D
1
4
Q
p
4
in
4
out
2
dyn








− ⋅








⋅ ⋅ =
π
ρΔ
(2.9)
[ ]
Pagzp
geo
⋅ ⋅ ∆ = ∆ ρ
(2.10)
(2.3)
(2.4)
(2.11)
(2.13)
(2.14)
(2.12)






= ⋅ + +
2
22
s
m
Constantzg
2
V
p
ρ
[ ]
Pappp
barrelabs
+ =
[ ]
m
g
p
H
tot
⋅
=
ρ
Δ
[ ]
WQpQgHP
tothyd
⋅ ∆ = ⋅⋅ ⋅ = ρ
[ ]
⋅ 100 %
[ ]
⋅ 100 %
[ ]
⋅ 100 %
=
2
hyd
hyd
P
P
η
=
1
hyd
tot
P
P
η
[ ]
WP
2
P
1
P
hyd
> >
(2.15)
(2.16)
(2.17)
(2.17a)
(2.18)
(2.19)
⋅⋅=
hydmotorcontroltot
ηηηη
( )
[ ]
m
g
pp
NPSH
vapourabs,tot,in
A
⋅
−
=
ρ
[ ]
mNPSH = NPSH
3%
NPSH
RA
0.5 +>
NPSH
A
>
[ ]
mNPSH = NPSH
3%
or
R
S
A
.
[ ]
m
g
p
H
g
p
NPSH
p
vapour
suction pipe
,loss
geo
bar
A
⋅
∆
− −
+
⋅ ⋅
=
ρ
ρ
9.81m
23
A
Pa 7375 3500 Pa
m 3
sm992.2kg
101300 Pa
NPSH −−−
⋅ 9.81m
23
sm992.2kg ⋅ 9.81m
23
sm992.2kg ⋅
=
9.81m
23
A
47400 Pa
1 m 3 m
sm973 kg
-27900 Pa + 101000 Pa
+ 500 Pa
NPSH − −+
⋅ 9.81m
23
sm973 kg ⋅
=
6.3mNPSH
A
=
4.7mNPSH
A
=
[ ]
m
g
p
HH
g
pp
NPSH
vapour
loss, pipegeo
barstat,in
A
⋅
−−+
⋅
+ +
=
ρ
ρ
[
( )
0.5
.
ρ
.
V 1
2
The QH curve will ideally be exactly the same if the test in figure 2.6 is made with
a fluid having a density dierent from water. Hence, a QH curve is independent
of the pumped fluid. It can be explained based on the theory in chapter 4 where it
is proven that Q and H depend on the geometry and speed but not on the density
of the pumped fluid.
The pressure increase across a pump can also be measured in meter water column
[mWC]. Meter water column is a pressure unit which must not be confused with
the head in [m]. As seen in the table of physical properties of water, the change
in density is significant at higher temperatures. Thus, conversion from pressure
to head is essential.
2. Performance curves
Figure 2.5: A typical QH curve for a centrifugal
pump; a small flow gives a high head and a
large flow gives a low head.
Figure 2.6: The QH curve can be determined
in an installation with an open pibe after
the pump. H is exactly the height of the fluid
column in the open pipe. measured from
inlet level.