Brochure

P1
P2
Q [m
3
/h]
P [W]
3838
2. Performance curves
2.7 Power
The power curves show the energy transfer rate as a function of flow, see
figure 2.7. The power is given in Watt [W]. Distinction is made between
three kinds of power, see figure 2.8:
• Suppliedpowerfromexternalelectricitysourcetothemotorand 
controller (P
1
)
• Shaftpowertransferredfromthemotortotheshaft(P
2
)
• Hydraulicpowertransferredfromtheimpellertotheuid(P
hyd
)
The power consumption depends on the fluid density. The power curves
are generally based on a standard fluid with a density of 1000 kg/m
3
which
corresponds to water at 4°C. Hence, power measured on fluids with another
density must be converted.
In the data sheet, P
1
is normally stated for integrated products, while P
2
is
typically stated for pumps sold with a standard motor.
2.7.1 Speed
Flow, head and power consumption vary with the pump speed, see section 3.4.4.
Pump curves can only be compared if they are stated with the same speed. The
curves can be converted to the same speed by the formulas in section 3.4.4.
2.8 Hydraulic power
The hydraulic power P
hyd
is the power transferred from the pump to the
fluid. As seen from the following formula, the hydraulic power is calculated
based on flow, head and density:
[ ]
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
An independent curve for the hydraulic power is usually not shown in data
sheets but is part of the calculation of the pump eciency.
Figure 2.8: Power transfer in a pump unit.
Figure 2.7: P
1
and P
2
power curves.
P
1
P
2
P
hyd