Brochure
9292
5. Pump losses
Model
Pfleiderer and Petermann (1990, p. 322) use the following model to deter-
mine the increased power consumption caused by disk friction:
(5.1)
(5.2)
(5.3)
(5.4)
(5.5)
(5.6)
(5.7)
(5.8)
(5.9)
(5.10)
(5.11)
(5.12)
(5.13)
(5.14)
(5.15)
constantPPP
loss, shaft sealloss, bearingloss, mechanical
=+=
g2
V
HH
2
dyn, inloss, friktion
⋅ ζ = ⋅ ζ =
g2D
LV
fH
h
2
loss, pipe
=
O
A4
D
h
=
ν
=
h
VD
Re
Re
64
f
laminar
=
0.0047
32mm
0.15mm
k/D Relative roughness:
110500
sm101
0.032m3.45m s
VD
Re
Reynolds number:
sm3.45
m0.032
4
sm(10/3600)
A
Q
VMean velocity:
h
26
h
22
3
==
=
⋅
⋅
=
ν
=
=
π
==
−
sm
sm
gD
LV
f
H
h
loss, pipe
1.2 m
9.8120.032m
)3.45(2m
0.031
2
Pipe loss:
2
2
2
=
⋅⋅
⋅
==
g2
V
HH
2
1
dyn,1loss, expansion
⋅ ζ
=
⋅ ζ =
2
2
1
A
A
1
− = ζ
g2
V
A
A
1H
2
0
2
2
0
loss, contraction
⋅
− =
g2
V
HH
2
2
dyn,2
loss, contraction
⋅ζ=⋅ζ=
g2
ww
g2
w
H
2
1, kanal1
2
s
loss, incidence
⋅
−
ϕ=
⋅
ϕ=
2
2
design1
loss, incidence
k)QQ(kH +−⋅=
m
22
6
4
22
3
2
loss, disk
DU
102
103.7k
)e5D(DUkρ
P
⋅ ν
⋅ =
+ =
−
( ) ( )
( )
( )
B
5
2
3
A
5
2
3
B
loss, disk
A
loss, disk
Dn
Dn
PP =
(5.16)
(5.17)
(5.18)
(5.19)
leakageimpeller
QQQ +=
( )
g8
DD
HH
2
gap
2
2
2
stat, impellerstat, gap
−
ω − =
g2
V
1.0
g2
V
s
L
f
g2
V
0.5H
222
stat, gap
++=
gap
leakage
stat, gap
VA
Q
1.5
s
L
f
2gH
V
=
+
=
where
D
2
= Impeller diameter [m]
e = Axial distance to wall at the periphery of the impeller [m], see figure
5.14
U
2
= Peripheral velocity [m/s]
n = Kinematic viscosity [m
2
/s], n =10
-6
[m
2
/s] for water at 20°C.
k = Emperical value
m = Exponent equals 1/6 for smooth surfaces and between 1/7 to 1/9
for rough surfaces
If changes are made to the design of the impeller, calculated disk friction
P
loss,disk,A
can be scaled to estimate the disk friction P
loss,disk,B
at another impel-
ler diameter or speed:
(5.1)
(5.2)
(5.3)
(5.4)
(5.5)
(5.6)
(5.7)
(5.8)
(5.9)
(5.10)
(5.11)
(5.12)
(5.13)
(5.14)
(5.15)
constantPPP
loss, shaft sealloss, bearingloss, mechanical
=+=
g2
V
HH
2
dyn, inloss, friktion
⋅ ζ = ⋅ ζ =
g2D
LV
fH
h
2
loss, pipe
=
O
A4
D
h
=
ν
=
h
VD
Re
Re
64
f
laminar
=
0.0047
32mm
0.15mm
k/D Relative roughness:
110500
sm101
0.032m3.45m s
VD
Re
Reynolds number:
sm3.45
m0.032
4
sm(10/3600)
A
Q
VMean velocity:
h
26
h
22
3
==
=
⋅
⋅
=
ν
=
=
π
==
−
sm
sm
gD
LV
f
H
h
loss, pipe
1.2 m
9.8120.032m
)3.45(2m
0.031
2
Pipe loss:
2
2
2
=
⋅⋅
⋅
==
g2
V
HH
2
1
dyn,1loss, expansion
⋅ ζ
=
⋅ ζ =
2
2
1
A
A
1
− = ζ
g2
V
A
A
1H
2
0
2
2
0
loss, contraction
⋅
− =
g2
V
HH
2
2
dyn,2
loss, contraction
⋅ζ=⋅ζ=
g2
ww
g2
w
H
2
1, kanal1
2
s
loss, incidence
⋅
−
ϕ=
⋅
ϕ=
2
2
design1
loss, incidence
k)QQ(kH +−⋅=
m
22
6
4
22
3
2
loss, disk
DU
102
103.7k
)e5D(DUkρ
P
⋅ ν
⋅ =
+ =
−
( ) ( )
( )
( )
B
5
2
3
A
5
2
3
B
loss, disk
A
loss, disk
Dn
Dn
PP =
(5.16)
(5.17)
(5.18)
(5.19)
leakageimpeller
QQQ +=
( )
g8
DD
HH
2
gap
2
2
2
stat, impellerstat, gap
−
ω − =
g2
V
1.0
g2
V
s
L
f
g2
V
0.5H
222
stat, gap
++=
gap
leakage
stat, gap
VA
Q
1.5
s
L
f
2gH
V
=
+
=
The scaling equation can only be used for relative small design changes.
5.3.7 Leakage
Leakage loss occurs because of smaller circulation through gaps between
the rotating and fixed parts of the pump. Leakage loss results in a loss in ef-
ficiency because the flow in the impeller is increased compared to the flow
through the entire pump: