Brochure
Q
design
Q
H
loss, incidence
k
2
e
9191
Incidence loss is alternatively modelled as a parabola with minimum at the
best eciency point. The incidence loss increases quadratically with the dif-
ference between the design flow and the actual flow, see figure 5.13.
(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
Q
design
= Design flow [m
3
/s]
k
1
= Constant [s
2
/m
5
]
k
2
= Constant [m]
5.3.6 Disk friction
Disk friction is the increased power consumption which occurs on the shroud
and hub of the impeller because it rotates in a fluid-filled pump casing. The
fluid in the cavity between impeller and pump casing starts to rotate and
creates a primary vortex, see section 1.2.5. The rotation velocity equals the
impeller’s at the surface of the impeller, while it is zero at the surface of
the pump casing. The average velocity of the primary vortex is therefore as-
sumed to be equal to one half of the rotational velocity.
The centrifugal force creates a secondary vortex movement because of the
dierence in rotation velocity between the fluid at the surfaces of the impel-
ler and the fluid at the pump casing, see figure 5.14. The secondary vortex in-
creases the disk friction because it transfers energy from the impeller surface
to the surface of the pump casing.
The size of the disk friction depends primarily on the speed, the impeller di-
ameter as well as the dimensions of the pump housing in particular the dis-
tance between impeller and pump casing. The impeller and pump housing
surface roughness has, furthermore, a decisive importance for the size of the
disk friction. The disk friction is also increased if there are rises or dents on
the outer surface of the impeller e.g. balancing blocks or balancing holes.
Figure 5.13: Incidence loss as function of
the flow.
Figure 5.14: Disk friction on impeller.
Secondary
vortex