Brochure

A
2
A
2
A
1
A
1
A
2
A
1
V
1
V
2
8686
5. Pump losses
5.3.2 Mixing loss at cross-section expansion
Velocity energy is transformed to static pressure energy at cross-section ex-
pansions in the pump, see the energy equation in formula (2.10). The conver-
sion is associated with a mixing loss.
The reason is that velocity dierences occur when the cross-section ex-
pands, see figure 5.7. The figure shows a diuser with a sudden expansion
beacuse all water particles no longer move at the same speed, friction occurs
between the molecules in the fluid which results in a diskharge head loss.
Even though the velocity profile after the cross-section expansion gradually
is evened out, see figure 5.7, a part of the velocity energy is turned into heat
energy instead of static pressure energy.
Mixing loss occurs at dierent places in the pump: At the outlet of the im-
peller where the fluid flows into the volute casing or return channel as well
as in the diuser.
When designing the hydraulic components, it is important to create small
and smooth cross-section expansions as possible.
Model
The loss at a cross-section expansion is a function of the dynamic head into
the component.
(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
V
1
= Fluid velocity into the component [m/s]
The pressure loss coecient ζ depends on the area relation between the com-
ponent’s inlet and outlet as well as how evenly the area expansion happens.
Figure 5.7: Mixing loss at cross-section
expansion shown for a sudden expansion.