Brochure

103103
S'
1
H'
1
H
1
H
2
H
z'
1
H'
2
z
2
S
1
S
2
S'
2
S'
1
S
1
S
2
S'
2
z
1
z'
2
z'
1
z'
M1
z'
M2
z
2
z
1
z'
2
z'
M1
z'
M2
p
M1
p
M2
Total head
Static head
p'
1
r
.
g
U'
1
2
2
.
g
U
1
2
2
.
g
p
1
r
.
g
U'
2
2
2
.
g
U
2
2
2
.
g
p
2
r
.
g
p'
2
r
.
g
H
loss,friction,1
H
loss,friction,2
Figure 6.8: General draft of a
pump test.
6.2.5 General calculation of head
In practise a pump test is not always made on a hori-
zontal pipe, see figure 6.7. This results in a dierence in
height between the centers of the pump in- and outlet,
z’
1
and z’
2
, and the centers of the inlet and outlet flanges,
z
1
and z
2
respectively. The manometer can, furthermore,
be placed with a dierence in height compared to the
pipe centre. These dierences in height must be taken
into consideration in the calculation of head.
Because the manometer only measures the static pres-
sure, the dynamic pressure must also be taken into ac-
count. The dynamic pressure depends on the pipe diam-
eter and can be dierent on each side of the pump.
Figure 6.8 illustrates the basic version of a pump test in
a pipe. The total head which is defined by the pressures
p
1
and p
2
and the velocities U
1
and U
2
in the inlet and
outlet flanges S
1
and S
2
can be calculated by means of
the following equation:
(6.1)
(6.2)
(6.3)
(6.4)
(6.5)
12
HHH − =
( ) ( )
12
''
loss, friction,2 loss, friction,1
HHHHH − − +=
Dynamic pressureStatic pressure
Geodetic pressure
g
UU
g
pp
zzH
⋅
−
+
⋅
−
+ − =
2
2
1
2
212
12
ρ






−
⋅
+








+
⋅
+
−






+
⋅
+








+
⋅
+ =
2
1
1
1
1
2
2
2
2
2
2
'
'
'
'
2
'
'
'
'
loss, friction,1 M
M
loss, friction, 2 M
M
H
g
U
z
g
p
z
H
g
U
z
g
p
zH
ρ
ρ
g
p
Hz
g
Vpp
NPSH
vapour
loss, friction, geo
barstat,in
A
⋅
− − +
⋅
⋅ ⋅ + +
=
ρρ
ρ
2
1
5.0
Using the measured sizes in S’
1
and S’
2
, the general
expression for the total head is:
(6.1)
(6.2)
(6.3)
(6.4)
(6.5)
12
HHH − =
( ) ( )
12
''
loss, friction,2 loss, friction,1
HHHHH − − +=
Dynamic pressureStatic pressure
Geodetic pressure
g
UU
g
pp
zzH
⋅
−
+
⋅
−
+ − =
2
2
1
2
212
12
ρ






−
⋅
+








+
⋅
+
−






+
⋅
+








+
⋅
+ =
2
1
1
1
1
2
2
2
2
2
2
'
'
'
'
2
'
'
'
'
loss, friction,1 M
M
loss, friction, 2 M
M
H
g
U
z
g
p
z
H
g
U
z
g
p
zH
ρ
ρ
g
p
Hz
g
Vpp
NPSH
vapour
loss, friction, geo
barstat,in
A
⋅
− − +
⋅
⋅ ⋅ + +
=
ρρ
ρ
2
1
5.0
Figure 6.7: Pump test where the pipes
are at an angle compared to horizontal.
S'
1
H'
1
H
1
H
2
H
z'
1
H'
2
z
2
S
1
S
2
S'
2
S'
1
S
1
S
2
S'
2
z
1
z'
2
z'
1
z'
M1
z'
M2
z
2
z
1
z'
2
z'
M1
z'
M2
p
M1
p
M2
Total head
Static head
p'
1
r
.
g
U'
1
2
2
.
g
U
1
2
2
.
g
p
1
r
.
g
U'
2
2
2
.
g
U
2
2
2
.
g
p
2
r
.
g
p'
2
r
.
g
H
loss,friction,1
H
loss,friction,2