7.3 Application Example of Similitude: Variable Rotational Speed with a Pump
263
For hydraulic turbines, a power specific speed is defined by
with P shaft the power measured at the shaft and H m the manometric head. This form
of specific speed is commonly used, as flow rate determination with a hydraulic turbine is not easy. Rotational speed, head and shaft power are the externally measurable quantities. The power specific speed is, strictly speaking, not a dimensionless
group of flow quantities. The internal power should be used for that, as mechanical losses do not follow the similitude laws of flows. Since internal power is not
directly measurable and mechanical efficiency is extremely close to unity, shaft
power is used.
7.3 Application Example of Similitude: Variable
Rotational Speed with a Pump
We consider a pump application as sketched in Fig. 7.10.
The  energy  rise  between  the  pressure  side  (  p)  and  the  suction  side  (  s) of the
pump is
where h m (machine) is the height difference between the pressure and suction flanges. The required energy increase follows from the load of the pump. Work equations
for the suction and the discharge pipes are
The sum of both expressions makes
or
shaft
SP
5/ 4
m
P
,
( gH )
W
W
r
=
2
2
p
s
p
s
m
m
p
p v v
E
gh ,
2
D
r
−
−
=
+
+
2
a
s
s
s
irr ,s
p
p v
0 0
gh q ,
2
r
r
+ + =
+ +
+
2
p
p
a
p
irr ,p
p
v
p
0
0 gh q .
2
r
r
+ + =
+ +
+
2
2
p
p
s
s
s
p
irr ,sp
p
v
p
v
g( h h ) q ,
2 2
r
r
− + − =
+
+
m
geo
irr ,sp
E
gh
q .
D =
+