7.2 Characteristic Numbers of Turbomachines
257
Generally, the notions specific speed, specific diameter, speed number and diameter
number are applied as defined here.
We further note that
e
m
D / 2
u
,
V
( 2 E )
W
s d
l
D
=
= =
with V e being an energy reference velocity. The ratio l is called speed ratio. This
notion has already been used in the foregoing chapter.
The foregoing expression is also
(7.8)
This expression demonstrates again that, if desirable, speed ratio or head factor may
be used as a shape parameter, instead of specific speed. Speed ratio (see Chap. 6) or
work coefficient (see Chap. 3) are sometimes more visual.
Older technical literature concerning pumps and hydraulic turbines often uses a
dimensional form or specific speed, mostly noted as n s or n q , defined by
where the units of n, Q and H m are rpm, m
3
/s and m. This number is not dimensionless and proportional to s
Ω according to [ ]
[ ].
s
s
n
53 W
≈
7.2.3 Relation Between Characteristic Numbers
and Machine Shape
In the foregoing sections we reasoned in an abstract way that the numbers Φ*, Ψ*,
Ω s , D s and λ characterise the shape of a machine. We reason now more concretely by
means of the specific speed (7.6). The mechanical energy change
m
E
∆
is, through
the internal efficiency, linked to the rotor work
2 2u
1 1u
W u v
u v .
D =
−
We now consider a given machine, namely a pump, the meridional section of which is rendered
by the full lines in Fig. 7.3. This machine has a certain specific speed. The specific
speed may be increased in different ways. A first way is keeping the rotational speed
constant, keeping the velocity triangles constant and increasing the flow rate. In this
case, the mean inner and outer diameters of the rotor stay the same. A higher flow
rate with the same velocity components requires a larger rotor width. This may result in the dashed form in Fig. 7.3. A second way is keeping the flow rate constant,
keeping the velocity triangles constant and increasing the rotational speed Ω. The
mean inner and outer diameters of the rotor then must decrease. The corresponding
1 4
m
s
r
D( 2 E )
D
1.054 D .
D'
2 Q
p
D
d =
=
≈
s s
m
D
1
D
2 2
.
E
W
W
l
D
Y
=
=
=
n
n Q
H
s
m
= 3 4
/
,
257
Generally, the notions specific speed, specific diameter, speed number and diameter
number are applied as defined here.
We further note that
e
m
D / 2
u
,
V
( 2 E )
W
s d
l
D
=
= =
with V e being an energy reference velocity. The ratio l is called speed ratio. This
notion has already been used in the foregoing chapter.
The foregoing expression is also
(7.8)
This expression demonstrates again that, if desirable, speed ratio or head factor may
be used as a shape parameter, instead of specific speed. Speed ratio (see Chap. 6) or
work coefficient (see Chap. 3) are sometimes more visual.
Older technical literature concerning pumps and hydraulic turbines often uses a
dimensional form or specific speed, mostly noted as n s or n q , defined by
where the units of n, Q and H m are rpm, m
3
/s and m. This number is not dimensionless and proportional to s
Ω according to [ ]
[ ].
s
s
n
53 W
≈
7.2.3 Relation Between Characteristic Numbers
and Machine Shape
In the foregoing sections we reasoned in an abstract way that the numbers Φ*, Ψ*,
Ω s , D s and λ characterise the shape of a machine. We reason now more concretely by
means of the specific speed (7.6). The mechanical energy change
m
E
∆
is, through
the internal efficiency, linked to the rotor work
2 2u
1 1u
W u v
u v .
D =
−
We now consider a given machine, namely a pump, the meridional section of which is rendered
by the full lines in Fig. 7.3. This machine has a certain specific speed. The specific
speed may be increased in different ways. A first way is keeping the rotational speed
constant, keeping the velocity triangles constant and increasing the flow rate. In this
case, the mean inner and outer diameters of the rotor stay the same. A higher flow
rate with the same velocity components requires a larger rotor width. This may result in the dashed form in Fig. 7.3. A second way is keeping the flow rate constant,
keeping the velocity triangles constant and increasing the rotational speed Ω. The
mean inner and outer diameters of the rotor then must decrease. The corresponding
1 4
m
s
r
D( 2 E )
D
1.054 D .
D'
2 Q
p
D
d =
=
≈
s s
m
D
1
D
2 2
.
E
W
W
l
D
Y
=
=
=
n
n Q
H
s
m
= 3 4
/
,