Power Plant Engineering

2. Specific speed. The equation indicates that a low specific speed machine such as impulse
turbine is required when the available head is high for the given speed and power output. On the other
hand, propeller turbines with high specific speed are required for low-heads.
The specific speed can be calculated using the equations and if the available head is known. The
specific speed versus head are shown in Fig. 11.29 for different turbines.
It is obvious from Fig. 11.29 that there is a considerable latitude in the specific speed of runners
which can be used for given conditions of head and power provided that the height of the runner above
tailrace level is such as to avoid the danger of cavitation as discussed earlier.
In all modern power plants, it is common practice to select a high specific speed runner because
it is more economical as the size of the turbo-generator as well as that of power house will be smaller.
High specific speed is essential when the available head is low and power output is high because
otherwise the rotational speed will be very low and it will increase the cost of turbo-generator and the
power house as the sizes of turbine, generator and power house required at low speed will be large. On
the other hand, there is no need of choosing high specific speed runner when the available head is
sufficiently large because even with low specific speed, high rotational speeds can be attained.
Now it has been shown with the above discussion that if the speed and power under a given head
are fixed (N
s
is fixed), the type of the runner required is also fixed.
2000
1500
1000
500
100
50
20
10
5
0
100
200
300
400
500
600
700
800
Head i
n m
et
er
s
Specific Speed N
S
4 Nozzles
(Impulse)
Fra
ns
is
Kapla
n Turb
ine 
 Fig. 11.29
In practice it may be possible to vary the specific speed through a considerable range of values.
The. speed and power required may be varied for a single runner and the choice is made wider.
Suppose turbine of a given power runs at 120 r.p.m. or at 900 r.p.m. and say available head is 200
meters, if the power is developed in a single unit at 120 r.p.m. is 18000 H.P. the required specific speed
of the runner is given by
N
s
= 
5 / 4
120 18000
(200)
= 
120 189.6
750
×
= 30.4
Now if the same power is developed at 900 r.p.m. in two runners, the required specific speed of
the runner is given by

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HYDRO-ELECTRIC POWER PLANTS
383
100
90
80
70
60
50
E
ff
ic
ienc
y
50
0
100
150
200 250 300 350 400 450 500
Specific Speed
Reaction Turbine
Pelton Wheel
N
s
= 
5 / 4
900 18000
(200)
= 
900 134
750
×
= 161
The above calculations show that the required power can be developed either with one impulse
turbine (Pelton) or two reaction turbines (Francis).
It is customary to choose a speed between certain limits, as neither a very low nor a very high
r.p.m. is desirable. The number of units into which a given power is divided is also limited. Nevertheless
considerable latitude is left concerning the choice of the prime-mover and number of units used. Ulti-
mately the choice of prime-mover is a matter of extensive experience instead of paper calculation.