Power Plant Engineering

11.11. SPECIFIC SPEED OF TURBINE
The specific speed of a turbine is defined as the speed at which the turbine runs developing one
B.H.P. under a head of one metre.
The equation for the specific speed of a turbine can be obtained by using the principle of similar-
ity.
(1)
V = 
60
DN
H
π
∝
∴
D 
∝
H
N
, where D and N are diameter and speed of a turbine and H is the head acting on
the turbine.
(2)
Q = 
π
DB . V
f
∝
D
2
H
where B is the height of the blade and V
f
is the velocity of flow.
Substituting the value of D in the above equation,
∴
Q 
∝
3 / 2
2
(
)
H
N
(3)
P = 
75
QH
ρ
where P is the power developed.

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POWER PLANT ENGINEERING
Substituting the value of Q in the above equation, we get
P 
∝
75
ρ
3 / 2
2
(
)
H
N






H 
∝
5 / 2
2
(
)
H
N
∴
N
2
∝
5 / 2
(
)
H
P
∴
N 
∝
5 / 4
(
)
H
P
= C 
5 / 4
(
)
H
P
where C is knour as constant depending upon the type of the turbine.
If the turbine develops 1 B.H.P. under one metre head then
C = N = N.
where N
s
is the specific speed as per the definition.
Substituting the value of C in the above equation, we get
N
s
= 
5 / 4
(
)
N P
H
when P is in H.P.
= 
5 / 4
1.165
(
)
N
KW
H
when the power is in kW.
...(1)
By definition, the specific speed is number of revolutions per minute at which a given runner
would revolve if it were so reduced in proportions that it would develop one H.P. under one metre-head.
Sometimes the power developed is given in kilowatts instead of metric H.P., the head being in
metre as before.
The specific speed of a single jet Pelton wheel in terms of diameter of runner and diameter of jet
in metric units is given by
N
s
(single jet petrol) = 244.75 
d
D
...(2)
In a multi-jet pelton wheel, the H.P. is directly proportional to the number of jet if the head
remains constant. The specific speed of multi jet Pelton wheel is given by
N
s
∝
n
as N
s
∝
P
and P 
∝
n.
Therefore, the specific speed of multi jet unit can be calculated by multiplying the specific speed
of single jet unit with a factor 
n
where n is number of jets used.
It is necessary to know a characteristic of an imaginary machine identical in shape for comparing
the characteristics of machines of different types. The imaginary turbine is called a specific turbine. The
specific speed provides a means of comparing the speed of all types of hydraulic turbines on the same
basis of head and horse power capacity.
The overall cost of installation (runner + generator + power house and auxiliary equipments) is
lower if a runner of high specific speed is used for a given head and H.P. output. The selection of too

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HYDRO-ELECTRIC POWER PLANTS
369
high specific speed reaction runner would reduce the size of the runner to such an extent that the dis-
charge velocity of water into the throat of draft tube would be excessive. This is objectionable because
a vacuum may be created in the extreme case.
The runner of too high specific speed with high available head increases the cost of turbine on
account of high mechanical strength required. The runner of two low specific speed with low available
head increases the cost of generator due to the low turbine speed.
An increase in specific speed of turbine is accompanied by lower maximum efficiency and greater
depth of excavation of the draft tube. In choosing a high specific speed turbine, an increase in cost of
excavation of foundation and draft tube should be considered in addition to the efficiency. The weighted
efficiency over the operating range of the turbine is more important in the selection of a turbine instead
of maximum efficiency.
Experience has determined that there is a range of heads and specific speeds for each type of
turbine. Special conditions may sometimes dictate departure from common practice.
The ranges of heads and specific speeds for different types of turbines are tabulated in
Tables 11.3 and 14.4.