Power Plant Engineering

11.13 MODELS AND MODEL TESTING
The size of the water turbines used in hydraulic power plant is usually very large (150,000 H.P. or
more). The turbines are manufactured to fulfill the required specific conditions and, therefore, the mass
production of hydraulic turbines used in power plants is not possible.
The cost of the turbine unit is considerably large, therefore, it is not economical to conduct the
test on the prototype units. The changes in dimensions, size and shape are not possible once the proto-
type is ready. The hydraulic limitations to conduct the test on prototype are listed below :
1. It is not possible to vary the head and speed of the unit as desired
2. The load cannot be maintained constant on the turbine.
Due to the above-mentioned limitations for conducting the test on prototype unit, it is always
necessary to conduct the tests on the models of the turbines which is geometrically similar and can
predict the behavior of the prototype units.
The model and prototype should be identical in shape and the other parts like casing, guide
mechanism and draft tubes must be also geometrically similar. It is always desirable to make a turbine
model having an output of not less than 5 H.P. and not greater than 50 H.P. Too small model may not
give accurate result and too large model may not be economical to study the performance of the proto-
type using the models, certain characteristics of turbine as unit power, unit speed and unit quantity must
be known.
1. Unit power. This is defined as the power developed by the turbine under a head of one meter.
P = 
75
QH
ρ
But
Q = AV
where A is area through which water flows and V is the velocity of water.
∴
P = 
75
AVH
ρ
= 
75
AH
ρ
2gH
as
V = 
2gH
...
P 
∝
H
3/2
or
P = K
1
H
3/2
where K
1
is the coefficient which varies with the speed and gate opening
when
H = 1, P = K
1
= P
u
(unit power by its definition)
∴
P = P
u
H
3/2
∴
P
u
= P/H
3/2
2. Unit speed. This is defined as the speed of the turbine under a head of 1 metre
V = 
60
DN
π

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HYDRO-ELECTRIC POWER PLANTS
379
N = 
60
D
π
. V = 
60
D
π
2gH
∴
N 
∝
H
∴
N = K
2
H
where K
2
is the coefficient which varies with the conditions of running.
If H = 1, then N = K
2
= N
u
(unit speed by its definition)
∴
N = N
u
H
∴
N
u
= 
N
H