HYDRO-ELECTRIC POWER PLANTS 379
N =60
πD. V =
60
πD2 gH∴ 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 = Nu (unit speed by its definition)
∴ N = Nu (^) H
∴ Nu =
N
H
- Unit quantity. This is defined as the volume of water passing through the turbine under a head
of 1 metre.
Q = AVQ ∝ H as V = 2 gHand A is constant for given turbine
∴ Q = K 3 H
If H = 1, then Q = K 3 = Qu (unit quantity by its definition)
∴ Q = Qu H∴ Qu =Q
H
If the question of reducing the performance of a turbine under head H to its performance under
any other head H, is required, then we can use the following equations.
P 0
P=3/ 2
H 0
H
N 0
N=^0H
Hand^0
Q
Q=^0H
H
The principle of similarity is applied to the turbines in order to predict the performance of actual
prime movers from the tests on the model.
The vane angle at inlet and outlet will be same for model and prototype. The velocity triangles
will also be identical for model and prototype when they are running under certain conditions.
The velocities are proportional to H for all similar turbines and hence :(a) Speed v =
60πdn∝ (^) h for model.