Question

A 65% efficient turbine receives 2 m^3/s of water from a reservoir. The reservoir water surface is 45 m above the centerline of the turbine. The water leaves the turbine through a 1-m diameter pipe into a river. How many kilowatts of power is generated by the turbine? Assume losses in the flow system to be 5 m.

Answer 1

Answer:

$P_{out} = 508.071 kW$

Given:

efficiency of the turbine, $\eta$ = 65% = 0.65

available gross head,  $H_{G}$ = 45 m

head loss,  $H_{loss}$ = 5 m

Discharge, Q =  $2 m^{3}$

Solution:

The nozzle is 100% (say)

Available power at the inlet of the turbine,  $P_{inlet}$ is given by:

$P_{inlet} = \rho Qg(H_{G} - H_{loss})$                  (1)

where

$\rho$ = density of water = 997 $kg/m^{3}$

acceleration due to gravity, g = $9.8 m^{2}$

Using eqn (1):

$P_{inlet} = 997\times 2\times 9.8(45 - 5) = 781.65 kW$

Also, efficency, $\eta$ is given by:

$\eta = \frac{P_{out}}{P_{inlet}}$

$0.65 = \frac{P_{out}}{781.648\times 1000}$

$P_{out} = 0.65\times 781.648\times 1000 = 508071 W = 508.071 kW$

$P_{out} = 508.071 kW$