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

`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* 2* 9.8(45 - 5) = 781.65 kW`

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

`\eta = (P_(out))/(P_(inlet))`

`0.65 = (P_(out))/(781.648* 1000)`

`P_(out) = 0.65* 781.648* 1000 = 508071 W = 508.071 kW`

`P_(out) = 508.071 kW`