Question

The water in a large lake is to be used to generate electricity by the installation of a hydraulic turbine-generator at a location where the depth of the water is 50 m. Water is to be supplied at a rate of 5000 kg/s. If the electric power generated is measured to be 1862 kW and the generator efficiency is 95 percent, determine (a) the overall efficiency of the turbine-generator, (b) the mechanical efficiency of the turbine, and (c) the shaft power supplied by the turbine to the generator.

Answer 1

c

Step-by-step explanation:

Answer 2

a) 0.76

b) 0.80

c) 1964 kW

Step-by-step explanation:

GIVEN DATA:

`\dot m = 5000 kg/s`

Assume Mechanical energy at exist is negligible

A) Take lake bottom as reference, and then kinetic and potential energy are taken as zero.

change in mechanical energy is givrn as

`e_(in) - e_(out) = (P)/(\rho) - 0 = gh = 9.81 * 50( (1 kJ/kg)/(1000 m^2/s^2)`

= 0.491 kJ/kg

`\Delta \dot E_(mec) = \dot m (e_(in) - e_(out)) = 5000 * 0.491 = 2455 kW`

`\eta_(OVERALL)  = (\dot W)/(\Delta \dot E_(mec)) = (1862)/(2455) = 0.76`

B)
`\eta -{gen} = (\eta_(overall))/(\eta_(gen)) = (0.76)/(0.95) = 0.80`

c)
`\dot W_(shaft) = \eta_(overall) \left | \Delta \dot E_(mec) \right | = 0.80(2455)`

`\dot W_(shaft) = 1964 kW`