Question

Consider a river flowing toward a lake at an average speed of 3m/s at a rate of 500 m^3/s at a location 58m above the lake surface. Determine the total mechanical energy of the river water per unit mass (in kJ/kg) and the power generation potential of the entire river at that location (in MW). The density of water is 1000 kg/m^3, and the acceleration due to gravity is 9.81 m/s^2.

Answer 1

Total power generation will be 291.465 MW

Step-by-step explanation:

We have given that river is flowing at rate of V =
`500m^3/sec`

Average speed v = 3 m/sec

Height h = 58 m

We know that total mechanical energy is given by

E = KE +PE

`E=(1)/(2)mv^2+mgh`

Energy per unit mass

`(E)/(m)=(1)/(2)v^2+gh=(1)/(2)* 3^2+9.81* 58=583.29j/kg`

Total power generation from the river is given by

`P=energy\ per\ unit\ mass* volume\ flow\ rate* density`

So
`P=583.29* 500* 1000=291.465MW`