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

Answer:

Total power generation will be 291.465 MW

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

$E=\frac{1}{2}mv^2+mgh$

Energy per unit mass

$\frac{E}{m}=\frac{1}{2}v^2+gh=\frac{1}{2}\times 3^2+9.81\times 58=583.29j/kg$

Total power generation from the river is given by

$P=energy\ per\ unit\ mass\times volume\ flow\ rate\times density$

So $P=583.29\times 500\times 1000=291.465MW$