Question

Consider a river flowing toward a lake at an average speed of 3 m/s at a rate of 550 m3/s at a location 58 m 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/m3, and the acceleration due to gravity is 9.81 m/s2. The total mechanical energy of the river per unit mass is kJ/kg. The power generation potential of the entire river at that location is MW..

Answer 1

1. 0.574 kJ/kg

2. 315.7 MW

Step-by-step explanation:

1. The mechanical energy per unit mass of the river is given by:

`E_(m) = E_(k) + E_(p)`

`E_(m) = (1)/(2)v^(2) + gh`

Where:

Ek is the kinetic energy

Ep is the potential energy

v is the speed of the river = 3 m/s

g is the gravity = 9.81 m/s²

h is the height = 58 m

`E_(m) = (1)/(2)(3 m/s)^(2) + 9.81 m/s^(2)*58 m = 0.574 kJ/Kg`

Hence, the total mechanical energy of the river is 0.574 kJ/kg.

2. The power generation potential on the river is:

`P = m(t)E_(m) = \rho*V(t)*E_(m) = 1000 kg/m^(3)*550 m^(3)/s*0.574 kJ/kg = 315.7 MW`

Therefore, the power generation potential of the entire river is 315.7 MW.

I hope it helps you!