Answer:
Step-by-step explanation:
To determine the total mechanical energy of the river water per unit mass, we need to consider both the kinetic energy and potential energy of the water.
i. Total mechanical energy per unit mass:
The kinetic energy per unit mass of the river water is given by:
KE/m = (1/2) v^2
where v is the velocity of the river water. Substituting the given values, we get:
KE/m = (1/2) (5 m/s)^2 = 12.5 J/kg
The potential energy per unit mass of the river water is given by:
PE/m = g h
where g is the acceleration due to gravity (9.81 m/s^2) and h is the height of the river above the lake surface. Substituting the given values, we get:
PE/m = 9.81 m/s^2 x 100 m = 981 J/kg
Therefore, the total mechanical energy per unit mass of the river water is:
TE/m = KE/m + PE/m = 12.5 J/kg + 981 J/kg = 993.5 J/kg
ii. Power generation potential of the entire river:
The power generation potential of the entire river can be calculated by multiplying the total mechanical energy per unit mass by the mass flow rate of the river, which is given as 450 3/ (cubic meters per second).
To convert cubic meters per second to kilograms per second, we need to multiply by the density of water, which is approximately 1000 kg/m^3. Therefore, the mass flow rate of the river is:
m_dot = 450 3/ x 1000 kg/m^3 = 450000 kg/s
The power generation potential of the entire river is then given by:
P = m_dot x TE/m = 450000 kg/s x 993.5 J/kg = 4.47 x 10^8 W
Therefore, the power generation potential of the entire river at the given location is approximately 447 MW.