Calculating Nonconservative Energy Loss in Pumped-Storage Reservoirs

[BMW25]

new problem!

A pumped-storage reservoir sits 136 m above its generating station and holds 9.0×10^9 kg of water. The power plant generates 346 MW of electric power while draining the reservoir over an 6.9 h period.
What fraction of the initial potential energy is lost to nonconservative forces (i.e., does not emerge as electricity)?

could you please guys help me with that? I gave up with that
I need that in hour guys please please.

 

[learningphysics]

136 m above its generating station and holds 9.0×10^9 kg. so what is the gravitational potential energy?

346 MW over an 6.9 h... what is the energy generated here?

so how much energy is lost?

what is the fraction of this energy to the original gravitational potential energy.

 

[ogb p]

I would approach this problem by first understanding the concept of nonconservative energy loss in pumped-storage reservoirs. This refers to the energy that is lost during the process of converting potential energy (stored in the water at a higher elevation) into electrical energy. This loss can be caused by various factors such as friction, turbulence, and inefficiencies in the system.

To calculate the nonconservative energy loss in this specific scenario, we can use the equation:

Nonconservative energy loss = Initial potential energy - Final electrical energy output

Since we are given the initial potential energy (9.0×10^9 kg x 136 m x 9.8 m/s^2 = 1.21×10^13 J) and the electrical energy output (346 MW x 6.9 h x 3600 s/h = 8.48×10^11 J), we can calculate the nonconservative energy loss as:

Nonconservative energy loss = 1.21×10^13 J - 8.48×10^11 J = 1.13×10^13 J

To determine the fraction of the initial potential energy lost to nonconservative forces, we can divide the nonconservative energy loss by the initial potential energy:

Fraction of initial potential energy lost = (1.13×10^13 J / 1.21×10^13 J) = 0.93 or 93%

This means that 93% of the initial potential energy is lost to nonconservative forces and only 7% is converted into electrical energy. This high percentage of energy loss highlights the importance of continuously improving and optimizing the design and operation of pumped-storage reservoirs to minimize nonconservative energy loss and increase overall efficiency.