Hydroelectric Power Plant Efficiency Calculation

[BrainMan]

Homework Statement

Homework Equations

The Attempt at a Solution

What I attempted to do is

.80(1/2)mv² = E_e

Where v is the velocity of the falling water, m is the mass of the falling water, and E_e is the electrical power generated by the electric plant.

So then I solved for m since you are given the E_e and the velocity and I got 3.86 x 10e5 kg/s.

 

[kuruman]

Your number is correct. To be strictly correct you should use dm/dt in your equation instead of m.

 

[haruspex]

Your number is correct. To be strictly correct you should use dm/dt in your equation instead of m.

But then it would be dE/dt on the other side, assuming E stands for energy, not power.
The OP equation can be justified by prefixing it with "in the time in which a mass m of water passes through".

 

[kuruman]

But then it would be dE/dt on the other side, assuming E stands for energy, not power.

If E stands for energy, .80(1/2)(dm/dt)v² = dE/dt is correct.
If E_e stands for power (as indicated by OP in attempt at solution), .80(1/2)(dm/dt)v² = E_e is correct.