Work, force, power turbine pump problem

[joseg707]

Homework Statement

Some electric-power companies use water to store energy. Water is pumped by reversible turbine pumps from a low to high reservoir. To store the energy produced in 1.0 hour by a 120*10⁶ electric-power plant, how many cubic meters of water will have to be pumped from the lower to the upper reservoir? Assume the upper reservoir is 520 m above the lower and we can neglect the small change in depths within each. Water has a mass of 1000 kg for every 1 m³

Homework Equations

P=W/t
W=Fd
F=ma

The Attempt at a Solution

I multiplied power by the total number of seconds in an hour to get work. I then divided the work by the distance of 520 m and I get force. This is where I'm stuck at. I have that force is equal to (120000000 kg*m²/s³)*(3600s)/(520m). I don't know how to solve for mass because it seems that the flow has a constant velocity and there is no acceleration. Can someone please point me in the right direction?

 

[Astronuc]

One has a 120 MW plant. One has to find how much water must be stored at 520 m, to provide the energy produced in one hour.

Energy = Power * time.

The mechanical energy in the turbine comes from the kinetic energy in the water flow, which is transformed from the gravitational potential energy of the water stored 520 m above the turbine. What is the GPE of the water at 520 m.

Once one finds the mass, the volume is easy to find given the density.

 

[joseg707]

Are you saying that the kinetic energy is equal to the output energy of the turbine, 120MW, and the the potential energy is equal to the kinetic energy?
KE=120 MW

PE(2)=KE(2)
mgh=120W
m(9.8)(520)=120MW?

I don't feel like I understood that right.

 

[Astronuc]

Power = 120 MW

Energy = Power * time. How many J of energy is produced by 120 MW in one hour?

 

[joseg707]

Oh! Haha yeah, I completely jumped right over that didn't I.
(120e6W/s)(3600s)=work
work=4.32e11J

 

[joseg707]

So does this hold true?

m(9.8)(520)=4.32e11
m=84772370.49 kg*1m³/1000kg=84772 m³