# Efficiency of a hydroelectric power station

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Homework Statement:
A hydroelectric power station uses the water in a reservoir to power the generators. The water
falls through a vertical height of 150m to the turbines which power the generators.
The efficiency of the power station is 90% and the output power of the power station is
1800 MW.
The gravitational field strength is 10Nkg–1 and the density of water is 1000 kgm–3.
What volume of water passes through the turbines in one minute?
A. 6.48 ×10^4 m3
B. 7.20 ×10^4 m3
C. 8.00 ×10^4 m3
D. 6.48 ×10^7 m3
E. 7.20 ×10^7 m3
F. 8.00 ×10^7 m3
Relevant Equations:
efficiency=useful output/tot input
Power=E/t
Kinetic energy=0.5mv^2
Density=m/v
I have found the input power through the efficiency formula, and I deducted that the input energy must derive only from water's kinetic energy... from which have mass/s and then finally the volume/s.
After all the calculations and having multiplied the volume/s by 60, I get the result of 6.48 x 10^10 m3 which isn't listed... what am I getting wrong?

Last edited:

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Just to be annoying they ask you for volume per minute !

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Just to be annoying they ask you for volume per minute !
Yes sure, I forgot to mention... the result I wrote comes from multiplying my Volume per second by 60!

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The dam converts the Potential Energy of a volume of water to electrical energy with an efficiency of 90%. What you say is correct but overcomplicated...one never need to worry about the speed explicitly.
So how much energy does one ##m^3## of water produce?

• greg_rack and Lnewqban
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The dam converts the Potential Energy of a volume of water to electrical energy with an efficiency of 90%. What you say is correct but overcomplicated...one never need to worry about the speed explicitly.
So how much energy does one ##m^3## of water produce?
I have barely did it... I had made everything unnecessarily complex! Homework Helper
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I have barely did it... I had made everything unnecessarily complex! • • 