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"In a hydro-electric scheme the catchment area is 57 km2 and the annual rainfall for the area is 1720 mm. The reservoir for the scheme is 380 m above sea level, and the power station is 50 m above sea level. What is the maximum possible annual generating capacity, i.e. energy output for this station in MWh"

Our lecturer, in his solution, calculates the potential energy from a height of (380-50)m. Why?

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The change in gravitational potential energy from the reservoir to the power station is proportional to the difference in height between the two things. So the lecturer just calculates this difference in height.

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  • $\begingroup$ More precisely, the work done is proportional to the distance traveled. The distance traveled is the difference between the initial height and the final height. Since presumably the water is ending up at the height of the power station, that height is subtracted from the reservoir height. $\endgroup$
    – Acccumulation
    Commented Apr 18, 2018 at 15:12
  • $\begingroup$ Ah ok, I was wondering why he didn't just use the height of the reservoir (380m). Thanks. $\endgroup$
    – user193025
    Commented Apr 18, 2018 at 15:15
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    $\begingroup$ @Acccumulation Just to be careful, the work done by gravity is proportional to the change in height, not the distance traveled. The water might not be traveling in a path straight down to the power station, so the distance traveled and the change in height are not necessarily equal. $\endgroup$
    – BioPhysicist
    Commented Apr 18, 2018 at 15:16
  • $\begingroup$ Yes, distance traveled in direction of the force (in this case gravity). $\endgroup$
    – Acccumulation
    Commented Apr 18, 2018 at 15:24