How much power would be produced by a stream of water falling at 10 kg/s for 1.0 meter?

Question

How much power would be produced by a stream of water falling at 10 kg/s for 1.0 meter?

Answer 1

Power = Work/time

Work = Force * Distance

Force =m*g

Start with Force. Take a basis of 1 second of flow, in that one second 10 kg would fall at gravity.

F = m*g

F = 10kg*9.8m/s^2

F = 98 kgm/s^2

Now Calculate the Work. Work is the dot product of force and the distance it acts over.

W=|F||D|Cos(0)

W=(98kgm/s^2)(1m)(1)

W=98Joules

The Power is the work per time. So for that 10kg takes 1s, so the Power is:

Power=(work)/(time)

Power=98joules/1s

Power=98 Watts

So the amount of power produced by that stream would be 98Watts.

Answer 2

in 1 second, the mass of water, m = 10kg.

PE lost = mgh

= 10 X 9.81 X 1.0

= 98.1 J

So power produced = 98.1 / 1 (in 1 second)

= 98.1 W