1 hour ago
This swan is was kind enough to frame this view of Geneva's impressive water fountain for me.
Thanks Swan. Now I'm gone.
Sucking in water from the lake surrounding it, the fountain uses a powerful pump to launch water high into the air. Initially imparting it with very high kinetic energy, which is transferred into gravitational potential energy as the water moves through Earths gravitational field. Let's do a back of the envelope calculation to work out the kinetic energy of the water, and thus the power use of the fountain.
First I'll have to estimate the height of the fountain. From what saw of it, I'll say 600m. In order for the water to come to a stop at the top of the fountain, its potential energy here must equal the kinetic energy it gains to begin with, assuming a negligible amount is lost to friction. The gravitational potential energy of a mass m at height 600m above the earth's surface is m*g*600.
Now, the fountain appears to fire water in "bullets" not continuously which actually will help me here. I'll guess again that each such bullet had a mass of 10kg. This means its potential energy at the top is equal to 58.8KJ. So this is the kinetic energy it has to begin with.
A few loose ends to tie up here. A 10kg bullet with this kinetic energy will have a speed at the bottom of about 108ms^-2.
Furthermore we can again guess that the fountain shoots a bullet 5 times per second. This gives a power use of 294kW . That's quite high. This assumes also: 100% efficiency.
That was fun eh
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