Water speed and volume from well pressure and jet height

[Physics is Phun]

Maybe this should be in the math section, I'm not sure. I have this friend that works in the water industry that tells me my town runs off of 3 wells that each have the pressure to shoot a stream of water 8" diameter 12.6m up. I was wondering from this information how I could figure out how fast that water must be moving and in turn the volume. So how could I go about doing this?

 

[Physics is Phun]

bump

anyone?

 

[lalbatros]

You can use energy conservation to solve that.
Take the potential energy as 0 at the output of the well.

The energy of the stream at the output of the well is

$$\frac{Mv^2}{2}$$​

(no potential energy, only kinetic energy, speed is v, M is the mass of a piece of water)

The energy of the stream at the highest reach, when the velocity drops to zero is:

$$Mg$$​

(no kinetic energy, only potential energy)

Since energy is conserved during the motion (without air friction), we have:

$$\frac{Mv^2}{2}=Mgh$$​

(h is the highest reach)

We get easily:

$$\frac{v^2}{2}=gh$$​

$$v={(2gh)}^{1/2}$$​

Finally, this gives v = 15.7 m/s .