Formula for water pressure, flow and power

[cens]

I feel like this should be readily available, but I cannot find any information about it through google.

I am trying to find a formula that will tell me the amount of energy necessary to inject water into a system at a given pressure.

Put another way: I have a pipe of a known size and water (pipe a) is flowing through it at a know pressure (pressure x). I want to hook a pipe (pipe b) up to that original pipe a to inject additional water into it. I want to make sure that I am injecting the water into that system at a fixed flow (measured in GPM). I need to find out how much energy (say in horsepower or kPA) I would need to use to inject the water.

or graphically what is the energy necessary to inject a constant stream of water at point O, given pressure x?:

PIPE A (pressure x)
-O--------->->->->----------------->->->->----------
|
^
|P
|I
|P
|E
^
|B
|



I know that if pressure x is low, then I will not need very much energy to inject the water into that pipe, and if it is high, I will require quite a bit of energy.

I however, do not know the specific formula that is used to calculate this energy requirement. Any links, or simply the formula, if known, would be greatly appreciated.

Thanks very much.

 

[FredGarvin]

P = p*\dot{V}

Where:
P is the power required
p is the pressure required
\dot{V} is the volumetric flow rate

Make sure your units are consistent, i.e. use the standard units, m, sec, N or Lbf, ft, s.

If you are pumping water and need it quick you can use this too:

HP = \frac{\tex{psi}*\tex{GPM}}{1714}

Where:
HP is the power in horesepower
psi is the pumping pressure in psi(g)
GPM is the flow rate in gallons per minute

 

[KristoferE]

I would like to calculate the power need for fulfilling a pressurized airflow stream. With water it is simple but since air is a compressible gas it gets more difficult, or not? I've seen different alternatives. Please help!

regards /k