Smart brains and/or internet surfers needed

I have this problem I am hoping I can pick this communities brain for an answer. I have a fan that I need to run at 3000rpm which is belt driven, and the belt is driven by a hydraulic motor, I have the hydraulic motor powered by a hydraulic pump direct driven off of the front of the crank on a truck motor. Currently I got it to run at 1750rpm with 35HP and 2200psi running the pump off the front of the motor, I fell short. What I am looking for is relationship equations for my variables so that I can correctly tweak the system to work properly, without shooting in the dark and buying a whole bunch of unnecessary pumps/motors. The relationship equations that I need include relations for the following.

Work(HP), Pressure(PSI), Volume(GPM)

and

Work(HP), RPM(Fan)

an example of what I am looking for but is obviously wrong is
Work=Pressure*Volume

I know there are probably some constants involved as well. Also do you think the relationship between Work applied to the fan is a linear relationship or parabolic? Essentially I need to get the HP from the motor to the fan, but in order to do so I have to use a hydraulic and belt system.

*cough Tak Almagest cough*

I think it should be linear, but there are constants dependent upon the efficiency of the motor and the pump.

Really it is linear? What you are saying then that if 35HP runs the fan at 1750rpm, 70HP should run it at 3500rpm ? I was under the impression that it took more work to increase the fans rpms, from 2000-2500 than it did from 1500-2000.

Do you know the generic equations that I can plug my numbers into?

Just going from physics equations, HP should relate to RPM in a quadratic fashion, i.e. you increase the power by 4 to increase RPM by 2.

YOU SHOULD KNOW THIS, TAK.

Thank you Almagest, that gives me a good start in the right direction. I had a gut feeling that it wasn't linear, we ALMOST bought went the routeof doubling the HP to double the RPM. With what you have told me it will be more likely to have to quadruple the HP to double the RPM, no exactly but a generic rule of thumb.

42.

Ah the answer to life the universe and everything.