HOW TO CALCULATE HYDRAULIC PUMP PRESSURE

All volumetric pumps develop a pressure function of the resistance the motor encounters.

Not possible. The load must be known.

The fastest way possible is to know the area of any one cylinder in your circuit, and the load it is pushing or pulling, and calc it out. Divide the load by the area, and you end up with pressure.

I'm betting you want to know the pressure the pump can safely handle. For that you should consult the manufacturer.

Max pressure for vane pump 160 Bar

Max pressure for gear pump 250 Bar

Max pressure for piston pump is more than 500 Bar

When you consult the manufacturers websites, you will often find pressure over revs diagrams, cc over revs diagrams and pressure over power diagrams. As you can now conclude there must be a third variable that gets fixed for each of these diagrams so your question is impossible to answer without the last variable.

Get the motor revs and power rating and then consult the manufacturers website to do the formula. If you are designing a system you need to do it the other way around. The design will tell you what cc and pressure you need which in turn will calculate the motor power.

Positive displacement (PD) pumps provide flow. = displacement X RPM.

Resistance to flow provides pressure.

The maximum pressure for a specific pump is in the manufacturer's literature.

for calculate pressure in vane gear pump we should know the outer tip speed of impeller if od increases pressure of pump with the same flow increases where as bhp also increases

You are making it hard on yourself. Be it vane, gear or piston, pressure is pressure, no matter which type of pump is used. It just depends on what you want the flow characteristics to be. Those are two different issues.

The short answer is no. As stated before in this conversation, pumps do not create pressure, only resistance to flow can cause a pressure rise or loss, depending on what you are looking for and why. ANY time you look at an hydraulic system, EVERYTHING is predicated on system load, and speed. You regulate load with a relief, regulate speed with a flow control (short of using a prop or servo). Any further refinements are dealt with in the arena of motion control.

To make your life easier when you question a pump, look at your load, speed, and available horsepower on your prime mover. Then look at ancillary system equipment for efficacy. Follow that approach, and you won't have as many sleepless nights as those that don't.