# Calculate hydraulic torque from motor HP, hydraulic pump and gearbox

I am curious about the design considerations for a hydraulic system.

Let's say you have a 3HP 1200RPM motor you also have a hydraulic pump that's rated 4LPM and pressure of 40MPA rated for 40RPM MAX

You can put many different types of gear box on the 3HP motor to get it to operate in the N-40RPM range

Let's forget about the power loss through heat when using the gearbox.

I am trying to understand the relationship between HP and RPM of the electric motor, Pressure of the system and output Torque.

Let's say I am working at 200Bar, electric motor doing 40RPM and the hydraulic motor running at 4LPM.

How would that compare to say going to 20RPM and keeping 200Bar and 4LPM.

I do understand that raising the pressure would increase the heat and possibly require cooling.

Any suggestions on how to calculate these relationships?

I think you need an equation to compare the hydraulic work with the mechanical work. Additionally you can add the speed to get the power, but it's not necessary...

$$W_{hydr}=p*V_{geom}=M*2*\pi=W_{mech}$$

and now with speed

$$P_{hydr}=p*V_{geom}*n=p*Q=M*2*\pi*n=P_{mech}$$

Now the units:

• $$p$$ $$[bar]$$
• $$V_{geom}$$ $$[cm^3/U]$$
• $$n$$ $$[1/s]$$
• $$Q$$ $$[l/min]$$
• $$M$$ $$[Nm]$$