HP = f * p / 1714
where-
HP = hydraulic horsepower
f = flow, in GPM
p = pressure, in psi
So assuming that you have 7.8 GPM at the hose and the Relief valve is set to 2000 PSI you would have HP=7.8*2000 / 1714 or HP = 9.1 Now If you knew what the brand of the motor is, you could look it up on the manufacturer's site and get the performance data. For example Prince Hyd makes Hyd motor model called the ADM that I used for a chute rotator I recently built for my front mounted snowblower. If you go to PRINCEHYD.COM, click on PRODUCTS, then on CATALOG.
Click on products, then motors and select ADM. This will take a while to load the catalog . click on ADM and then GO TO THIS PRODUCT. This take awhile even on a T1 conection. Hang in there it is worth it. Click the displacement size you want I used 100 (10 Cu in) then click 4 for 4 bolt pattern, then click R for standard 1" keyed shaft, then P for 1/2 inch port size for the hose connection. Then NO for Case drain port option. Unfortunately I can't copy and paste the perfomance data into this post so I will just pick some values that you might be interested in:
At 7 GPM flow and 2400PSI this pump will put out 2016 in/LBS of torque and 176 RPM. At 7 GPM and 1600 PSI it puts out 1334 In/LBS of Torque and 214 RPM. Since they don't have 2000 PSI on the chart lets call it 1500 In/LBS of Torque and maybe 190 RPM as a guess. If you take the formula that is on the performance page HP = RPM * Torque (in In/Lbs) / 63025, We get HP=190*1500/63025 and that gives us 285000/63025=HP or HP = 4.5. Sooo running this motor at these pressure and flow values provide 4.5 HP and you say that the electric motor supplied is 3/4 HP ? Sounds like this motor would be more than enough. If we back off a little and say that the GPM is only 5 and the pressure is only 1600 PSI then the chart says that the torque is 1344 In/LBS and the RPM is 142. Put that into the HP formula and we get 142*1344/63025=HP, that translates to 190848/63025=3.0 HP; still 4 times the value that the electric motor can supply.
The motor that I am using as an exaple is available in at NORTHERNTOOL.COM and is $157. I have used this very motor and it is teriffic. Very powerful and heavy. Not a toy motor. They also make larger ones that you can see in the catalog and best of all the motor is reverseable when you switching the hoses.
I hope that I haven't gone too far with this, I'm no math wiz, but I did do all the research for my project, so I finally have something to say....... Hope this helps..