The relief valve cannot be rated for less GPM then your pump can make. It can't be too big, but you don't want it too small.
The best pump size is determined by how big the cylinders are on the hoe. Small cylinders need less oil to fill them up. It also has to do with what kind of engine speed you want to hear when using the hoe. Backhoes usually have big pumps so you can run the engine fairly slow and still get decent speed from the hoe functions. So, a hoe might have a 28 GPM pump (at 3000 RPM) but only gets run at 1500 RPM when the pump is only making 14 GPM.
Are you 100% sure the backhoe you have is made for an open-center hydraulic system? If it's made for a closed-center tractor - it won't work.
I'm also wondering . . .if you plan on mounting this pump in front (run off the crank-pulley) . . how are you going to prevent blowing it to pieces when you remove this three-point backhoe? Front pump will be turning all the time and the oil needs to flow freely. Yes you could have guick disconnects and when the hoe was off -you could plug them together.
Much simpler - if this is a part-time use hoe that will be going on and off - to have a PTO pump. The pump would be permanently connected to the backhoe. When the hoe comes off the tractor - so does the pump. A Prince # HC-PTO-9A or a # HC-PTO-7A would be the correct size for your tractor.
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