Hydraulic Pump and Motor Selection - from scratch?

Hydraulic motors and pumps typically about 80% efficient. With both a pump and motor, gets to about 65% or so. Unlikely to beat your mechanical setup.

You need help from a brilliant mechanical engineer. Hiope you know one!

Best solution is to use direct drive with a high speed water wheel, and a slow speed generator. I assume you are unwilling or unable to do so.

Next choice is to go with a custom designed drive chain. [Note that drive chain is the mechanical connection; it does not imply that a link chain is used]. Each stage looses more power, so fewest feasible number is desireable. 4:1 is typical max, but for a low powered application, possible to go higher. So, let's target two stages. Possible to use large gears (like a flywheel and starter pinion, but this requires tight tolerances. A chain or timing belt driven system is probably best. You can use a tensioner/idler to give compliance, allowing loose tolerances.

Consider a bicycle. A human can do about 1 HP, so drive chain rating is probably about this. Front sprocket is perhaps 10" diameter, at 60 to 120 RPM's. Rear sprockets go down to about 2 or 3 inch diameter. To get 100:1 step up, perhaps 40" to 60" sprocket and 3" or so driven sprocket. Large sprocket should be attached to waterwheel axle, use same bearings.

You could use a single additional shaft with the small drive sprocket and a larger sprocket, perhaps the 10" or so from the front of a ten-speed bike. I'm not fond of chain; better to use timing belts like some of the motorcycles now. You need to consider where to buy or how to make the gears economically though.

This type of system should be able to transmit over 95% of the energy.

There are also low friction transmissions, such as elliptical drives. Probably pretty costly.

Edit:

You are correct that hydraulic pistons are fairly efficient. The main losses are seal friction, with some minor pressure drops in the hydraulic circuit. Pumps though, have lots of parts and seals, and sources of friction.

Commercial gearboxes tend to have low efficency. I'm not sure why, except that low cost, compact size, and manufacturability are design goals, rather than efficiency. I still think a custom design with super efficiency is the way to go.

Rather than use a gear the same size as the waterwheel, why not use one small enough to stay out of the water? I'm not a big fan of chains, but a toothed belt should be able to work.

To answer your questions, start sizing a system by selecting the design (max) pressure. Often 3000 psi, but both higher and lower pressures are available.

Next, look at the pump. Power is the through variable times the across variable. For electricity, P = E * I. For hydraulic pump, Input Power = torque * angular velocity. A.V. is RPM * 2pi radians/rev * min/60 sec. The time conversion is optional.

Output pressure is Q * P = flowrate * pressure. The difference between input and output power is loss.

You will find a very large pump is needed to absorb 1 HP at 12 RPM's. It will be hard to find, as pumps are normally designed for electric motor speeds, like 1800 RPM's.

Now, find a motor for the pressure and output RPM's you need. The flowrates will automatically match those for the pump, since the pressure and output speed are fixed.

Datasheets on the pump and motor should indicate losses. I think you will be hard pressed to find a suitable pump at a reasonable price. High torque components are generally rare.

Good luck!

Hydraulic Motor Selection

hydraulics are terribly, terribly efficient because liquids are incompressible. Pneumatics suffer from inefficiency because air is a compressible fluid. The only losses in hydraulics will be due to mechanical friction, viscosity of the liquid and flow friction in small tubing. Practically, there is also the problem of leaking hydraulic fluid.

800 NM HYDRO MOTOR