I have a 5000 watt, 3600 rpm 60 hz generator.I plan to connect it to a 1500 watt baseboard heater. Assuming the water wheel can supply sufficient power to the generator, how will water wheel rpm affect power output? In other words if I supply all the power it needs to the generator, but the generator runs at say 500 rpm can I still in theory get full power from it or do I have to gear up 3600 rpm? I am planning to run one or more electric baseboards only
So, briefly and you can research detailed information about water wheels and electricity generation.
Power = Q (flow in L/s) * g (gravity) * H (height) * efficiency
Gravity can be assumed as 10 due to the inaccuracies - because none of the other items will be precise...
High head tends towards Pelton wheel installations while Low head high flow are Kaplan turbines. There are several different turbines available and Pelton for example can have a single or multiple jets...
Any installation will need intake valve control and usually a surge pipe to deal with rapid intake valve closing and dissipating the inertial forces...
There are lots of other things to be considered, one of the most important is having permission to extract the water from the source and also to put it back into the source after it has been through the turbine. For that you will need to contact the relevant authority.
There are, in many countries, people who specialize in this sort of thing, try looking under renewable energy and check out those who have successful installations...
The voltage and frequency that the generator will produce will be proportional to speed. At 1800 RPM, you will get 30 Hz and about half of the voltage that it is designed to produce at 3600 RPM. The required torque to get the rated power will be about 10 pounds-feet or about 13.6 Newton-meters. You will need the same torque to get half of rated power at half-speed.
I bet after the electricity exists, it would be nice to use it for other purposes, too. Then it must have the right voltage and frequency. A small amount of an unstable output of course could be converted electronically to perfect mains AC with minimal cost.
This is not a trivial engineering task for a hobbyist. A pro wouldn't ask. As commented you must have some data of the available water flow to decide what mechanical turbine would provide the needed torque and rpm. Then you must decide how to control it. You must control the input water like you would control a gasoline engine. A synchronous generator in addition must have magetization control system. A massive flywheel is possible in fixed installations to remove the need of fast actions.
Unfortunately without knowing your generator the water, terrain nor climate conditions I cannot write better. But one thing is sure. You must have a local waterfall - maybe inside of your system, but it must exist. Nothing else generates the power. You seemingly already have got other answers of it.
ADD A comment suggests that you would be satisfied with some power, far below the max capacity of the generator and maybe at sub-normal frequency. But you do not know would the generator make it; I assume you plan to have a sturdy waterwheel + simple gearing which rotates the generator well below the nominal speed, but generates surely all the needed torque to keep it rotating under the load.
I don't know your generator. DC generator (you haven't it) or synchronous AC generator with properly controlled magnetization circuit can work as you hope.
But your unit can be the common asynchronous one with cage rotor. It's basically a 2- or 3-phase motor which is rotated faster than the nominal synced speed to turn it to generator mode.
Connection to AC grid is replaced by an oscillating resonant circuit (=dummy reactive circuit in parallel with the actual load). Often adding capacitors are enough due the inductance of the motor windings. Rotation must happen with a slightly bigger rpm than the resonant rpm. Otherwise you get nothing, the output simply stops totally if you cannot keep the rotation speed in certain limits which is defined by the properties of your generator and the extra reactive load. Sub-60Hz can be possible with proper reactive load, but the resonance can vanish if there's not enough inductive reactance. You cannot compensate it by making only capacitors bigger.
If the theory of asynchronous generators is interesting, start by searching for "induction generator" That's the popular alternative name for it.
- electronic parts in your heating system (=something more than mechanical thermostats) can require proper mains AC supply voltage.
- do not assume your insurances are valid if you design or build (or both) fixed electric installations without having proper certificates. In certain countries where the state patronizes everything, you can in addition get hefty fines if everything isn't circulated properly through the right bureaus.