Alternative not encouraged...

FreeBear

Netexporter said:

The power output would surely be more dependent on the water flow rate & head.

The head is 3 metres on a 3 metre overshot. Can't be any more or less.

These guys are getting 3KW out of a small water powered turbine - https://cat.org.uk/info-resources/free-information-service/energy/micro-hydro/ - With sufficient funds, I would have thought a 5KW could be viable if there is a big enough flow.

You need a hell of a lot of head for a turbine. There's on on the edge of my village and the pipe goes miles up the hill. The cost of the actual turbine is minuscule compared to the other work.

Depending on the design and power output of your turbine, you may need a considerable head. But there are designs for micro generation that will operate with as little as 1m head. OK, power output isn't great (some just 100W or so), but if you are topping up batteries, you don't necessarily need a big generator.

Quick fag packet calculation - If I consume 6KWh each day, a 250W generator running constantly charging a set of batteries would suffice. Would need to factor in system losses and variable flow rates..

This company has a selection of low head & low flow turbines - https://www.powerspout.com/

And for something a little less reliable - https://www.mdpi.com/1996-1073/16/4/1660 - Might generate some useful power in somewhere like Cumbria, a waste of time in the South East of England.

Netexporter

This company has a selection of low head & low flow turbines

Great stuff but as the example in the calculator shows you need 50 metres of head to generate just over 800W. Not many houses have land that rises that far. Or you need a high flow rate , which probably would entail a dam, to ensure seasonal availability of power. I'm not saying it isn't possible to go hydro, just that having the optimal circumstances and enough cash isn't a given.

Qyburn

At 100% efficiency, a head of 1 metre,  flow rate of 1 litre per second gives 9.8W. Multiply that as appropriate. 

Netexporter

Qyburn said:

At 100% efficiency, a head of 1 metre,  flow rate of 1 litre per second gives 9.8W. Multiply that as appropriate. 

I like that. You can directly see the gravity of the situation.