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Reply from Mike Innes, forwarded by RedR KP moderator.

Good luck with your project, Rebecca. As you've already discovered there are various options on the type of turbine you could use, and the minimum head varies with he type of turbine you choose (or are stuck with). I'm afraid the selection process is going to be a bit iterative.

For propeller or Kaplan turbines all of the blades of the impeller have to be in the flow; that is, the flow of water must fill the pipe in which the turbine is submerged. This can be hard to attain and difficult to maintain.

The crossflow turbine is an impulse type and can work with variable flow rates (within some limits). This article does a nice job explaining the pros and cons of the different turbines

https://energy.gov/energysaver/microhydropower-systems

I'm presuming you have a maximum head, if only from some practical limitations (height of the hill/house/tower etc.). Given that maximum you can select the turbine that best suits it, then use these guidelines

https://energy.gov/energysaver/planning-microhydropower-system

to calculate the minimum. If the scheme still works, you're done, if not you'll need to change something about the head, the flow rate or the turbine type and go back around the loop.

hope this helps

mike