Calculate hydroelectric power achievable in a pipe?

I am working on an internet-of-things gadget that connects to a home plumbing system. It needs a small amount of energy in order to run its circuitboard. So, how should we power this device. One option would be to use replaceable batteries or a power plug. But, I thought a more elegant solution would be to use a turbine in the pipe to collect a little bit of energy each time the water runs. We could store that energy in a small rechargeable battery.

The main question

I would like to calculate the power that can be generated by a turbine in a water pipe. Here are our assumptions:

• The turbine is inside a pipe that is connected to a municipal water supply that has a pressure of 50 PSI.
• When the water tap is turned on, the water will flow at 1 gallon per minute, and this flow rate is restricted by an aerator on the end of the faucet.
• I don’t know if this matters, but let’s assume the inner diameter of the pipe is 1/2 inch.

From the above (and any other information that you think we need to know), I’d like to be able to calculate: how much power (in Watts) can be collected from such a system?

Other considerations

Also, I am curious whether there is a tradeoff on (a) how much energy to collect and (b) the flow rate of the system, since the turbine would probably have some resistance.

When I google search this topic, I have found lots of tutorials on calculating hydroelectric power from a turbine on a river (e.g. this one). These tutorials assume the water is moving due to gravity, and they use the gravitational constant of 9.81 m/s^2. However, in our system, we are thinking about water pressure from a municipal water service, and the pressure in this pipe may be due to gravity (if there’s a water tower), or it may be due to a mechanical pump. So, I am not sure how to rephrase this in terms of pressure, instead of gravity.