# 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.

Physics Asked on November 11, 2021

Extracting work from water flowing in your pipes is possible. An easy example is sprinklers using flowing water to change the direction of the stream so all parts of the garden are watered.

But this does a low energy job. If you extract too much energy, you will reduce the flow. Also, water only flows while the faucet (or spinklers, shower, etc) are running. If you want to keep a small battery charged, this might be OK.

Another consideration is that water flows inside a pipe, and you want the energy outside. This means you need a hole in the pipe. You might run a rotating shaft through the hole for example. This means a seal. Seals can leak.

There is an easy way to get power already built into homes. So it doesn't seem like there is a large need to be filled. But for a fun project, sure you can make it work.

Answered by mmesser314 on November 11, 2021

The concept you seek is called fluid horsepower. It is equal to the mass flow rate times the driving pressure, in consistent units. I suggest you convert everything to metric units before beginning.

Answered by niels nielsen on November 11, 2021

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