How to calculate motion of a rotary turbine in water flow

How to calculate motion of a rotary turbine in water flow

I have come up with a simple and low cost idea for a river turbine to be used in impoverished countries with river flow. The basic design would be a two foot diameter pipe with a flare on the end approximately three feet diameter at the opening. Inside the pipe would be a turbine with anywhere from eight to twelve simple blades placed at a 45 degree angle. since the river flow is around 2 miles per hour, i am trying to figure the rpm generated from this. I have made a scale model and tried it and camu up with around 4 rotations per second but it is difficult to count and I do not have the resources to accurately measure it. much of my experience has been mechanical and I am not sure how to calculate the motion of the turbine in water flow such as this. The design must be simple and made from readily available materials, so hi tech engineering is out of the questions and I am trying to work this to be as simple as possible. the pipe would rest on the underside of a float or raft


I will start of with a question:

Why do you have the pipe opening up at the end? This will slow down the speed of the water exiting the pipe. If anything you should be reducing the diameter to form a nozzle to ensure that the the speed of the water exiting the pipe is as high as possible. Remember the kinetic energy of a moving object or liquid is governed by the equation E=1/2m*V^2 [1]

As for calculating the rotational speed of your turbine you need to two things.

1. the radius of your turbine blades (R)
2. the speed that the water is flowing (V)

The rotational speed of your turbine = V / R

If the water is flowing 2 miles per hour or 2.93 feet / second

and your turbine has a radius of 8 inches or 2/3 of a foot

The rotational speed of your turbine is 4.4 rps or 264 RPM. This is assuming that there are no losses. Since you will not capture all the energy the turbine speed will be slightly lower than this.

It sounds like you have reinvented a water turbine [2] called a Francis Turbine [3]. You may want to look at the information on water turbines to see what people are doing to make these systems work in low tech applications.

Niel Leon
Community Developer –

Niel, thank you that is what I thought it would be but my physics was over 20 years ago and I never got much involved in hydrodynamics or flow characteristics. Perhaps I misstated my question they only allow so many characters. Basically it would be a wide flare going to a smaller diameter pipe with the turbine in the pipe. Yes it is reinventing the wheel per se, but I am trying to design with parts that can be had in most places that we would take for granted. As there are many turbines available commercially and the technology is out there, but these are people who have only boat and foot transport, little if any budget, and little education so it has to be something they can use and learn to keep up so putting this on the underside of a tethered raft would likely be the best solution so as the water level changes, the turbine moves up and down and still generates power. The technology for this has been around for ages starting with the water wheel, but I want to make it such that they could use anything laying around and have the variables to improvise should something go wrong. This would use a steel drum with the ends cut out, a flare or funnel to increase the speed of water coming in, and simple, low tech blades which could be easily replaced or cleaned if needed. Their current means is an angled shaft in the water with three blades made from composites. of course if the blade breaks they have issues, with common materials they can replace them, though with my idea the blades would be strong enough not to break but readily available from local sources.


There is a heck of a lot of information on “low head micro turbines” out there on the Internet. I did project for a client about 30 months ago. There were a couple of designs that used PVC pipe. If you are looking for off the shelf stuff you might want to search on the quoted phrase above and see what comes up.