# I Water wheels and mathematical equation

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1. Sep 3, 2016

### Nodir Musaev

Hello everyone, currently working on a physics project.
I was very curios about waterwheels and actually have an overshot waterwheel setup. I was testing how the efficiency of a waterwheel would be effected by the drop height of water onto the waterwheel. Do any of you have any idea how I can create a mathematical equation that would explain the findings. By efficiency I mean its ability to convert potential energy into kinetic energy.

I am assuming that by increasing the drop height I am increasing the total energy of the water, but I have researched into topics such as moment of inertia and realized I can find that since I know what distance from the center the water wheel the water hits it at but I realize I would then have to go into angular momentum and then use that calculate the KE through which I can then compare to the original energy given.

2. Sep 3, 2016

### Staff: Mentor

Do an internet search on hydro turbine efficiency. I'm sure you'll find some hits. There are also numerous videos on Youtube about backyard hydro turbines, some of them discuss calculating efficienty. As a first guess, assume that the turbine is 100% efficient in converting the potential and kinetic energy of the water. Do you know how to calculate those?

When the kinetic energy begins to dominate over potential energy, the optimum design shape of a turbine changes. The Pelton Wheel shape is used when kinetic energy is very high. Here are some pictures of Pelton turbines.

http://www.absak.com/catalog/images/HP-WHEEL.jpg [Broken]

Last edited by a moderator: May 8, 2017
3. Sep 3, 2016

### Nodir Musaev

Thanks I will be looking into that, but I found a great website here that explains the way that moment of inertia and torque is found but I cant exactly understand the calculations. I've just recently began learning calculus.
http://ffden-2.phys.uaf.edu/211_fall2010.web.dir/Brooks/water-wheel-physics.html

Last edited by a moderator: May 8, 2017
4. Sep 4, 2016

### CWatters

The water starts off with some PE and KE and ends up with zero PE but it usually still has some KE as it exits the wheel with some non zero velocity. I wondered if there were ways to extract that last bit of KE? Perhaps by discharging water from the wheel into a wider but slower wheel?