Water wheels and mathematical equation

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The discussion focuses on the efficiency of overshot waterwheels and how drop height affects energy conversion from potential to kinetic energy. Participants suggest researching hydro turbine efficiency and highlight the importance of understanding moment of inertia and angular momentum in calculations. They mention that the design of turbines, like the Pelton Wheel, changes when kinetic energy predominates. There are recommendations for online resources and videos that explain these concepts further. The conversation also touches on strategies for maximizing kinetic energy extraction as water exits the wheel.
Nodir Musaev
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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.
 
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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.

hqdefault.jpg

http://www.absak.com/catalog/images/HP-WHEEL.jpg
 
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anorlunda said:
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.

hqdefault.jpg

http://www.absak.com/catalog/images/HP-WHEEL.jpg
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 can't 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
 
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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?
 

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