Water wheels and mathematical equation

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Discussion Overview

The discussion revolves around the efficiency of waterwheels, specifically overshot waterwheels, and how the drop height of water affects their ability to convert potential energy into kinetic energy. Participants explore mathematical equations and concepts related to energy conversion, moment of inertia, and angular momentum.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant is investigating how the drop height of water influences the efficiency of an overshot waterwheel, linking it to potential and kinetic energy conversion.
  • Another suggests searching for information on hydro turbine efficiency and mentions the assumption of 100% efficiency as a starting point for calculations.
  • A participant points out that the design of a turbine, such as the Pelton Wheel, may change when kinetic energy becomes more significant than potential energy.
  • There is a discussion about the potential for extracting remaining kinetic energy from water exiting the wheel, with a suggestion to discharge water into a wider but slower wheel.
  • One participant expresses difficulty understanding the calculations related to moment of inertia and torque, indicating a learning curve with calculus.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the best approach to calculate efficiency or the optimal design for waterwheels. Multiple competing views and suggestions remain present in the discussion.

Contextual Notes

Some participants mention assumptions about efficiency and the need for further research into hydro turbine designs, indicating that the discussion may depend on specific definitions and conditions not fully explored.

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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