Water wheels and mathematical equation

In summary, the conversation discusses the topic of waterwheel efficiency in converting potential energy into kinetic energy. The speaker is trying to find a mathematical equation to explain the findings of their experiment on how the drop height of water affects the efficiency. They mention researching topics such as moment of inertia and angular momentum, and also suggest searching for information on hydro turbine efficiency and Pelton turbines. They also mention finding a website that explains the calculation of moment of inertia and torque, but are still struggling to understand the calculations due to limited knowledge in calculus. The conversation ends with a question about extracting the remaining kinetic energy from the water wheel.
  • #1
Nodir Musaev
2
0
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.
 
Physics news on Phys.org
  • #2
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
 
Last edited by a moderator:
  • Like
Likes Nodir Musaev
  • #3
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
 
Last edited by a moderator:
  • #4
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?
 

1. What is a water wheel?

A water wheel is a mechanical device that uses the energy of flowing water to power machinery or generate electricity. It is typically a large wheel or turbine that rotates when water flows over or under it.

2. How does a water wheel work?

A water wheel works by harnessing the kinetic energy of flowing water. The water strikes the blades of the wheel, causing it to rotate. The rotation of the wheel can then be used to power a variety of machinery or generate electricity.

3. What is the mathematical equation for calculating the power of a water wheel?

The mathematical equation for calculating the power of a water wheel is P = ρghQ, where P is power, ρ is the density of water, g is the acceleration due to gravity, h is the height of the water, and Q is the flow rate of the water.

4. How do factors like water flow rate and wheel diameter affect the power output of a water wheel?

The power output of a water wheel is directly affected by the flow rate of the water and the diameter of the wheel. A higher flow rate or larger wheel diameter will result in a greater power output, while a lower flow rate or smaller wheel diameter will result in a lower power output.

5. What are some real-world applications of water wheels and their mathematical equations?

Water wheels have been used for centuries to power various types of machinery, such as mills, sawmills, and water pumps. In modern times, water wheels are also used to generate electricity in hydroelectric power plants. The mathematical equations for water wheels are essential in designing and optimizing these systems for maximum efficiency.

Similar threads

I How to transfer angular momentum between two flywheels?
    • Mechanics
Replies
8
Views
2K
What is the moment of inertia for a water bottle?
    • Mechanics
Replies
5
Views
3K
I Why is momentum considered a vector and kinetic energy a scalar?
    • Mechanics
Replies
15
Views
2K
What would be the optimum torque/angular velocity for a waterwheel?
    • Mechanical Engineering
Replies
2
Views
1K
Making ancient time water wheel to lift water
    • Mechanics
Replies
23
Views
5K
I Question about a Rotating system with mass moving inwards
    • Mechanics
Replies
19
Views
1K
I How to interpret this definition of potential energy?
    • Mechanics
Replies
10
Views
952
I Question about transfer of Energy and Momentum in Ballistics
    • Mechanics
Replies
34
Views
2K
Confusion about tidal locking and rotational kinetic energy
    • Mechanics
Replies
3
Views
895
Energy of a water tank with compressed air
    • Introductory Physics Homework Help
Replies
5
Views
421

Hot Threads

Recent Insights

Back
Top