What would be the optimum torque/angular velocity for a waterwheel?

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In summary, the conversation involves designing a pitchback waterwheel with a head of 1m and flow rate of 20l/min. The theoretical power available is 3.27W and the mechanical power is the product of torque and angular velocity. The optimum rotational speed for overshot wheels is 21/√D, but it is unclear if this applies to pitchback wheels as well. It is also unclear if higher torque is better for waterwheels. The goal is to maximize efficiency and a manual by William G. Ovens is recommended for further research on calculating losses and analyzing forces.
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I am designing a pitchback waterwheel for a head of 1m and flow rate of 20l/min. I've calculated that the theoretical power available to me is 3.27W and I know that the mechanical power I can extract is the product of torque and angular velocity but I'm struggling to find information on optimum torques/angular velocities. I've read online that overshot wheeels have an optimum rotational speed of 21/√D (where does this come from?) but would that be the same for pitchback too since I've heard they're quite similar? Is higher torque better for waterwheels? Also, I want to maximise the efficiency of the waterwheel so could anyone link me to an article that lists how to calculate losses in the various components and analyzes the forces acting on it? Thanks for the help.
 
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1. What is torque and angular velocity?

Torque is a measure of the force that causes an object to rotate around an axis. It is often described as a twisting or turning force. Angular velocity, on the other hand, is the rate of change of an object's angular position over time. It is measured in radians per second.

2. How do torque and angular velocity affect a waterwheel?

The torque and angular velocity of a waterwheel are important factors in determining its efficiency and power output. A higher torque allows the waterwheel to rotate with more force, while a higher angular velocity allows it to rotate faster. The optimum combination of torque and angular velocity will depend on the specific design and purpose of the waterwheel.

3. What factors influence the optimum torque and angular velocity for a waterwheel?

The optimum torque and angular velocity for a waterwheel can be influenced by several factors, including the volume and speed of the water flow, the size and shape of the waterwheel, and the load or resistance placed on the waterwheel.

4. How can the optimum torque and angular velocity be calculated for a waterwheel?

There are various mathematical equations and simulations that can be used to calculate the optimum torque and angular velocity for a waterwheel. These calculations often take into account the specific design and operating conditions of the waterwheel.

5. Can the optimum torque and angular velocity change over time?

Yes, the optimum torque and angular velocity for a waterwheel can change over time due to various factors such as changes in water flow, wear and tear on the waterwheel, and changes in the load or resistance. Regular maintenance and adjustments may be necessary to maintain the optimum performance of a waterwheel.

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