Hi,

I used to think that a water wheel with 100 l/s of water would produce 98 watts theoretical, considering that I was told 1 kg of mass going down would produce 9.8 watts.

Recently I discovered the wheel and axle mechanical advantage which causes me to re-think what I know (because it doesn't make sense)

If we have a wheel that's 100 cm in diameter, and an axle of 1 cm in diameter, according to the internet - the power amplification at the axle would be 100 times.

If we have a generator connected to the axle it would be turned with that amplified force. That would mean that 1 liter of water acting on the wheel would create the force of 100 liters to the generator.

And therefore, 100 l/s of water on the wheel would create the force of 10,000 liters of water at the axle and generator, and then create 98 kW of power theoretical.

Which seems too much to be true.

So I'm trying to understand how does the wheel and axle mechanical advantage affect electrical power production, and in the example above - on a wheel of 100 cm diameter, axle 1 cm diameter, 100 l/s water flow, how much watt power would that produce? (I'm stuck between 98 watts and 98 kW)

Thank you.

 

If we have a wheel that's 100 cm in diameter, and an axle of 1 cm in diameter, according to the internet - the power amplification at the axle would be 100 times.

The power is not amplified. 100W in would still be 100W out (less the inevitable losses).
Read this: https://www.khanacademy.org/science/physics/torque-angular-momentum/torque-tutorial/a/torque

 

A general rule, which is a very easy way to test something like this, is to look for some additional input of energy. If there is none there can be no amplification

This is an inviolable rule..Amplification is using a small signal or force to control a larger one in proportion. Without an additional input of power you can trade off between volume and pressure, or current and voltage, or distance and force.

For example, a nozzle on a hose reduces flow and increases pressure; a transformer can raise a voltage if current is reduced, or vice versa; and a lever can allow lifting more weight but requires trading distance. In each case the total of the energy oin the system—power which can be expressed in Watts—can never increase and in fact must decrease due to frictional losses, that power becomes heat.

So you don’t have to know too much to vet something like this. If there is no second poser source to control you can’t have amplification, only conversion.

[EDIT: Fixed a little confused wording, I hope.]

 

Work (energy) is force times distance. You have multiplied the force by 100 but divided the distance by 100. So there is no change in energy.

Bob

 

The power is not amplified. 100W in would still be 100W out (less the inevitable losses).
Read this: https://www.khanacademy.org/science/physics/torque-angular-momentum/torque-tutorial/a/torque

Thank you for the link, Albert.

 

A general rule, which is a very easy way to test something like this, is to look for some additional input of energy. If there is none there can be no amplification

This is an inviolable rule..Amplification is using a small signal or force to control a larger one in proportion. Without an additional input of power you can trade off between volume and pressure, or current and voltage, or distance and force.

For example, a nozzle on a hose reduces flow and increases pressure; a transformer can raise a voltage if current is reduced, or vice versa; and a lever can allow more force but requires trading distance. In each case the total of the energy oin the system—power which can be expressed in Watts—can never increase and in fact must decrease due to frictional losses, that power becomes heat.

So you don’t have to know too much to vet something like this. If there is no second poser source to control you can’t have amplification, only conversion.

Thank you, Yaakov. I knew it was too good to be true, it just had me confused for a moment so I wanted to confirm what I knew.

 

Work (energy) is force times distance. You have multiplied the force by 100 but divided the distance by 100. So there is no change in energy.

Bob

Thank you, Bob.

 

according to the internet - the power amplification at the axle would be 100 times.

The internet is wrong. A force at the wheel rim would indeed be multiplied at the axle rim, but the torque and power remain the same.

 

The internet is wrong. A force at the wheel rim would indeed be multiplied at the axle rim, but the torque and power remain the same.

Force is amplified over a shorter distance as a trade off. Yet, this allows more mass to be rotated without becoming an additional load to the input. As long as input continues running amplified output continues to drive more mass of stored energy turning it into rotational kinetic energy. Mass here could be a generator that is about 20% less than the amplification value.

 

Hi,

I used to think that a water wheel with 100 l/s of water would produce 98 watts theoretical, considering that I was told 1 kg of mass going down would produce 9.8 watts.

Recently I discovered the wheel and axle mechanical advantage which causes me to re-think what I know (because it doesn't make sense)

If we have a wheel that's 100 cm in diameter, and an axle of 1 cm in diameter, according to the internet - the power amplification at the axle would be 100 times.

If we have a generator connected to the axle it would be turned with that amplified force. That would mean that 1 liter of water acting on the wheel would create the force of 100 liters to the generator.

And therefore, 100 l/s of water on the wheel would create the force of 10,000 liters of water at the axle and generator, and then create 98 kW of power theoretical.

Which seems too much to be true.

So I'm trying to understand how does the wheel and axle mechanical advantage affect electrical power production, and in the example above - on a wheel of 100 cm diameter, axle 1 cm diameter, 100 l/s water flow, how much watt power would that produce? (I'm stuck between 98 watts and 98 kW)

Thank you.

As long as you have input running you will have amplified force at the axle. How to use that is an engineering solution. Cheers!

 

I used to think that a water wheel with 100 l/s of water would produce 98 watts theoretical, considering that I was told 1 kg of mass going down would produce 9.8 watts.

This statement already has holes in it. You can't tell how much energy, even in the limit, is transferred to a water wheel based solely on the total flow rate of water through it.

A one kilogram mass dropping through one meter will convert 9.8 N·m of gravitational potential energy into some of other form of energy. Your description gives no indication of the height through which this water is dropping. That is a critical value.

On top of that, there are other forms of energy that need to be taken into consideration. One in particular is the kinetic energy of the water at the point where the water starts out and at the bottom where it exits the wheel. It will almost certainly have considerably more kinetic energy at the bottom and that energy also came from the gravitational potential energy and is thus not available for extraction.

Then there is the efficiency, which varies widely with different designs and can easily be less than 10% or, with very careful design, in the range of 90%.

Recently I discovered the wheel and axle mechanical advantage which causes me to re-think what I know (because it doesn't make sense)

If we have a wheel that's 100 cm in diameter, and an axle of 1 cm in diameter, according to the internet - the power amplification at the axle would be 100 times.

If we have a generator connected to the axle it would be turned with that amplified force. That would mean that 1 liter of water acting on the wheel would create the force of 100 liters to the generator.

And therefore, 100 l/s of water on the wheel would create the force of 10,000 liters of water at the axle and generator, and then create 98 kW of power theoretical.

Which seems too much to be true.

So I'm trying to understand how does the wheel and axle mechanical advantage affect electrical power production, and in the example above - on a wheel of 100 cm diameter, axle 1 cm diameter, 100 l/s water flow, how much watt power would that produce? (I'm stuck between 98 watts and 98 kW)

You are confusing mechanical advantage with power amplification. Mechanical advantage is a ratio of forces (or torques), not ratios of powers. You are limited by the power available, so doing something that increases the force/torque is going to have a corresponding change in something else (usually the speed) such that the power remains the same (or, in practice, drops a bit because of inevitable inefficiencies).

 

If we have a wheel that's 100 cm in diameter, and an axle of 1 cm in diameter, according to the internet - the power amplification at the axle would be 100 times.

The force is amplified 100 times.
But the speed is reduced by a factor of 100.
Power = Force * Speed.
. . . so it remains the same.

Think about gears. When you change down a gear to go up a hill, you use the same amount of power, there is more force required to overcome the force of gravity pushing you back down the hill, but you climb the hill at a slower speed.