# Electricity generator - wheel and axle advantage effect on power generation

#### humptydumptyaac

Joined Nov 3, 2021
24
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.

#### AlbertHall

Joined Jun 4, 2014
12,023
• humptydumptyaac

#### Ya’akov

Joined Jan 27, 2019
5,666
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.]

Last edited:
• humptydumptyaac

#### BobTPH

Joined Jun 5, 2013
4,923
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

• humptydumptyaac

#### humptydumptyaac

Joined Nov 3, 2021
24
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.

• Ya’akov

#### humptydumptyaac

Joined Nov 3, 2021
24
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.

#### Alec_t

Joined Sep 17, 2013
12,817
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.