Physics and Archimedes Screw

Mechanical advantage is the ratio of the amount of force applied to a machine over the force exerted or output created by the machine. The force applied to the machine is the amount of force that you put on the machine. For example, if you were riding a bike, the amount of force you use to push the pedals to make the bike go would be the force applied to the machine, or in this case, the bike. The force exerted by the machine is the force that the machine creates or produces. For example, if you were riding a bike, the exerted force would be the wheels of the bike turning and moving the bike.

If you were to apply Archimedes’ Screw to mechanical advantage, it would be explained as follows: The force applied to the screw would be the force you use to turn the handle of the screw. The force exerted by the machine would be the force with which the screw turns and pushes water.

 Mechanical Advantage can be expressed in the following equation:

Fr* pitch = Fe*2πr

Pitch= space (distance) between blades, Fr= amount of force machine puts out (output), Fe= amount of force you put in (input), 2πr = The Circumference of the Screw.
           
 In this equation Fr is directly proportional to pitch, also, Fe is directly proportional to 2πr.

Example Problem 1:
           
 A greek slave is using Archimedes Screw to help irigate the plants. How much water would he transport in one rotation of Archimedes screw assuming each rotation has a full amount of water? Also knowing the radius of the screw is 2m and the mecanical advantage is 15.

Equation:

If we are trying to find how much water Archimedes Screw would carry in one rotation of the screw, we would use a modified equation for the volume of a cylinder. When V= volume.9

V of water in one rotation = πr^2pitch

Solve:

The first thing we need to find is the pitch and to find the pitch we need to find Se using this equation:

Se= 2πr

and we know that r = 2 meters (2m) so,

Se=(2π) (2m)→ 4π m = Se

Now using this information we can plug it into the following equation, also knowing that the Mechanical 
Advantage is 15.

MA= 15 = Fe/pitch → 15= 4π m/ pitch

Multiply both sides by pitch and divide both sides by 15 you get,

Pitch= 4π/15m

Now using this information we can find the volume of one rotation with this equation,

Vrotation = πr^2pitch → π(2m)^2(4π/15m)

Which equals:

V of water in one rotation = 16π^2/15m^3

A big part of mechanical advantage is efficiency. In the example problem we did not include efficiency to make it more simple. Efficiency is the work you put in divided by the work that comes out multiplied by 100%. This can be shown in the following equation:

Efficeincy = Work in/Work out x 100%.

 When talking about efficiency you want it to be high, like 70-100%, meaning you get out most of the work you put in. The higher the percentage, the better the efficiency. This relates to Archimedes’ Screw because the screw itself is inside a tube to ensure that whatever is being transported doesn’t fall out. When the blades of the screw turn they rub up against the casing which lowers the efficiency because of friction.