Archimedes' screw

  The Archimedes' screw, Archimedean screw, or screwpump, is a machine historically used for transferring water from a low-lying body of water into irrigation ditches. It was one of several inventions and discoveries traditionally attributed to Archimedes in the 3rd century BC.

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Workings

  The machine consists of a screw inside a hollow pipe. A screw can be thought of as an inclined plane (another simple machine) wrapped around a cylinder.

The screw is turned (usually by a windmill or by manual labour). As the bottom end of the tube turns, it scoops up a volume of water. This amount of water will slide up in the spiral tube as the shaft is turned, until it finally pours out from the top of the tube and feeds the irrigation systems.

The contact surface between are the screw and the pipe does not need to be perfectly water-tight because of the relatively large amount of water being scooped at each turn in respect to the angular speed of the screw. Also, water leaking from the top section of the screw leaks into the previous one and so on, so a sort of equilibrium is achieved while using the machine, thus preventing a decrease in efficiency.

The "screw" does not necessarily need to turn inside the casing, but can be allowed to turn with it in one piece. A screw could be sealed with pitch or some other adhesive to its casing, or, cast as a single piece in bronze, as some researchers have postulated as being the devices used to irrigate Nebuchadnezzar II's Hanging Gardens of Babylon. Depictions of Greek and Roman water screws show the screws being powered by a human treading on the outer casing to turn the entire apparatus as one piece, which would require that the casing be rigidly attached to the screw.

  Along with transferring water to irrigation ditches, this device was also used for "stealing" land from under sea level in the Netherlands and other places in the creation of polders. A part of the sea would be enclosed and the water would be pushed up out of the enclosed area, starting the process of draining the land for use in farming. Depending on the length and diameter of the screws, more than one machine could be used to successively lift the same water.

Archimedes' screws are used in sewage treatment plants because they cope well with varying rates of flow and with suspended solids. An auger in a snow blower or grain elevator is essentially an Archimedes' screw.

The principle is also found in pescalators, which are Archimedes screws designed to lift fish safely from ponds and transport them to another location. This technology is primarily used at fish hatcheries, where it is desirable to minimize the physical handling of fish.

Mathematics behind the screw

The slope of the outside of the screw's helical blades with respect to its sides is 2. This requires that the slope the screw makes with respect to a horizontal line be less than 2 (an angle of 63°) in order for the buckets or pockets of water to form. In the profile of the screw, the projection of each helical blade consists of two sinusoidal curves with the same periods and phases. One has an amplitude equal to the radius of the outer cylinder and the other has an amplitude equal to the radius of the inner cylinder. The horizontal water level of each full bucket of water is tangent to the inner sinusoidal curve. Thus, if the equation on the inner sinusoidal curve is y = sin x, then the water level is tangent to it at x = arccos(−3/4) = 138.59°.

d = diameter of centre tube

D = diameter of blades

β = angle of installation

H₀ = civil head

H₁ = difference of medium levels, effective head

H₂ = maximum difference of medium levels, delivery head

H₃ = hydraulic head

J = number of flights

L = length of helix

S = rise

References

• "Archimedean Screw" by Sándor Kabai, The Wolfram Demonstrations Project, 2007.

• The Turn of the Screw: Optimal Design of an Archimedes Screw, by Chris Rorres, PhD.

• Plywood archimedean screw water pump , how to build a functioning Archimedes' screw pump