Archimedes' screw

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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 is one of several inventions and discoveries reputed to have been made by Archimedes, though writings about the Hanging Gardens of Babylon hint that a similar device was used by the Mesopotamians as early as 600 BC – over 300 years before his birth.

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1 Workings
2 Uses
3 Mathematics behind the screw
4 See also
5 External links

[edit] Workings

Image:Archimedes' screw.jpg

Archimedes' screw

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 lower end of the device is put in the water, and the screw is then turned (usually by a windmill or by manual labor). 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 interface between 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 Sennacherib'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.

The design of the everyday Greek and Roman water screw, in contrast to the heavy bronze device of Sennacherib, with its problematic drive chains, has a powerful simplicity. A double or triple helix was built of wood strips (or occasionally bronze sheeting) around a heavy wooden pole. A cylinder was built around the helices using long, narrow boards fastened to their periphery and waterproofed with pitch

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[edit] Uses

Along with transferring water to irrigation ditches, this device was also used for "stealing" land from under sea level in the Netherlands. Since the primary objective in this case is to lift water to a given height rather than simply move it from a river to the irrigation field, more than one machine was used to successively lift the same water volume, due to the limitations of this machine.

[edit] 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 63.435°) 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°.

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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

[edit] See also

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Archimedes' screw

[edit] External links

Technology and Culture Volume 44, Number 1, January 2003 (PDF) Dalley, Stephanie. Oleson, John Peter. "Sennacherib, Archimedes, and the Water Screw: The Context of Invention in the Ancient World"