Editing Archimedes' screw (section)

== Design ==
The Archimedes screw consists of a screw (a [[helicoid|helical]] surface surrounding a central cylindrical shaft) inside a hollow pipe. The screw is usually turned by windmill, manual labor, cattle, or by modern means, such as a motor. As the shaft turns, the bottom end scoops up a volume of water. This water is then pushed up the tube by the rotating helicoid until it pours out from the top of the tube.

The contact surface between the screw and the pipe does not need to be perfectly watertight, as long as the amount of water being scooped with each turn is large compared to the amount of water leaking out of each section of the screw per turn. If water from one section leaks into the next lower one, it will be transferred upwards by the next segment of the screw.

In some designs, the screw is fused to the casing and they both rotate together, instead of the screw turning within a stationary casing. The screw could be sealed to the casing with pitch resin or other adhesive, or the screw and casing could be cast together as a single piece in bronze.

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.<ref name="DO" />

Studies show that the volume of flow passes through Archimedes screws is a function of inlet depth, diameter and rotation speed of the screw. Therefore, the following analytical equation could be used to design Archimedes screws:

<math>D_O =\sqrt[3]{\frac{16\pi Q}{\sigma\omega (2\theta_O-sin2\theta_O-\delta^2(2\theta_i-sin(2\theta_i))}}</math>

where <math>D_O</math> is in <math>(m)</math> and:

<math>\omega</math>: Rotation speed of the Archimedes screw (rad/s)

<math>Q</math>: Volumetric flow rate <math>(m^3/s)</math>

Based on the common standards that the Archimedes screw designers use this analytical equation could be simplified as:<ref name=":4">{{Cite journal|last1=YoosefDoost|first1=Arash|last2=Lubitz|first2=William David|date=December 2021|title=Design Guideline for Hydropower Plants Using One or Multiple Archimedes Screws|journal=Processes|language=en|volume=9|issue=12|pages=2128|doi=10.3390/pr9122128|doi-access=free}}</ref>

<math>D_O\approx \eta Q^{3/7}</math>

The value of η could simply determinate using the <math>\eta</math> graph or <math>\Theta</math> graph.<ref name=":4" /> By determination of <math>D_O</math>, other design parameters of Archimedes screws can be calculated using a step-by-step analytical method.