Archimedes' screw 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
Archimedes and the Cylinder I, II", "On Spirals", "On Conoids and Spheroids", "On Floating Bodies I, II", "On the Measurement of a Circle", "The Sand Reckoner". c. Boyer, Carl Benjamin "A History of Mathematics" (1991) "Arabic scholars inform us that the familiar area formula for a triangle in terms of its three sides, usually known as Heron's formula — "k" = , where "s" is the semiperimeter — was known to Archimedes several centuries before Heron lived. Arabic scholars also attribute to Archimedes the 'theorem on the broken chord' ... Archimedes is reported by the Arabs to have given several proofs