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The equilateral cylinder is characterized by being a right circular cylinder in which the diameter of the base is equal to the value of the height (geratrix). [ 4 ] Then, assuming that the radius of the base of an equilateral cylinder is r {\displaystyle r\,} then the diameter of the base of this cylinder is 2 r {\displaystyle 2r\,} and its ...
Having a constant diameter, measured at varying angles around the shape, is often considered to be a simple measurement of roundness.This is misleading. [3]Although constant diameter is a necessary condition for roundness, it is not a sufficient condition for roundness: shapes exist that have constant diameter but are far from round.
If the elements of the cylinder are perpendicular to the planes containing the bases, the cylinder is a right cylinder, otherwise it is called an oblique cylinder. If the bases are disks (regions whose boundary is a circle) the cylinder is called a circular cylinder. In some elementary treatments, a cylinder always means a circular cylinder. [2]
The hydraulic diameter, D H, is a commonly used term when handling flow in non-circular tubes and channels. Using this term, one can calculate many things in the same way as for a round tube. When the cross-section is uniform along the tube or channel length, it is defined as [1] [2] =, where
The term circumference is used when measuring physical objects, as well as when considering abstract geometric forms. When a circle's diameter is 1, its circumference is . When a circle's radius is 1—called a unit circle—its circumference is .
For the thin-walled assumption to be valid, the vessel must have a wall thickness of no more than about one-tenth (often cited as Diameter / t > 20) of its radius. [4] This allows for treating the wall as a surface, and subsequently using the Young–Laplace equation for estimating the hoop stress created by an internal pressure on a thin-walled cylindrical pressure vessel:
Proposition one states: The area of any circle is equal to a right-angled triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference of the circle. Any circle with a circumference c and a radius r is equal in area with a right triangle with the two legs being c and r.
For all these radius ratios a compact packing is known that achieves the maximum possible packing fraction (above that of uniformly-sized discs) for mixtures of discs with that radius ratio. [9] All nine have ratio-specific packings denser than the uniform hexagonal packing, as do some radius ratios without compact packings.