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The tun (Old English: tunne, Latin: tunellus, Medieval Latin: tunna) is an English unit of liquid volume (not weight), used for measuring wine, [1] oil or honey. Typically a large vat or vessel, most often holding 252 wine gallons, but occasionally other sizes (e.g. 256, 240 and 208 gallons) were also used. [2] The modern tun is about 954 litres.
[nb 2] Note that a 252-gallon tun of wine has a mass of approximately 2060 pounds, [6] between a short ton (2000 pounds) and a long ton (2240 pounds). The tun is approximately the volume of a cylinder with both diameter and height of 42 inches, as the gallon was originally a cylinder with diameter of 7 inches and height of 6.
The wine gallon, which some sources relate to the volume occupied by eight medieval merchant pounds of wine, was at one time defined as the volume of a cylinder 6 inches deep and 7 inches in diameter, i.e. 6 in × (3 + 1 / 2 in) 2 × π ≈ 230.907 06 cubic inches.
It is a holdover from when spirits, wines and brandies, ale, and beer all had different standard measures of capacity. An Ale Gill (based on the Ale gallon) and a Beer Gill (based on the Beer gallon) were different sizes until standardized as Ale / Beer gallons in 1688, Beer gallons in 1803, and Imperial gallons in 1824. Half (imp.) 284 mL
For a given volume, the right circular cylinder with the smallest surface area has h = 2r. Equivalently, for a given surface area, the right circular cylinder with the largest volume has h = 2r, that is, the cylinder fits snugly in a cube of side length = altitude ( = diameter of base circle). [8]
Some SI units of volume to scale and approximate corresponding mass of water. To ease calculations, a unit of volume is equal to the volume occupied by a unit cube (with a side length of one). Because the volume occupies three dimensions, if the metre (m) is chosen as a unit of length, the corresponding unit of volume is the cubic metre (m 3).
The Winchester bushel is the volume of a cylinder 18.5 in (470 mm) in diameter and 8 in (200 mm) high, which gives an irrational number of approximately 2150.4202 cubic inches. [4] The modern American or US bushel is a variant of this, rounded to exactly 2150.42 cubic inches, less than one part per ten million less. [ 5 ]
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 ...