Definition:Imperial/Volume

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Definition

The imperial units of volume are based on a binary system, in which each unit is a factor of $2$ larger than the next smaller unit.

Fluid Ounce

The fluid ounce is an imperial unit of volume.

It is also part of the apothecaries' system of volume.

\(\ds \) \(\) \(\ds 1\) fluid ounce
\(\ds \) \(=\) \(\ds 8\) fluid drachms
\(\ds \) \(=\) \(\ds \dfrac 1 {20}\) (imperial) pint
\(\ds \) \(=\) \(\ds 28 \cdotp 41306 \, 25\) millilitres


Gill

\(\ds \) \(\) \(\ds 1\) gill
\(\ds \) \(=\) \(\ds 5\) fluid ounces
\(\ds \) \(=\) \(\ds 0 \cdotp 14206 \, 53125\) litres
\(\ds \) \(=\) \(\ds 142 \cdotp 06531 \, 25\) millilitres


Chopin

\(\ds \) \(\) \(\ds 1\) chopin
\(\ds \) \(=\) \(\ds 2\) gills
\(\ds \) \(=\) \(\ds 0 \cdotp 28413 \, 0625\) litres
\(\ds \) \(=\) \(\ds 284 \cdotp 13062 \, 5\) millilitres


Pint

The pint is an imperial unit of volume.

It is also part of the apothecaries' system of volume.

\(\ds \) \(\) \(\ds 1\) pint (imperial)
\(\ds \) \(=\) \(\ds 20\) fluid ounces
\(\ds \) \(=\) \(\ds 2\) chopins
\(\ds \) \(=\) \(\ds 0 \cdotp 5682 \, 6125\) litres
\(\ds \) \(=\) \(\ds 568 \cdotp 26125\) millilitres


Quart

\(\ds \) \(\) \(\ds 1\) quart (imperial)
\(\ds \) \(=\) \(\ds 2\) pints (imperial)
\(\ds \) \(=\) \(\ds 1 \cdotp 13652 25\) litres
\(\ds \) \(=\) \(\ds 1 \, 136 \cdotp 5225\) millilitres


Pottle

\(\ds \) \(\) \(\ds 1\) pottle
\(\ds \) \(=\) \(\ds 2\) quarts
\(\ds \) \(=\) \(\ds 2 \cdotp 273045\) litres
\(\ds \) \(=\) \(\ds 2 \, 273 \cdotp 045\) millilitres


Gallon

The (imperial) gallon is an imperial unit of volume.

It is defined as the volume of $10$ pounds of water under a specific set of conditions.

\(\ds \) \(\) \(\ds 1\) imperial gallon
\(\ds \) \(=\) \(\ds 2\) pottles
\(\ds \) \(=\) \(\ds 4\) quarts
\(\ds \) \(=\) \(\ds 277 \cdotp 4198\) cubic inches
\(\ds \) \(=\) \(\ds 0 \cdotp 1605\) cubic feet
\(\ds \) \(=\) \(\ds 4 \, 546 \cdotp 09\) millilitres
\(\ds \) \(=\) \(\ds 4 \cdotp 54609\) litres
\(\ds \) \(=\) \(\ds 4 \cdotp 54609 \times 10^{-3}\) cubic metres


Peck

\(\ds \) \(\) \(\ds 1\) peck
\(\ds \) \(=\) \(\ds 2\) (imperial) gallons
\(\ds \) \(=\) \(\ds 9 \cdotp 09218\) litres


Demi-Bushel

\(\ds \) \(\) \(\ds 1\) demi-bushel
\(\ds \) \(=\) \(\ds 2\) pecks
\(\ds \) \(=\) \(\ds 18 \cdotp 18436\) litres


Bushel

\(\ds \) \(\) \(\ds 1\) bushel
\(\ds \) \(=\) \(\ds 2\) demi-bushels
\(\ds \) \(=\) \(\ds 0 \cdotp 03636 \, 872\) cubic metres
\(\ds \) \(=\) \(\ds 36 \cdotp 36872\) litres


Kilderkin

\(\ds \) \(\) \(\ds 1\) kilderkin
\(\ds \) \(=\) \(\ds 2\) bushels
\(\ds \) \(=\) \(\ds 0 \cdotp 07273 \, 744\) cubic metres
\(\ds \) \(=\) \(\ds 72 \cdotp 73744\) litres


Barrel

\(\ds \) \(\) \(\ds 1\) barrel
\(\ds \) \(=\) \(\ds 2\) kilderkins
\(\ds \) \(=\) \(\ds 0 \cdotp 14547 \, 488\) cubic metres
\(\ds \) \(=\) \(\ds 145 \cdotp 47488\) litres


Hogshead

\(\ds \) \(\) \(\ds 1\) hogshead
\(\ds \) \(=\) \(\ds 2\) barrels
\(\ds \) \(=\) \(\ds 0 \cdotp 29094 \, 976\) cubic metres
\(\ds \) \(=\) \(\ds 290 \cdotp 94976\) litres


Pipe

\(\ds \) \(\) \(\ds 1\) pipe
\(\ds \) \(=\) \(\ds 2\) hogsheads
\(\ds \) \(=\) \(\ds 0 \cdotp 58189 \, 952\) cubic metres
\(\ds \) \(=\) \(\ds 581 \cdotp 89952\) litres


Tun

\(\ds \) \(\) \(\ds 1\) tun
\(\ds \) \(=\) \(\ds 2\) pipes
\(\ds \) \(=\) \(\ds 1 \cdotp 16379 \, 904\) cubic metres
\(\ds \) \(=\) \(\ds 1 \, 163 \cdotp 79904\) litres


Example

As the imperial volume measure are related by powers of two, it is possible to use them to express a volume as a binary number of gills.

Thus a volume equal to $3815$ gills is:

$1$ gill
$1$ chopin
$1$ pint
$0$ quarts
$0$ pottles
$1$ gallon
$0$ pecks
$1$ demi-bushel
$1$ bushel
$1$ kilderkin
$0$ barrels
$0$ hogsheads
$1$ pipe


Thus $3815$ gills can be expressed as:

$1001110100111$ gills in binary.


Sources