Copyright | Copyright (C) 2006-2018 Bjorn Buckwalter |
---|---|
License | BSD3 |
Maintainer | bjorn@buckwalter.se |
Stability | Stable |
Portability | GHC only |
Safe Haskell | None |
Language | Haskell2010 |
Summary
This module defines units that are not part of the SI, with the exception of those defined in the Numeric.Units.Dimensional.SIUnits module (units outside of the SI accepted for use with the SI).
Any chapters, sections or tables referenced are from [1] unless otherwise specified.
Neper, bel, shannon and the like
The units of section 5.1.2 are purposefully (but not permanently) omitted. In fact the logarithmic units (see section 8.7) are problematic and it is not clear how to implement them. Perhaps with a conversion function similar to for degrees Celsius.
References
- electronVolt :: Floating a => Unit Metric DEnergy a
- unifiedAtomicMassUnit :: Floating a => Unit Metric DMass a
- dalton :: Floating a => Unit Metric DMass a
- gee :: Fractional a => Unit Metric DAcceleration a
- poundMass :: Fractional a => Unit NonMetric DMass a
- ounce :: Fractional a => Unit NonMetric DMass a
- poundForce :: Fractional a => Unit NonMetric DForce a
- horsepower :: Fractional a => Unit NonMetric DPower a
- btu :: Fractional a => Unit NonMetric DEnergy a
- shortTon :: Fractional a => Unit NonMetric DMass a
- nauticalMile :: Num a => Unit NonMetric DLength a
- knot :: Fractional a => Unit NonMetric DVelocity a
- revolution :: Floating a => Unit NonMetric DOne a
- solid :: Floating a => Unit NonMetric DOne a
- slug :: Fractional a => Unit NonMetric DMass a
- psi :: Fractional a => Unit NonMetric DPressure a
- teaspoon :: Fractional a => Unit NonMetric DVolume a
- foot :: Fractional a => Unit NonMetric DLength a
- inch :: Fractional a => Unit NonMetric DLength a
- mil :: Fractional a => Unit NonMetric DLength a
- yard :: Fractional a => Unit NonMetric DLength a
- mile :: Fractional a => Unit NonMetric DLength a
- acre :: Fractional a => Unit NonMetric DArea a
- usSurveyFoot :: Fractional a => Unit NonMetric DLength a
- usSurveyInch :: Fractional a => Unit NonMetric DLength a
- usSurveyMil :: Fractional a => Unit NonMetric DLength a
- usSurveyYard :: Fractional a => Unit NonMetric DLength a
- usSurveyMile :: Fractional a => Unit NonMetric DLength a
- usSurveyAcre :: Fractional a => Unit NonMetric DArea a
- year :: Num a => Unit NonMetric DTime a
- century :: Num a => Unit NonMetric DTime a
- bar :: Num a => Unit Metric DPressure a
- atmosphere :: Num a => Unit NonMetric DPressure a
- technicalAtmosphere :: Fractional a => Unit NonMetric DPressure a
- mmHg :: Fractional a => Unit NonMetric DPressure a
- inHg :: Fractional a => Unit NonMetric DPressure a
- inHg_UCUM :: Fractional a => Unit NonMetric DPressure a
- inHg_NIST :: Fractional a => Unit NonMetric DPressure a
- torr :: Fractional a => Unit NonMetric DPressure a
- rad :: Fractional a => Unit Metric DAbsorbedDose a
- stokes :: Fractional a => Unit Metric DKinematicViscosity a
- degreeFahrenheit :: Fractional a => Unit NonMetric DThermodynamicTemperature a
- degreeRankine :: Fractional a => Unit NonMetric DThermodynamicTemperature a
- imperialGallon :: Fractional a => Unit NonMetric DVolume a
- imperialQuart :: Fractional a => Unit NonMetric DVolume a
- imperialPint :: Fractional a => Unit NonMetric DVolume a
- imperialCup :: Fractional a => Unit NonMetric DVolume a
- imperialGill :: Fractional a => Unit NonMetric DVolume a
- imperialFluidOunce :: Fractional a => Unit NonMetric DVolume a
- usGallon :: Fractional a => Unit NonMetric DVolume a
- usQuart :: Fractional a => Unit NonMetric DVolume a
- usPint :: Fractional a => Unit NonMetric DVolume a
- usCup :: Fractional a => Unit NonMetric DVolume a
- usGill :: Fractional a => Unit NonMetric DVolume a
- usFluidOunce :: Fractional a => Unit NonMetric DVolume a
- angstrom :: Fractional a => Unit NonMetric DLength a
- gauss :: Fractional a => Unit NonMetric DMagneticFluxDensity a
Units Defined By Experiment
From Table 7, units accepted for use with the SI whose values in SI units are obtained experimentally.
When [1] was published the electron volt had a standard combined uncertainity of 0.00000049e-19 J and the unified atomic mass unit had a combined uncertainty of 0.0000010e-27 kg.
Standard Gravity
gee :: Fractional a => Unit Metric DAcceleration a Source #
One gee is the standard value of the acceleration due to gravity at the Earth's surface, as standardized by CIPM.
Note that local values of acceleration due to gravity will differ from the standard gravity.
See here for further information.
>>>
1 *~ gee
9.80665 m s^-2
>>>
1 *~ gee :: Acceleration Rational
196133 % 20000 m s^-2
Inch-pound Units
Some US customary (that is, inch-pound) units.
poundMass :: Fractional a => Unit NonMetric DMass a Source #
One avoirdupois pound is a mass, exactly defined in terms of the kilogram by the international yard and pound agreement of 1959.
See here for further information.
>>>
1 *~ poundMass
0.45359237 kg
>>>
1 *~ poundMass :: Mass Rational
45359237 % 100000000 kg
poundForce :: Fractional a => Unit NonMetric DForce a Source #
The pound-force is equal to the gravitational force exerted on a mass of one avoirdupois pound on the surface of Earth.
This definition is based on standard gravity (the gee
) and the
international avoirdupois poundMass
.
See here for further information.
>>>
1 *~ poundForce
4.4482216152605 m kg s^-2
1 *~ poundForce === 1 *~ poundMass * (1 *~ gee)
>>>
1 *~ poundForce :: Force Rational
8896443230521 % 2000000000000 m kg s^-2
horsepower :: Fractional a => Unit NonMetric DPower a Source #
One mechanical horsepower is by definition the power necessary
to apply a force of 550 poundForce
through a distance of one foot
per second
.
See here for further information.
>>>
1 *~ horsepower
745.6998715822702 m^2 kg s^-3
1 *~ horsepower === 550 *~ poundForce * (1 *~ foot) / (1 *~ second)
>>>
1 *~ horsepower :: Power Rational
37284993579113511 % 50000000000000 m^2 kg s^-3
btu :: Fractional a => Unit NonMetric DEnergy a Source #
One btu is is the QuantityOfHeat
required to raise the temperature
of 1 avoirdupois poundMass
of liquid water by 1 degreeFahrenheit
at a constant pressure of one atmosphere
.
Because this value must be determined experimentally and varies with temperature, several standardized values of the btu have arisen. This is the value based on the International Steam Table calorie, defined by the Fifth International Conference on the Properties of Steam.
See here for further information.
>>>
1 *~ btu
1055.05585262 m^2 kg s^-2
>>>
1 *~ btu :: Energy Rational
52752792631 % 50000000 m^2 kg s^-2
nauticalMile :: Num a => Unit NonMetric DLength a Source #
One nautical mile is a unit of length, set by international agreement as being exactly 1 852 meters.
Historically, it was defined as the distance spanned by one minute of arc along a meridian of the Earth.
See here for further information.
>>>
1 *~ nauticalMile
1852.0 m
>>>
1 *~ nauticalMile :: Length Rational
1852 % 1 m
knot :: Fractional a => Unit NonMetric DVelocity a Source #
One knot is a velocity equal to one nauticalMile
per hour
.
See here for further information.
>>>
1 *~ knot
0.5144444444444445 m s^-1
>>>
1 *~ knot :: Velocity Rational
463 % 900 m s^-1
revolution :: Floating a => Unit NonMetric DOne a Source #
One revolution is an angle equal to 2 pi radians; a full circle.
See here for further information.
>>>
1 *~ revolution
6.283185307179586
1 *~ revolution === _2 * pi * (1 *~ radian)
1 *~ revolution === 360 *~ degree
slug :: Fractional a => Unit NonMetric DMass a Source #
The slug is a unit of mass associated with Imperial units and United States customary units. It is a mass that accelerates by 1 foot per second per second when a force of one pound is exerted on it.
This definition is based on standard gravity (the gee
), the international foot
, and the international avoirdupois poundMass
.
See here for further information.
>>>
1 *~ slug
14.593902937206364 kg
>>>
1 *~ slug :: Mass Rational
8896443230521 % 609600000000 kg
psi :: Fractional a => Unit NonMetric DPressure a Source #
One psi is a pressure of one poundForce
per square
inch
of area.
See here for further information.
>>>
1 *~ psi
6894.757293168362 m^-1 kg s^-2
>>>
1 *~ psi :: Pressure Rational
8896443230521 % 1290320000 m^-1 kg s^-2
International Foot
acre :: Fractional a => Unit NonMetric DArea a Source #
One acre is 43 560 square feet.
This acre is based on the international foot
. For the acre based on the US Survey Foot,
see usSurveyAcre
. While both acres are in use, the difference between them is of little consequence
for most applications in which either is used.
See here for further information.
>>>
1 *~ acre
4046.8564224 m^2
1 *~ acre === 43560 *~ foot ^ pos2
>>>
1 *~ acre :: Area Rational
316160658 % 78125 m^2
US Survey Foot
usSurveyFoot :: Fractional a => Unit NonMetric DLength a Source #
usSurveyInch :: Fractional a => Unit NonMetric DLength a Source #
One inch is one twelth of a foot.
This inch is based on the usSurveyFoot
. For the inch based on the international foot,
see inch
. Note that this is not the inch in routine use in the United States.
See here for further information.
>>>
1 *~ usSurveyInch
2.54000508001016e-2 m
12 *~ usSurveyInch === 1 *~ usSurveyFoot
>>>
1 *~ usSurveyInch :: Length Rational
100 % 3937 m
usSurveyMil :: Fractional a => Unit NonMetric DLength a Source #
One mil is one thousandth of an inch.
This mil is based on the usSurveyInch
. For the mil based on the international inch,
see mil
. Note that this is not the mil in routine use in the United States.
See here for further information.
>>>
1 *~ usSurveyMil
2.54000508001016e-5 m
1000 *~ usSurveyMil === 1 *~ usSurveyInch
>>>
1 *~ usSurveyMil :: Length Rational
1 % 39370 m
usSurveyYard :: Fractional a => Unit NonMetric DLength a Source #
One yard is three feet.
This yard is based on the usSurveyFoot
. For the international yard,
see yard
. Note that this is not the yard in routine use in the United States.
See here for further information.
>>>
1 *~ usSurveyYard
0.9144018288036576 m
1 *~ usSurveyYard === 3 *~ usSurveyFoot
>>>
1 *~ usSurveyYard :: Length Rational
3600 % 3937 m
usSurveyMile :: Fractional a => Unit NonMetric DLength a Source #
One US survey mile is 5 280 US survey feet.
This mile is based on the usSurveyFoot
. For the mile based on the international foot,
see mile
. Note that this is not the mile in routine use in the United States.
See here for further information.
>>>
1 *~ usSurveyMile
1609.3472186944373 m
1 *~ usSurveyMile === 5280 *~ usSurveyFoot
>>>
1 *~ usSurveyMile :: Length Rational
6336000 % 3937 m
usSurveyAcre :: Fractional a => Unit NonMetric DArea a Source #
One acre is 43 560 square feet.
This acre is based on the usSurveyFoot
. For the acre based on the international foot,
see acre
. While both acres are in use, the difference between them is of little consequence
for most applications in which either is used. This is the only acre defined by the UCUM.
See here for further information.
>>>
1 *~ usSurveyAcre
4046.872609874252 m^2
1 *~ usSurveyAcre === 43560 *~ usSurveyFoot ^ pos2
>>>
1 *~ usSurveyAcre :: Area Rational
62726400000 % 15499969 m^2
Years
The IAU recommends [2] that:
Although there are several different kinds of year (as there are several kinds of day), it is best to regard a year as a julian year of 365.25 days (31.5576 Ms) unless otherwise specified.
century :: Num a => Unit NonMetric DTime a Source #
One mean Julian century is one hundred mean Julian year
s.
>>>
1 *~ century
3.15576e9 s
>>>
1 *~ century :: Time Rational
3155760000 % 1 s
Pressure Units
It seems that nearly every area of application has its own customary unit for measuring pressure.
We include some of the common ones here. psi
was defined earlier.
bar :: Num a => Unit Metric DPressure a Source #
The bar is exactly 100 000 pascal
.
From Wikipedia:
It is about equal to the atmospheric pressure on Earth at sea level.
>>>
1 *~ bar
100000.0 m^-1 kg s^-2
>>>
1 *~ bar :: Pressure Rational
100000 % 1 m^-1 kg s^-2
atmosphere :: Num a => Unit NonMetric DPressure a Source #
The "standard atmosphere".
From Wikipedia [3]:
The standard atmosphere (atm) is an established constant. It is approximately equal to typical air pressure at earth mean sea level.
>>>
1 *~ atmosphere
101325.0 m^-1 kg s^-2
>>>
1 *~ atmosphere :: Pressure Rational
101325 % 1 m^-1 kg s^-2
technicalAtmosphere :: Fractional a => Unit NonMetric DPressure a Source #
The "technical atmosphere"
From Wikipedia:
A technical atmosphere (symbol: at) is a non-SI unit of pressure equal to one kilogram-force per square centimeter.
>>>
1 *~ technicalAtmosphere
98066.5 m^-1 kg s^-2
>>>
1 *~ technicalAtmosphere :: Pressure Rational
196133 % 2 m^-1 kg s^-2
mmHg :: Fractional a => Unit NonMetric DPressure a Source #
The conventional value for the pressure exerted by a 1 mm high column of mercury.
Per Wikipedia [4], one mmHg (millimeter of mercury) is defined as:
The pressure exerted at the base of a column of fluid exactly 1 mm high, when the density of the fluid is exactly 13.5951 g/cm^3, at a place where the acceleration of gravity is exactly 9.80665 m/s^2.
The chosen fluid density approximately corresponds to that of mercury
at 0 deg. Under most conditions, 1 mmHg is approximately equal to 1 torr
.
>>>
1 *~ mmHg
133.322 m^-1 kg s^-2
>>>
1 *~ mmHg :: Pressure Rational
66661 % 500 m^-1 kg s^-2
inHg :: Fractional a => Unit NonMetric DPressure a Source #
The conventional value for the pressure exerted by a 1 inch high column of mercury.
Column inches of mercury are also used to measure pressure, especially in meteorological or aeronautical contexts in the United States.
This is the value defined by UCUM. For the value defined by NIST, see inHg_NIST
.
>>>
1 *~ inHg
3386.3788 m^-1 kg s^-2
>>>
1 *~ inHg :: Pressure Rational
8465947 % 2500 m^-1 kg s^-2
inHg_UCUM :: Fractional a => Unit NonMetric DPressure a Source #
The conventional value for the pressure exerted by a 1 inch high column of mercury.
Column inches of mercury are also used to measure pressure, especially in meteorological or aeronautical contexts in the United States.
This is the value defined by UCUM. For the value defined by NIST, see inHg_NIST
.
>>>
1 *~ inHg_UCUM
3386.3788 m^-1 kg s^-2
>>>
1 *~ inHg_UCUM :: Pressure Rational
8465947 % 2500 m^-1 kg s^-2
inHg_NIST :: Fractional a => Unit NonMetric DPressure a Source #
The conventional value for the pressure exerted by a 1 inch high column of mercury.
Column inches of mercury are also used to measure pressure, especially in meteorological or aeronautical contexts in the United States.
This is the value defined by NIST. For the value defined by UCUM, see inHg_UCUM
.
>>>
1 *~ inHg_NIST
3386.389 m^-1 kg s^-2
>>>
1 *~ inHg_NIST :: Pressure Rational
3386389 % 1000 m^-1 kg s^-2
torr :: Fractional a => Unit NonMetric DPressure a Source #
One torr (symbol: Torr) is defined as 1/760 atmosphere
, which is approximately equal to 1 mmHg
.
See here for further information.
>>>
1 *~ torr
133.32236842105263 m^-1 kg s^-2
>>>
1 *~ torr :: Pressure Rational
20265 % 152 m^-1 kg s^-2
Radiation Units
rad :: Fractional a => Unit Metric DAbsorbedDose a Source #
The rad is a deprecated unit of AbsorbedDose
, defined as
0.01 gray
.
See here for further information.
>>>
1 *~ rad
1.0e-2 m^2 s^-2
>>>
1 *~ rad :: AbsorbedDose Rational
1 % 100 m^2 s^-2
Kinematic Viscosity
stokes :: Fractional a => Unit Metric DKinematicViscosity a Source #
One Stokes is a unit of KinematicViscosity
equal to 1 cm^2 / s
.
See here for further information.
>>>
1 *~ stokes
1.0e-4 m^2 s^-1
>>>
1 *~ stokes :: KinematicViscosity Rational
1 % 10000 m^2 s^-1
Temperature
These units of temperature are relative. For absolute temperatures, see fromDegreeCelsiusAbsolute
.
degreeFahrenheit :: Fractional a => Unit NonMetric DThermodynamicTemperature a Source #
One degree Fahrenheit is a unit of relative temperature equal to 5/9 kelvin
.
Note that although the Fahrenheit scale is an absolute temperature scale, this unit is a unit of difference within that scale and measures relative temperature.
See here for further information.
>>>
1 *~ degreeFahrenheit
0.5555555555555556 K
>>>
1 *~ degreeFahrenheit :: ThermodynamicTemperature Rational
5 % 9 K
degreeRankine :: Fractional a => Unit NonMetric DThermodynamicTemperature a Source #
One degree Rankine is a unit of relative temperature equal to 5/9 kelvin
.
Note that although the Rankine scale is an absolute temperature scale, this unit is a unit of difference within that scale and measures relative temperature.
See here for further information.
>>>
1 *~ degreeRankine
0.5555555555555556 K
>>>
1 *~ degreeRankine :: ThermodynamicTemperature Rational
5 % 9 K
Imperial Volumes
Per http://en.wikipedia.org/wiki/Imperial_units and http://en.wikipedia.org/wiki/Cup_(unit)#Imperial_cup.
imperialGallon :: Fractional a => Unit NonMetric DVolume a Source #
imperialQuart :: Fractional a => Unit NonMetric DVolume a Source #
One imperial quart is one quarter of an imperialGallon
.
See here for further information.
>>>
1 *~ imperialQuart
1.1365225e-3 m^3
>>>
1 *~ imperialQuart :: Volume Rational
454609 % 400000000 m^3
imperialPint :: Fractional a => Unit NonMetric DVolume a Source #
One imperial pint is one half of an imperialQuart
.
See here for further information.
>>>
1 *~ imperialPint
5.6826125e-4 m^3
>>>
1 *~ imperialPint :: Volume Rational
454609 % 800000000 m^3
imperialCup :: Fractional a => Unit NonMetric DVolume a Source #
One imperial cup is one half of an imperialPint
.
This unit is not in common use and is does not appear in some sources describing the imperial fluid volume units.
See here for further information.
>>>
1 *~ imperialCup
2.84130625e-4 m^3
>>>
1 *~ imperialCup :: Volume Rational
454609 % 1600000000 m^3
imperialGill :: Fractional a => Unit NonMetric DVolume a Source #
One imperial gill is one quarter of an imperialPint
.
See here for further information.
>>>
1 *~ imperialGill
1.420653125e-4 m^3
>>>
1 *~ imperialGill :: Volume Rational
454609 % 3200000000 m^3
imperialFluidOunce :: Fractional a => Unit NonMetric DVolume a Source #
One imperial fluid ounce is one twentieth of an imperialPint
.
See here for further information.
>>>
1 *~ imperialFluidOunce
2.84130625e-5 m^3
>>>
1 *~ imperialFluidOunce :: Volume Rational
454609 % 16000000000 m^3
US Customary Volumes
Per http://www.nist.gov/pml/wmd/pubs/upload/2012-hb44-final.pdf page 452 and http://en.wikipedia.org/wiki/United_States_customary_units#Fluid_volume Note that there exist rarely-used "dry" variants of units with overlapping names.
usGallon :: Fractional a => Unit NonMetric DVolume a Source #
One US liquid gallon is a volume of 231 cubic inches.
See here for further information.
>>>
1 *~ usGallon
3.785411784e-3 m^3
>>>
1 *~ usGallon :: Volume Rational
473176473 % 125000000000 m^3
usFluidOunce :: Fractional a => Unit NonMetric DVolume a Source #
Atomic-Scale Units
Units from the Centimeter-Gram-Second Electrostatic System of Units
gauss :: Fractional a => Unit NonMetric DMagneticFluxDensity a Source #