Numeric.Units.Dimensional.Quantities

Summary

This module defines type synonyms for common dimensionalities and the associated quantity types. Additional dimensionalities and quantity types will be added on an as-needed basis.

The definitions in this module are grouped so that a type synonym for the dimensionality is defined first in terms of base dimension exponents. Then a type synonym for the corresponding quantity type is defined. If there are several quantity types with the same dimensionality type synonyms are provided for each quantity type.

References

1. http://physics.nist.gov/Pubs/SP811/

Quantities from the NIST Guide

The following quantities are all from the NIST publication "Guide for the Use of the International System of Units (SI)" [1]. Any chapters, sections or tables referenced are from [1] unless otherwise specified.

For lack of better organization we provide definitions grouped by table in [1].

Table 2

"Examples of SI derived units expressed in terms of SI base units."

type Area = Quantity DArea

type Volume = Quantity DVolume

type Velocity = Quantity DVelocity

type Acceleration = Quantity DAcceleration

type WaveNumber = Quantity DWaveNumber

type MassDensity = Quantity DMassDensity

type Density = MassDensity

type SpecificVolume = Quantity DSpecificVolume

type CurrentDensity = Quantity DCurrentDensity

type MagneticFieldStrength = Quantity DMagneticFieldStrength

type AmountOfSubstanceConcentration = Quantity DAmountOfSubstanceConcentration

type Concentration = AmountOfSubstanceConcentration

type Luminance = Quantity DLuminance

Table 3

SI coherent derived units with special names and symbols.

type PlaneAngle = Dimensionless

type SolidAngle = Dimensionless

type Frequency = Quantity DFrequency

type Force = Quantity DForce

type Pressure = Quantity DPressure

type Stress = Quantity DStress

type Energy = Quantity DEnergy

type Work = Quantity DWork

type QuantityOfHeat = Quantity DQuantityOfHeat

type Power = Quantity DPower

type RadiantFlux = Quantity DRadiantFlux

type ElectricCharge = Quantity DElectricCharge

type QuantityOfElectricity = Quantity DQuantityOfElectricity

type ElectricPotential = Quantity DElectricPotential

type PotentialDifference = Quantity DPotentialDifference

type ElectromotiveForce = Quantity DElectromotiveForce

type Capacitance = Quantity DCapacitance

type ElectricResistance = Quantity DElectricResistance

type ElectricConductance = Quantity DElectricConductance

type MagneticFlux = Quantity DMagneticFlux

type MagneticFluxDensity = Quantity DMagneticFluxDensity

type Inductance = Quantity DInductance

type LuminousFlux = Quantity DLuminousFlux

type Illuminance = Quantity DIlluminance

type CelsiusTemperature = Quantity DCelsiusTemperature

type Activity = Quantity DActivity

type AbsorbedDose = Quantity DAbsorbedDose

type SpecificEnergy = Quantity DSpecificEnergy

type Kerma = Quantity DKerma

type DoseEquivalent = Quantity DDoseEquivalent

type AmbientDoseEquivalent = DoseEquivalent

type DirectionalDoseEquivalent = DoseEquivalent

type PersonalDoseEquivalent = DoseEquivalent

type EquivalentDose = DoseEquivalent

type CatalyticActivity = Quantity DCatalyticActivity

Table 4

"Examples of SI coherent derived units expressed with the aid of SI derived units having special names and symbols."

We use the same grouping as for table 2.

type AngularVelocity = Quantity DAngularVelocity

type AngularAcceleration = Quantity DAngularAcceleration

type DynamicViscosity = Quantity DDynamicViscosity

type MomentOfForce = Quantity DMomentOfForce

type SurfaceTension = Quantity DSurfaceTension

type HeatFluxDensity = Quantity DHeatFluxDensity

type Irradiance = Quantity DIrradiance

type RadiantIntensity = Quantity DRadiantIntensity

type Radiance = Quantity DRadiance

type HeatCapacity = Quantity DHeatCapacity

type Entropy = Quantity DEntropy

type SpecificHeatCapacity = Quantity DSpecificHeatCapacity

type SpecificEntropy = Quantity DSpecificEntropy

type ThermalConductivity = Quantity DThermalConductivity

type EnergyDensity = Quantity DEnergyDensity

type ElectricFieldStrength = Quantity DElectricFieldStrength

type ElectricChargeDensity = Quantity DElectricChargeDensity

type ElectricFluxDensity = Quantity DElectricFluxDensity

type Permittivity = Quantity DPermittivity

type Permeability = Quantity DPermeability

type MolarEnergy = Quantity DMolarEnergy

type MolarEntropy = Quantity DMolarEntropy

type MolarHeatCapacity = Quantity DMolarHeatCapacity

type Exposure = Quantity DExposure

type AbsorbedDoseRate = Quantity DAbsorbedDoseRate

Quantities not from the NIST Guide

Here we define additional quantities on an as-needed basis. We also provide some synonyms that we anticipate will be useful.

type Impulse = Quantity DImpulse

type Momentum = Quantity DMomentum

type MassFlow = Quantity DMassFlow

type VolumeFlow = Quantity DVolumeFlow

type GravitationalParameter = Quantity DGravitationalParameter

type KinematicViscosity = Quantity DKinematicViscosity

type FirstMassMoment = Quantity DFirstMassMoment

type MomentOfInertia = Quantity DMomentOfInertia

type AngularMomentum = Quantity DAngularMomentum

type ThermalResistivity = Quantity DThermalResistivity

type ThermalConductance = Quantity DThermalConductance

type ThermalResistance = Quantity DThermalResistance

type HeatTransferCoefficient = Quantity DHeatTransferCoefficient

type ThermalAdmittance = HeatTransferCoefficient

type ThermalInsulance = Quantity DThermalInsulance

type Jerk = Quantity DJerk

type Angle = PlaneAngle

type Thrust = Force

type Torque = MomentOfForce

type EnergyPerUnitMass = SpecificEnergy

Powers of Unit Lengths

It is permissible to express powers of length units by prefixing square and cubic (see section 9.6 "Spelling unit names raised to powers" of [1]).

These definitions may seem slightly out of place but these is no obvious place where they should be. Here they are at least close to the definitions of DArea and DVolume.

square :: (Fractional a, Typeable m) => Unit m DLength a -> Unit NonMetric DArea a

Constructs a unit of area from a unit of length, taking the area of a square whose sides are that length.

>>> 64 *~ square meter == (8 *~ meter) ^ pos2
True

cubic :: (Fractional a, Typeable m) => Unit m DLength a -> Unit NonMetric DVolume a

Constructs a unit of volume from a unit of length, taking the volume of a cube whose sides are that length.

>>> 64 *~ cubic meter == (4 *~ meter) ^ pos3
True

Dimension Aliases

For each Quantity alias supplied above, we also supply a corresponding Dimension alias.

These dimension aliases may be convenient for supplying type signatures for Units or for other type-level dimensional programming.

type DArea = Dim Pos2 Zero Zero Zero Zero Zero Zero

type DVolume = Dim Pos3 Zero Zero Zero Zero Zero Zero

type DVelocity = Dim Pos1 Zero Neg1 Zero Zero Zero Zero

type DAcceleration = Dim Pos1 Zero Neg2 Zero Zero Zero Zero

type DWaveNumber = Dim Neg1 Zero Zero Zero Zero Zero Zero

type DMassDensity = Dim Neg3 Pos1 Zero Zero Zero Zero Zero

type DDensity = DMassDensity

type DSpecificVolume = Dim Pos3 Neg1 Zero Zero Zero Zero Zero

type DCurrentDensity = Dim Neg2 Zero Zero Pos1 Zero Zero Zero

type DMagneticFieldStrength = Dim Neg1 Zero Zero Pos1 Zero Zero Zero

type DAmountOfSubstanceConcentration = Dim Neg3 Zero Zero Zero Zero Pos1 Zero

type DConcentration = DAmountOfSubstanceConcentration

type DLuminance = Dim Neg2 Zero Zero Zero Zero Zero Pos1

type DPlaneAngle = DOne

type DSolidAngle = DOne

type DFrequency = Dim Zero Zero Neg1 Zero Zero Zero Zero

type DForce = Dim Pos1 Pos1 Neg2 Zero Zero Zero Zero

type DPressure = Dim Neg1 Pos1 Neg2 Zero Zero Zero Zero

type DStress = DPressure

type DEnergy = Dim Pos2 Pos1 Neg2 Zero Zero Zero Zero

type DWork = DEnergy

type DQuantityOfHeat = DEnergy

type DPower = Dim Pos2 Pos1 Neg3 Zero Zero Zero Zero

type DRadiantFlux = DPower

type DElectricCharge = Dim Zero Zero Pos1 Pos1 Zero Zero Zero

type DQuantityOfElectricity = DElectricCharge

type DElectricPotential = Dim Pos2 Pos1 Neg3 Neg1 Zero Zero Zero

type DPotentialDifference = DElectricPotential

type DElectromotiveForce = DElectricPotential

type DCapacitance = Dim Neg2 Neg1 Pos4 Pos2 Zero Zero Zero

type DElectricResistance = Dim Pos2 Pos1 Neg3 Neg2 Zero Zero Zero

type DElectricConductance = Dim Neg2 Neg1 Pos3 Pos2 Zero Zero Zero

type DMagneticFlux = Dim Pos2 Pos1 Neg2 Neg1 Zero Zero Zero

type DMagneticFluxDensity = Dim Zero Pos1 Neg2 Neg1 Zero Zero Zero

type DInductance = Dim Pos2 Pos1 Neg2 Neg2 Zero Zero Zero

type DLuminousFlux = DLuminousIntensity

type DIlluminance = Dim Neg2 Zero Zero Zero Zero Zero Pos1

type DCelsiusTemperature = DThermodynamicTemperature

type DActivity = DFrequency

type DAbsorbedDose = Dim Pos2 Zero Neg2 Zero Zero Zero Zero

type DSpecificEnergy = DAbsorbedDose

type DKerma = DAbsorbedDose

type DDoseEquivalent = DAbsorbedDose

type DAmbientDoseEquivalent = DDoseEquivalent

type DDirectionalDoseEquivalent = DDoseEquivalent

type DPersonalDoseEquivalent = DDoseEquivalent

type DEquivalentDose = DDoseEquivalent

type DCatalyticActivity = Dim Zero Zero Neg1 Zero Zero Pos1 Zero

type DAngularVelocity = DFrequency

type DAngularAcceleration = Dim Zero Zero Neg2 Zero Zero Zero Zero

type DDynamicViscosity = Dim Neg1 Pos1 Neg1 Zero Zero Zero Zero

type DMomentOfForce = DEnergy

type DSurfaceTension = Dim Zero Pos1 Neg2 Zero Zero Zero Zero

type DHeatFluxDensity = Dim Zero Pos1 Neg3 Zero Zero Zero Zero

type DIrradiance = DHeatFluxDensity

type DRadiantIntensity = DPower

type DRadiance = DIrradiance

type DHeatCapacity = Dim Pos2 Pos1 Neg2 Zero Neg1 Zero Zero

type DEntropy = DHeatCapacity

type DSpecificHeatCapacity = Dim Pos2 Zero Neg2 Zero Neg1 Zero Zero

type DSpecificEntropy = DSpecificHeatCapacity

type DThermalConductivity = Dim Pos1 Pos1 Neg3 Zero Neg1 Zero Zero

type DEnergyDensity = DPressure

type DElectricFieldStrength = Dim Pos1 Pos1 Neg3 Neg1 Zero Zero Zero

type DElectricChargeDensity = Dim Neg3 Zero Pos1 Pos1 Zero Zero Zero

type DElectricFluxDensity = Dim Neg2 Zero Pos1 Pos1 Zero Zero Zero

type DPermittivity = Dim Neg3 Neg1 Pos4 Pos2 Zero Zero Zero

type DPermeability = Dim Pos1 Pos1 Neg2 Neg2 Zero Zero Zero

type DMolarEnergy = Dim Pos2 Pos1 Neg2 Zero Zero Neg1 Zero

type DMolarEntropy = Dim Pos2 Pos1 Neg2 Zero Neg1 Neg1 Zero

type DMolarHeatCapacity = DMolarEntropy

type DExposure = Dim Zero Neg1 Pos1 Pos1 Zero Zero Zero

type DAbsorbedDoseRate = Dim Pos2 Zero Neg3 Zero Zero Zero Zero

type DImpulse = Dim Pos1 Pos1 Neg1 Zero Zero Zero Zero

type DMomentum = DImpulse

type DMassFlow = Dim Zero Pos1 Neg1 Zero Zero Zero Zero

type DVolumeFlow = Dim Pos3 Zero Neg1 Zero Zero Zero Zero

type DGravitationalParameter = Dim Pos3 Zero Neg2 Zero Zero Zero Zero

type DKinematicViscosity = Dim Pos2 Zero Neg1 Zero Zero Zero Zero

type DFirstMassMoment = Dim Pos1 Pos1 Zero Zero Zero Zero Zero

type DMomentOfInertia = Dim Pos2 Pos1 Zero Zero Zero Zero Zero

type DAngularMomentum = Dim Pos2 Pos1 Neg1 Zero Zero Zero Zero

type DThermalResistivity = Dim Neg1 Neg1 Pos3 Zero Pos1 Zero Zero

type DThermalConductance = Dim Pos2 Pos1 Neg3 Zero Neg1 Zero Zero

type DThermalResistance = Dim Neg2 Neg1 Pos3 Zero Pos1 Zero Zero

type DHeatTransferCoefficient = Dim Zero Pos1 Neg3 Zero Neg1 Zero Zero

type DThermalAdmittance = DHeatTransferCoefficient

type DThermalInsulance = Dim Zero Neg1 Pos3 Zero Pos1 Zero Zero

type DJerk = Dim Pos1 Zero Neg3 Zero Zero Zero Zero

type DAngle = DPlaneAngle

type DThrust = DForce

type DTorque = DMomentOfForce

type DEnergyPerUnitMass = DSpecificEnergy