FCSys.Quantities

Types to represent physical values

Information

In FCSys, the unit attribute of each Real variable actually denotes the dimension.¹ The fundamental dimensions are angle (A), length (L), mass (M), particle number (N), and time (T). These are combined according to the rules established for unit strings [Modelica2010, p. 210]. Temperature and charge are derived dimensions (see the Units package).

The quantity attribute is not used since the type is the quantity. The displayUnit attribute is only used for quantities that imply a certain display unit.

Methods for unit checking have been established [Mattsson2008, Broman2008, Aronsson2009] and can, in theory, be applied to dimension checking instead.

The Quantities package is abbreviated as Q throughout the rest of FCSys.

The quantities are generally named with adjectives following the noun so that the quantities are grouped when alphabetized. Some quantities are aliases to other quantities but with special implied display units. For example, Temperature is an alias for Potential with a default display unit of K.ootnote{Temperature is a potential in the chosen system of units; see the next section ( ef{sec:Units}).} Also, some quantities have minimum values (e.g., zero for PressureAbsolute). For more information, please see the documentation of the Units package.

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1. This misnomer is necessary because Real variables do not have a dimension attribute.

Extends from Modelica.Icons.TypesPackage (Icon for packages containing type definitions).

Package Content

Name	Description
Examples	Examples
Acceleration
Amount
AmountReciprocal	Reciprocal of amount
Angle
Angle2	Solid angle
Area
AreaSpecific	Specific area
Capacitance
Density
DensityRate	Rate of density
ConductanceElectrical	Electrical conductance
ConductivityElectrical	Electrical conductivity
Continuity
Current
CurrentAreic	Areic current
CurrentAreicAbsolute	Absolute areic current
CurrentRate	Rate of current
Diffusivity
DiffusivityMassSpecific	Product of diffusivity and specific mass
Energy
Fluidity
Force
ForceSpecific	Specific force
Frequency
Inductance
Length
LengthReciprocal	Reciprocal of length
LengthSpecific	Specific length
MagneticFlux	Magnetic flux
MagneticFluxAreic	Areic magnetic flux
MagneticFluxReciprocal	Reciprocal of magnetic flux
Mass
MassSpecific	Specific mass
MassVolumic	Volumic mass
Mobility
MomentumRotational	Rotational momentum
Number
NumberAbsolute	Absolute number
Permeability
Permittivity
PermittivityReciprocal	Reciprocal of permittivity
Potential
PotentialAbsolute	Absolute potential
PotentialPerWavenumber	Potential per wavenumber
PotentialRate	Rate of potential
Power
PowerArea	Power times area
PowerAreic	Areic power
PowerAreicPerPotential4	Areic power per 4th power of potential
PowerRadiant	Radiant power
Pressure
PressureAbsolute	Absolute pressure
PressureRate	Rate of pressure
PressureReciprocal	Reciprocal of pressure
ResistanceElectrical	Electrical resistance
ResistanceThermal	Thermal resistance
SurfaceTension	Surface tension
Resistivity
Time
TimeAbsolute	Absolute time
TimeLineic	Lineic time
Velocity
Velocity2	Squared velocity
VelocityAmount
Volume
VolumeRate	Rate of volume
VolumeSpecific	Specific volume
VolumeSpecificAbsolute	Absolute specific volume
VolumeSpecificRate	Rate of specific volume
Wavenumber
CapacityThermal	Thermal capacity
CapacityThermalSpecific	Specific thermal capacity
CapacityThermalVolumic	Volumic thermal capacity
PotentialChemical	Chemical potential
Temperature
TemperatureAbsolute	Absolute temperature
TemperatureRate	Rate of temperature
ResistivityThermal	Thermal resistivity
Conductance	Conductance

Types and constants

type Acceleration = TypeReal (final unit="L/T2");

type Amount = TypeReal (final unit="N", min=0);

type AmountReciprocal = TypeReal (final unit="1/N", min=0) 
  "Reciprocal of amount";

type Angle = TypeReal (final unit="A");

type Angle2 = TypeReal (final unit="A2") "Solid angle";

type Area = TypeReal (final unit="L2", min=0);

type AreaSpecific = TypeReal (final unit="L2/N", min=0) "Specific area";

type Capacitance = TypeReal (final unit="N2.T2/(L2.M)", min=0);

type Density = TypeReal (final unit="N/L3", min=0);

type DensityRate = TypeReal (final unit="N/(L3.T)") "Rate of density";

type ConductanceElectrical = TypeReal (final unit="N2.T/(L2.M)", min=0) 
  "Electrical conductance";

type ConductivityElectrical = TypeReal (final unit="N2.T/(L3.M)", min=0) 
  "Electrical conductivity";

type Continuity = TypeReal (final unit="L.M/(N.T)", min=0);

type Current = TypeReal (final unit="N/T");

type CurrentAreic = TypeReal (final unit="N/(L2.T)") "Areic current";

type CurrentAreicAbsolute = TypeReal (final unit="N/(L2.T)", min=0) 
  "Absolute areic current";

type CurrentRate = TypeReal (final unit="N/T2") "Rate of current";

type Diffusivity = TypeReal (final unit="L2.M/(N.T)", min=0);

type DiffusivityMassSpecific = TypeReal (final unit="L2.M/(N.T)", min=0) 
  "Product of diffusivity and specific mass";

type Energy = TypeReal (final unit="L2.M/T2");

type Fluidity = TypeReal (final unit="L.T/M", min=0);

type Force = TypeReal (final unit="L.M/T2");

type ForceSpecific = TypeReal (final unit="L.M/(N.T2)") "Specific force";

type Frequency = TypeReal (final unit="A/T");

type Inductance = TypeReal (final unit="L2.M/N2", min=0);

type Length = TypeReal (final unit="L", min=0);

type LengthReciprocal = TypeReal (final unit="1/L", min=0) 
  "Reciprocal of length";

type LengthSpecific = TypeReal (final unit="L/N", min=0) "Specific length";

type MagneticFlux = TypeReal (final unit="L2.M/(A.N.T)") "Magnetic flux";

type MagneticFluxAreic = TypeReal (final unit="M/(A.N.T)") 
  "Areic magnetic flux";

type MagneticFluxReciprocal = TypeReal (final unit="A.N.T/(L2.M)") 
  "Reciprocal of magnetic flux";

type Mass = TypeReal (final unit="M", min=0);

type MassSpecific = TypeReal (final unit="M/N", min=0) "Specific mass";

type MassVolumic = TypeReal (final unit="M/L3", min=0) "Volumic mass";

type Mobility = TypeReal (final unit="N.T/M", min=0);

type MomentumRotational = TypeReal (final unit="L2.M/(A.T)") 
  "Rotational momentum";

type Number = TypeReal (final unit="1");

type NumberAbsolute = TypeReal (final unit="1", min=0) "Absolute number";

type Permeability = TypeReal (final unit="L.M/N2", min=0);

type Permittivity = TypeReal (final unit="N2.T2/(L3.M)", min=0);

type PermittivityReciprocal = TypeReal (final unit="L3.M/(N2.T2)", min=0) 
  "Reciprocal of permittivity";

type Potential = TypeReal (final unit="L2.M/(N.T2)");

type PotentialAbsolute = TypeReal (final unit="L2.M/(N.T2)", min=0) 
  "Absolute potential";

type PotentialPerWavenumber = TypeReal (final unit="L3.M/(A.N.T2)") 
  "Potential per wavenumber";

type PotentialRate = TypeReal (final unit="L2.M/(N.T3)") "Rate of potential";

type Power = TypeReal (final unit="L2.M/T3");

type PowerArea = TypeReal (final unit="L4.M/T3") "Power times area";

type PowerAreic = TypeReal (final unit="M/T3") "Areic power";

type PowerAreicPerPotential4 = TypeReal (final unit="M.T5/L8") 
  "Areic power per 4th power of potential";

type PowerRadiant = TypeReal (final unit="L2.M/(A2.T3)") "Radiant power";

type Pressure = TypeReal (final unit="M/(L.T2)");

type PressureAbsolute = TypeReal (final unit="M/(L.T2)", min=0) 
  "Absolute pressure";

type PressureRate = TypeReal (final unit="M/(L.T3)") "Rate of pressure";

type PressureReciprocal = TypeReal (final unit="L.T2/M", min=0) 
  "Reciprocal of pressure";

type ResistanceElectrical = TypeReal (final unit="L2.M/(N2.T)", min=0) 
  "Electrical resistance";

type ResistanceThermal = TypeReal (final unit="T/N", min=0) 
  "Thermal resistance";

type SurfaceTension = TypeReal (final unit="M/T2") "Surface tension";

type Resistivity = TypeReal (final unit="L.T/N", min=0);

type Time = TypeReal (final unit="T");

type TimeAbsolute = TypeReal (final unit="T", min=0) "Absolute time";

type TimeLineic = TypeReal (final unit="T/L") "Lineic time";

type Velocity = TypeReal (final unit="L/T");

type Velocity2 = TypeReal (final unit="L2/T2") "Squared velocity";

type VelocityAmount = TypeReal (final unit="L.N/T");

type Volume = TypeReal (final unit="L3", min=0);

type VolumeRate = TypeReal (final unit="L3/T") "Rate of volume";

type VolumeSpecific = TypeReal (final unit="L3/N") "Specific volume";

type VolumeSpecificAbsolute = TypeReal (final unit="L3/N", min=0) 
  "Absolute specific volume";

type VolumeSpecificRate = TypeReal (final unit="L3/(N.T)") 
  "Rate of specific volume";

type Wavenumber = TypeReal (final unit="A/L");

type CapacityThermal = Amount (displayUnit="J/K") "Thermal capacity";

type CapacityThermalSpecific = NumberAbsolute (displayUnit="J/(mol.K)") 
  "Specific thermal capacity";

type CapacityThermalVolumic = Density (displayUnit="J/(m3.K)") 
  "Volumic thermal capacity";

type PotentialChemical = Potential (displayUnit="J/mol") "Chemical potential";

type Temperature = Potential (displayUnit="K");

type TemperatureAbsolute = PotentialAbsolute (displayUnit="degC") 
  "Absolute temperature";

type TemperatureRate = PotentialRate (displayUnit="K/s") "Rate of temperature";

type ResistivityThermal = Resistivity (displayUnit="m.K/W") 
  "Thermal resistivity";

type Conductance = Current (displayUnit="W/K") "Conductance";