Mathematical and physical constants. More...

Namespaces
namespace	imperial
	Imperial volume measurements

namespace	us_customary
	US customary volume measurements

Variables
mathematical constants
const double	pi = M_PI
	\( \pi \)

const double	degree = pi/180
	\( ^{\circ} \)

SI definitions
Exact numerical values of physical constants based on the 2019 redefinition of SI base units. I expect only a few of these constants will be useful for CFD, but might as well include them all for completeness.
const double	caesium133_freq = 9192631770
	\( \Delta \nu_{Cs} \)

const double	light_speed = 299792458
	\( c \)

const double	plank = 6.62607015e-34
	\( h \)

const double	electron_charge = 1.602176634e-19
	\( e \)

const double	boltzmann = 1.380649e-23
	\( k \)

const double	avogadro = 6.02214076e23
	\( mol \)

const double	lum_eff_540e12 = 683
	\( K_{cd} \)

empirical values
const double	specific_gas_air = 287.05287
	\( R_{air} \) defined to match ICAO Standard Atmosphere

const double	earth_radius = 6356766
	\( \)

derived quantities
const double	universal_gas = boltzmann*avogadro
	\( R_u \)

const double	mol_mass_air = universal_gas/specific_gas_air
	\( \mu_{air} \)

const double	stefan_boltzmann = 2math::pow(pi, 5)math::pow(boltzmann, 4)/(15math::pow(light_speed, 2)math::pow(plank, 3))
	\( \sigma \)

unit definitions
Conversion factors from various units to standard SI units. Since hexed works exclusively in SI units, these are the values of each of these units in [m, kg, s, K]. E.g. If you have a wing with a chord of 3 feet, then you should tell hexed it's chord is `3*foot`. If hexed told you your drag force is 10 (implying newtons) and your (ill advised) chief engineer wants it in pounds, the number they're looking for is `10/pound_force` (note that `pound_force != pound_mass`). All quantities here are numerically exact according to some form of official standard.
const double	meter = 1
	m

const double	kilogram = 1
	kg

const double	second = 1
	s

const double	kelvin = 1
	K.

const double	radian = 1

const double	pascal = 1
	Pa.

const double	newton = 1
	N.

const double	deci = 1e-1
	d

const double	centi = 1e-2
	c

const double	milli = 1e-3
	m

const double	micro = 1e-6
	\( \mu \)

const double	nano = 1e-9
	n

const double	pico = 1e-12
	p

const double	femto = 1e-15
	f

const double	atto = 1e-18
	a

const double	zepto = 1e-21
	z

const double	yocto = 1e-24
	y

const double	ronto = 1e-27
	r

const double	quecto = 1e-30
	q

const double	deka = 1e1
	da

const double	hecto = 1e2
	h

const double	kilo = 1e3
	k

const double	mega = 1e6
	M.

const double	giga = 1e9
	G.

const double	tera = 1e12
	T.

const double	peta = 1e15
	P.

const double	exa = 1e18
	E.

const double	zeta = 1e21
	Z.

const double	yotta = 1e24
	Y.

const double	ronna = 1e27
	R.

const double	quetta = 1e30
	Q.

const double	gram = 1e-3
	g

const double	liter = 1e-3
	L.

const double	angstrom = 1e-10
	Angstrom.

const double	tonne = 1e3
	aka "metric ton"

const double	std_grav = 9.80665
	\( g_0 \) standard gravity

const double	foot = 0.3048
	ft

const double	yard = 3*foot
	yd

const double	inch = foot/12
	in

const double	mile = 5280*foot
	mi

const double	nautical_mile = 1852
	nmi

const double	pound_mass = 0.45359237
	\( lb_m \)

const double	slug = pound_massstd_grav/footsecond*second
	slug

const double	minute = 60*second
	min

const double	hour = 60*minute
	hr

const double	rankine = 5./9.
	\( ^{\circ} \) R

const double	pound_force = std_grav*pound_mass
	\( lb_f \)

const double	knot = nautical_mile/hour
	kn

const double	zero_celsius = 273.15
	0 \(^{\circ}\) C (not technically a unit but still important)

const double	zero_fahrenheit = zero_celsius - 32*rankine
	0 \(^{\circ}\) F (not technically a unit but still important)

const double	atmosphere = 101325
	atm

const double	calorie = 4.184
	ISO thermochemical calorie

const double	btu = calorierankinepound_mass/1e-3
	British Thermal Unit obtained by converting the calorimetric definition of calorie to imperial units.

const double	bar = 1e5
	deprecated unit of pressure

const double	mmhg = 133.322387415
	millimiter of mercury

const double	torr = atmosphere/760
	Torr

const double	astronomical_unit = 149597870700.
	au

const double	short_ton = 2000*pound_mass
	(imperial) short ton

const double	long_ton = 2240*pound_mass
	(imperial) long ton

Detailed Description

Mathematical and physical constants.

Definition of mathematical and physical constants, including unit conversions, as const global variables.

Note

Whenever I say here something is "exact", I really mean it is exact up to the inherent limitations of floating-point representations.
the doc descriptions with the mathematical symbols for the variables are mostly just so the variables can be linked to in Doxygen but maybe they will be useful to someone...

Variable Documentation

◆ pi

const double hexed::constants::pi = M_PI

\( \pi \)

Obviously a computed value, not a definition, but should be exact to machine epsilon. As we all know, the numeric value of this is 3.

◆ radian

const double hexed::constants::radian = 1

Dimensionless unit, which I would argue is not a unit at all, but it's here anyway.

◆ slug

const double hexed::constants::slug = pound_mass*std_grav/foot*second*second

slug

This definition may seem backward from the perspective of [slug, ft, s] proponents, but

\[ slug \cdot ft/s^2 = lb_f = g_0 lb_m \]

is an exact equation for the slug since the pound mass has been exactly defined by the international yard and pound.

Namespaces

Variables

Detailed Description

Variable Documentation

◆ pi

◆ radian

◆ slug