Aero formulas

Resources on physics related to aerodynamics

The List of elementary physics formulae on wikipedia is useful.

List of variables

Variable	Meaning	Unit (SI)
γ (gamma)	Surface tension or Heat capacity ratio (adiabatic process in thermodynamics)	N.m-1 (Newton per meter)
μ (mu) or η (eta)	Viscosity	Pa·s (Pascal second) or P (Poise, 1 Poise is 0.1 Pa.s)
ρ (rho)	Density	kg.m-3 (kg per cubic meter)
C, Cp, CV	Heat capacity, general, at constant pressure, at constant volume.	J.K-1 (Joule per Kelvin)
G	Gibbs free energy	J (Joule)
H	Enthalpy: total energy of a thermodynamic system.	J (Joule)
ΔHvap or L	Vaporization heat or Latent heat of vaporization: energy required to vaporize a mole of liquid at a given temperature.	J.mol-1 (Joule per mole)
M	Mach number	no unit
Q	Amount of Heat	J (Joule)
T	Temperature. T0 or Tt is the stagnation temperature.	K (Kelvin)
S	Entropy	J.K-1 (Joule per Kelvin)
U	Internal energy of a system (see first law of Thermodynamics below)	J (Joule)
V	Volume	m3 (cubic meter)
W	Work: mechanical constraints on the system.	J (Joule)
a	Speed of sound in medium (used to calculate Mach number)	m.s-1
c	Velocity of a flow in thermodynamics, also noted V; generally noted u in fluid dynamics.	m.s-1
n	Quantity of matter	mol (mole)
p	Pressure. pt is the stagnation pressure.	Pa (Pascal)

List of constants

Constant	Meaning	Value	Unit (SI)
NA or N	Avogadro constant, number of atoms or molecules in a mole.	6.02214129.1023	mol-1
R	ideal gas constant	8.3144621	J.K−1.mol−1
kB or k	Boltzmann constant, gas constant R divided by Avogadro number.	1.3806488.10-23	J.K-1

List of equations

Equation	Name	Meaning
	Ideal gas equation	Relation between properties of an ideal gas (state equation). k is kB.
	Clausius-Clapeyron relation	Relation between the pressure, latent heat of vaporization and temperature of a vapour at two temperatures (approximation, at low temperatures).
	Heat at state change for an ideal gas.	The heat required to change the state of a some matter, L being the latent heat. Delta H equals Q only when pressure is constant (isobaric).
	First law of thermodynamics	Variations of internal energy of a system between two states is the sum of the received heat and work (minus the given work).
	Enthalpy	Total amount of energy of a system, defined as the sum of the internal energy U of the system and pressure * volume at the boundary of the system and its environment.
	Work of gas expansion.	Work done by expanding an ideal gas.
	Entropy	Internal energy related to entropy variation for a closed system in thermal equilibrium (fundamental thermodynamic relation).
ΔSuniverse = ΔSsurroundings + ΔSsystem	Entropy variation as a whole.	Entropy variation of a system is generally compensated by the inverse variation of the surroundings, not including losses.
	Second law of thermodynamics	A change in the entropy of a system is the infinitesimal transfer of heat to a closed system driving a reversible process, divided by the equilibrium temperature of the system.
	Gibbs free energy / Free enthalpy	Useful work obtainable from a system at isobaric and isothermal conditions. Since H is U + pV, it can be replaced in the equation, making G = H - TS.
	Gibbs free energy variation.	If ΔG < 0, the system's transformation can be spontaneous, if ΔG = 0 the transformation is inversible and the system is in an equilibrium state, if ΔG > 0 it can't be spontaneous.
	Density of an ideal gas.	M is molar mass. This means that the density of an ideal gas can be doubled by doubling the pressure, or by halving the absolute temperature.