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)
p	Momentum p = m*v, with m the mass and v the velocity, not to be confused with volume.	kg.m.s-1

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
G	Gravitational constant	6.674	m3.kg-1.s-2
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.
	Internal energy change related to entropy	Internal energy related to entropy variation for a closed system in thermal equilibrium (fundamental thermodynamic relation).
	Enthalpy change	Enthalpy change depending on entropy and pressure changes, equation created from the mix of the basic ones above.
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.