Aero formulas: Difference between revisions

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The [https://en.wikipedia.org/wiki/List_of_elementary_physics_formulae List of elementary physics formulae] on wikipedia is useful.
The [https://en.wikipedia.org/wiki/List_of_elementary_physics_formulae List of elementary physics formulae] on wikipedia is useful.
A page is dedicated to [[heat transfer]].


==List of variables==
==List of variables==
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|-
|-
| γ (gamma)
| γ (gamma)
| [https://en.wikipedia.org/wiki/Surface_tension Surface tension]
| [https://en.wikipedia.org/wiki/Surface_tension Surface tension] or [https://en.wikipedia.org/wiki/Heat_capacity_ratio Heat capacity ratio] (adiabatic process in thermodynamics)
| N.m<sup>-1</sup> (Newton per meter)
| N.m<sup>-1</sup> (Newton per meter)
|-
|-
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| [https://en.wikipedia.org/wiki/Viscosity Viscosity]
| [https://en.wikipedia.org/wiki/Viscosity Viscosity]
| Pa·s (Pascal second) or P (Poise, 1 Poise is 0.1 Pa.s)
| Pa·s (Pascal second) or P (Poise, 1 Poise is 0.1 Pa.s)
|-
| ρ (rho)
| [https://en.wikipedia.org/wiki/Density Density]
| kg.m<sup>-3</sup> (kg per cubic meter)
|-
|-
| C, C<sub>p</sub>, C<sub>V</sub>
| C, C<sub>p</sub>, C<sub>V</sub>
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| [https://en.wikipedia.org/wiki/Vaporization_heat Vaporization heat] or [https://en.wikipedia.org/wiki/Latent_heat Latent heat of vaporization]: energy required to vaporize a mole of liquid at a given temperature.
| [https://en.wikipedia.org/wiki/Vaporization_heat Vaporization heat] or [https://en.wikipedia.org/wiki/Latent_heat Latent heat of vaporization]: energy required to vaporize a mole of liquid at a given temperature.
| J.mol<sup>-1</sup> (Joule per mole)
| J.mol<sup>-1</sup> (Joule per mole)
|-
| M
| [https://en.wikipedia.org/wiki/Mach_number Mach number]
| no unit
|-
|-
| Q
| Q
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|-
|-
| T
| T
| Temperature
| Temperature. T<sub>0</sub> or T<sub>t</sub> is the [https://en.wikipedia.org/wiki/Stagnation_temperature stagnation temperature].
| K (Kelvin)
| K (Kelvin)
|-
|-
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| [https://en.wikipedia.org/wiki/Work_(thermodynamics) Work]: mechanical constraints on the system.
| [https://en.wikipedia.org/wiki/Work_(thermodynamics) Work]: mechanical constraints on the system.
| J (Joule)
| J (Joule)
|-
| a
| [https://en.wikipedia.org/wiki/Speed_of_sound Speed of sound] in medium (used to calculate Mach number)
| m.s<sup>-1</sup>
|-
| c
| Velocity of a flow in thermodynamics, also noted V; generally noted u in fluid dynamics.
| m.s<sup>-1</sup>
|-
|-
| n
| n
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|-
|-
| p
| p
| Pressure
| Pressure. p<sub>t</sub> is the [https://en.wikipedia.org/wiki/Stagnation_pressure stagnation pressure].
| Pa (Pascal)
| Pa (Pascal)
|-
| p
| [https://en.wikipedia.org/wiki/Momentum Momentum] p = m*v, with m the mass and v the velocity, not to be confused with volume.
| kg.m.s<sup>-1</sup>
|}
|}


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| 8.3144621
| 8.3144621
| J.K<sup>−1</sup>.mol<sup>−1</sup>
| J.K<sup>−1</sup>.mol<sup>−1</sup>
|-
| G
| [https://en.wikipedia.org/wiki/Gravitational_constant Gravitational constant]
| 6.674
| m<sup>3</sup>.kg<sup>-1</sup>.s<sup>-2</sup>
|-
|-
| k<sub>B</sub> or k
| k<sub>B</sub> or k
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!Meaning
!Meaning
|-
|-
|style="background:white"| {{SERVER}}/images/formulas_mirror/pvnrtk.png
|{{SERVER}}/images/formulas_mirror/pvnrtk_neg.png
|Ideal gas equation
|Ideal gas equation
|Relation between properties of an ideal gas ([https://en.wikipedia.org/wiki/State_equation state equation]). k is k<sub>B</sub>.
|Relation between properties of an ideal gas ([https://en.wikipedia.org/wiki/State_equation state equation]). k is k<sub>B</sub>.
|-
|-
|style="background:white"| {{SERVER}}/images/formulas_mirror/clausius-clapeyron.png
|{{SERVER}}/images/formulas_mirror/clausius-clapeyron_neg.png
|[https://en.wikipedia.org/wiki/Clausius%E2%80%93Clapeyron_relation#Ideal_gas_approximation_at_low_temperatures Clausius-Clapeyron relation]
|[https://en.wikipedia.org/wiki/Clausius%E2%80%93Clapeyron_relation#Ideal_gas_approximation_at_low_temperatures Clausius-Clapeyron relation]
|Relation between the pressure, latent heat of vaporization and temperature of a vapour at two temperatures (approximation, at low temperatures).
|Relation between the pressure, latent heat of vaporization and temperature of a vapour at two temperatures (approximation, at low temperatures).
|-
|-
|style="background:white"| {{SERVER}}/images/formulas_mirror/QeqmL.png
|{{SERVER}}/images/formulas_mirror/QeqmL_neg.png
|Heat at [https://en.wikipedia.org/wiki/Latent_heat#Specific_latent_heat state change] for an ideal gas.
|Heat at [https://en.wikipedia.org/wiki/Latent_heat#Specific_latent_heat 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).
|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).
|-
|-
|style="background:white"| {{SERVER}}/images/formulas_mirror/dUeqdQmindW.png
|{{SERVER}}/images/formulas_mirror/dUeqdQmindW_neg.png
|[https://en.wikipedia.org/wiki/First_law_of_thermodynamics First law of thermodynamics]
|[https://en.wikipedia.org/wiki/First_law_of_thermodynamics 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).
|Variations of internal energy of a system between two states is the sum of the received heat and work (minus the ''given'' work).
|-
|-
|style="background:white"| {{SERVER}}/images/formulas_mirror/enthalpy.png
|{{SERVER}}/images/formulas_mirror/enthalpy_neg.png
|[https://en.wikipedia.org/wiki/Enthalpy Enthalpy]
|[https://en.wikipedia.org/wiki/Enthalpy 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.
|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.
|-
|-
|style="background:white"| {{SERVER}}/images/formulas_mirror/workExpand.png
|{{SERVER}}/images/formulas_mirror/workExpand_neg.png
|Work of gas expansion.
|Work of gas expansion.
|Work done by expanding an ideal gas.
|Work done by expanding an ideal gas.
|-
|-
|style="background:white"| {{SERVER}}/images/formulas_mirror/entropy_dueqtdsmpdv.png
|{{SERVER}}/images/formulas_mirror/entropy_dueqtdsmpdv_neg.png
|[https://en.wikipedia.org/wiki/Entropy Entropy]
|[https://en.wikipedia.org/wiki/Internal_energy Internal energy] change related to [https://en.wikipedia.org/wiki/Entropy entropy]
|Internal energy related to entropy variation for a closed system in thermal equilibrium ([https://en.wikipedia.org/wiki/Fundamental_thermodynamic_relation fundamental thermodynamic relation]).
|Internal energy related to entropy variation for a closed system in thermal equilibrium ([https://en.wikipedia.org/wiki/Fundamental_thermodynamic_relation fundamental thermodynamic relation]).
|-
|{{SERVER}}/images/formulas_mirror/dheqtds_neg.png
|[https://en.wikipedia.org/wiki/Enthalpy Enthalpy] change
|Enthalpy change depending on entropy and pressure changes, equation created from the mix of the basic ones above.
|-
|-
|ΔS<sub>universe</sub> = ΔS<sub>surroundings</sub> + ΔS<sub>system</sub>
|ΔS<sub>universe</sub> = ΔS<sub>surroundings</sub> + ΔS<sub>system</sub>
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|Entropy variation of a system is generally compensated by the inverse variation of the surroundings, not including losses.
|Entropy variation of a system is generally compensated by the inverse variation of the surroundings, not including losses.
|-
|-
|style="background:white"| {{SERVER}}/images/formulas_mirror/dS.png
|{{SERVER}}/images/formulas_mirror/dS_neg.png
|[https://en.wikipedia.org/wiki/Second_law_of_thermodynamics Second law of thermodynamics]
|[https://en.wikipedia.org/wiki/Second_law_of_thermodynamics 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.
|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.
|-
|-
|style="background:white"| {{SERVER}}/images/formulas_mirror/gibbs.png
|{{SERVER}}/images/formulas_mirror/gibbs_neg.png
|[https://en.wikipedia.org/wiki/Gibbs_free_energy Gibbs free energy] / Free enthalpy
|[https://en.wikipedia.org/wiki/Gibbs_free_energy 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.
|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.
|-
|-
|style="background:white"| {{SERVER}}/images/formulas_mirror/deltaG.png
|{{SERVER}}/images/formulas_mirror/deltaG_neg.png
|[https://en.wikipedia.org/wiki/Gibbs_free_energy Gibbs free energy] variation.
|[https://en.wikipedia.org/wiki/Gibbs_free_energy 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.
|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.
|-
|{{SERVER}}/images/formulas_mirror/density_ideal_neg.png
|[https://en.wikipedia.org/wiki/Density#Changes_of_density 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.
|}
|}

Latest revision as of 22:42, 20 November 2012

Resources on physics related to aerodynamics

The List of elementary physics formulae on wikipedia is useful.

A page is dedicated to heat transfer.

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
pvnrtk_neg.png Ideal gas equation Relation between properties of an ideal gas (state equation). k is kB.
clausius-clapeyron_neg.png Clausius-Clapeyron relation Relation between the pressure, latent heat of vaporization and temperature of a vapour at two temperatures (approximation, at low temperatures).
QeqmL_neg.png 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).
dUeqdQmindW_neg.png 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_neg.png 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.
workExpand_neg.png Work of gas expansion. Work done by expanding an ideal gas.
entropy_dueqtdsmpdv_neg.png Internal energy change related to entropy Internal energy related to entropy variation for a closed system in thermal equilibrium (fundamental thermodynamic relation).
dheqtds_neg.png 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.
dS_neg.png 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_neg.png 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.
deltaG_neg.png 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_ideal_neg.png 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.