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# Aerostatics

A subfield of fluid statics, Aerostatics is the study of gases that are not in motion with respect to the coordinate system in which they are considered. The corresponding study of gases in motion is called aerodynamics.

Aerostatics studies density allocation, especially in air. One of the applications of this is the barometric formula.

An aerostat is a lighter than air craft, such as an airship or balloon, which uses the principles of aerostatics to float.

Basic Laws

Treatment of the equations of gaseous behaviour at rest is generally taken, as in hydrostatics, to begin with a consideration of the general equations of momentum for fluid flow, which can be expressed as:

\( {\displaystyle \rho [{\partial U_{j} \over \partial t}+U_{i}{\partial U_{j} \over \partial t}]=-{\partial P \over \partial x_{j}}-{\partial \tau _{ij} \over \partial x_{i}}+\rho g_{j}} , \)

where \( {\displaystyle \rho } \) is the mass density of the fluid, \( {\displaystyle U_{j}} \) is the instantaneous velocity, \( {\displaystyle P} is fluid pressure, \( {\displaystyle g} are the external body forces acting on the fluid, and \( {\displaystyle \tau _{ij}} \) is the momentum transport coefficient. As the fluid's static nature mandates that \( {\displaystyle U_{j}=0} \) , and that \( {\displaystyle \tau _{ij}=0} \) , the following set of partial differential equations representing the basic equations of aerostatics is found.[1]

\( {\displaystyle {\partial P \over \partial x_{j}}=\rho g_{j}} \)

However, the presence of a non-constant density as is found in gaseous fluid systems (due to the compressibility of gases) requires the inclusion of the ideal gas law:

\)

\( {\displaystyle {P \over \rho }=RT} ,

where \( {\displaystyle R} \) denotes the universal gas constant, and \( {\displaystyle T} \) the temperature of the gas, in order to render the valid aerostatic partial differential equations:

\( {\displaystyle {\partial P \over \partial x_{j}}=\rho {\hat {g_{j}}}={P \over \ RT}{\hat {g_{j}}}} \) ,

which can be employed to compute the pressure distribution in gases whose thermodynamic states are given by the equation of state for ideal gases.[2]

Fields of study

Atmospheric pressure fluctuation

Composition of mountain air

Cross-section of the atmosphere

Gas density

Gas diffusion in soil

Gas pressure

Kinetic theory of gases

Partial pressures in gas mixtures

Pressure measurement

See also

Aeronautics

References

Durst, Franz (1 September 2008). An Introduction to Theory of Fluid Flows. 6.1: Springer science and business media, 2008. p. 154. ISBN 3540713425. Retrieved January 2014.

Durst, Franz (1 September 2008). An Introduction to Theory of Fluid Flows. 6.4: Springer science and business media, 2008. p. 183. ISBN 3540713425. Retrieved January 2014.

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