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2.2 Air 135 v=0 2.2.2.2 Stack Stack or buoyancy in gases and liquids has two causes: differences in temperature and differences in composition. Confined to the atmosphere, the decrease in air pressure with height (h) above sea-level is: dPa ˆ ρag dh where g is the acceleration due to gravity. Inserting the ideal gas law gives: dPa Pa ˆ g dh RaT (2.12) With the temperature (T) constant, the solution of this differential equation is: g h Pa ˆ Pa0 exp RaT (2.13) a result knownas the barometric relation. Air pressure thus depends on height. However, temperature differences and another gas composition change the gas constant (Ra) intoa variable inducing pressure gradients at the same height, which is called stack. The pressure difference between two points, one at height h1, the other at height h2, is: ΔPa ˆ g Pa;ho …h2 h1†=…RaT† with the suffix ho denoting the average height. The stack potential at height h is then given by the pressure difference between that point in an air mass at variable temperature and composition, and a point at the same height in an air mass at constant temperature and composition: h Pstack ˆ g Pa;ho ∫ hˆo dh Ra…h†T…h† 0 @ 1 A h …RaT† o 2 4 3 5 ˆ g Pa;hoh 1 …RaT† m 1 …RaT† o where (RaT)m is the harmonic average of the product Ra(h)T(h) at height h: …RaT† m h ˆ h ∫ hˆo dh Ra…h†T…h† , ν Fig. 2.2 Bernouilli’s law and the wind pressure field around a building


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