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Methodology for the Evaluation of Natural Ventilation in ... - Cham

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PP P P gH I , HO,H O,0I , 0O I(2.5)It is assumed that air is a perfect gas, so <strong>the</strong> ideal gas law is used:P (2.6)RTand substituted <strong>in</strong>to equation 2.5 <strong>for</strong> <strong>the</strong> ρ O and ρ I terms. S<strong>in</strong>ce <strong>the</strong> difference between P O and P Iis negligible compared to atmospheric pressure, <strong>the</strong> term P/RT B is moved outside <strong>of</strong> <strong>the</strong>paren<strong>the</strong>sis, and <strong>the</strong> ideal gas law aga<strong>in</strong> applied. Equation 2.5 to describe <strong>the</strong> pressure differencedue to buoyancy-driven flow <strong>the</strong>n becomes: TITOP TOgH(2.7) TIThe Bouss<strong>in</strong>esq approximation is used <strong>for</strong> ideal gases, so that β=1/T I . The density differencesare assumed to be negligible <strong>in</strong> <strong>the</strong> Bouss<strong>in</strong>esq approximation except to determ<strong>in</strong>e ΔP T , s<strong>in</strong>ce <strong>the</strong>density <strong>of</strong> air does not vary significantly with temperature over <strong>the</strong> range <strong>of</strong> temperaturedifferences found <strong>in</strong> <strong>the</strong> reference build<strong>in</strong>g. The value <strong>for</strong> β used is <strong>the</strong> <strong>in</strong>verse <strong>of</strong> an average<strong>in</strong>ternal temperature. The Bouss<strong>in</strong>esq approximation is generally valid as long as ΔT

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