Fire ventilation

The hydrodynamic pressure difference between point 1 and point 3 is:v 1 = 0 ρ 1 = ρ 3 = ρ g h 1 = h 3 = h uρ 3 v 2 3P 1 – P 3 = −−−−−2ρ g v g2ΔP u = −−−−− Equation 22We can obtain the speed through the upper opening by using the equations1 and 2:ρ g v 2 g−−−−− = h u g (ρ a − ρ g )2√2h u g(ρ a –ρ g )v g = −−−−−−−−−−− Equation 3ρ gThe relationship between temperature and density is given by the gas law, andwe can use this to determine the relationship between the density and temperature.At normal atmospheric pressure we obtain the relationship:ρPM = RTP = 101.3 kPaM = 0.0289 kg/molR = 8.314 J/Kmolgas lawnormal atmospheric pressuremolar density for airgas constant353ρ = −−−−−relationship between density andTtemperatureThe mass flow in the opening is given by ṁ = C d AvρBy doing the same thing for the flow into the lower opening and equalisingthe obtained expression with equation 3, an expression is obtained for theposition of the neutral plane in relation to the size of the openings:h n A u 2 ρ g−−− = −−− × −−−− Equation 4h u A n ρ a32