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 u
ρ 3v 2
3
P 1– P 3 = −−−−−
2
ρgv g 2
ΔP u = −−−−− Equation 2
2
We can obtain the speed through the upper opening by using the equations
1 and 2:
ρ gv 2 g
−−−−− = h u g (ρ a− ρ g)
2
32
√
2h ug(ρ a–ρ g)
vg = −−−−−−−−−−− Equation 3
ρg The relationship between temperature and density is given by the gas law, and
we can use this to determine the relationship between the density and temperature.
At normal atmospheric pressure we obtain the relationship:
ρPM = RT gas law
P = 101.3 kPa normal atmospheric pressure
M = 0.0289 kg/mol molar density for air
R = 8.314 J/Kmol gas constant
353
ρ = −−−−− relationship between density and
T
temperature
The mass fl ow in the opening is given by m˙ = CdAvρ By doing the same thing for the fl ow into the lower opening and equalising
the obtained expression with equation 3, an expression is obtained for the
position of the neutral plane in relation to the size of the openings:
hn Au 2
ρg −−− = −−− × −−−− Equation 4
hu An ρa