Wikipedia gives the equations with no explanation or
proof. The references don't help much.
The driving force is buoyancy of the hot gas on
cooler gas. In most materials, density reduces as temperature increase.
Force is proportional to difference in density.
The pressure difference between lower side and upper
side of the building or chimney is according to Bernoulli's principle, based on
conversation of energy
P + ρ g h + ½ ρ v2 = constant[1]
Where:
v = fluid flow speed
g = gravity acceleration
h = elevation above a
reference plane
P = [[pressure]] at the
chosen point
ρ = [[density]] of the
fluid at all points in the fluid.
For low speed, pressure difference :
∆P = (ρa – ρ) ∆h
ρa
= ambient density of fluid, outside the building
∆h
= vertical distance
Assuming air to be ideal (or perfect) gas
ρ = P/ RT
R =
gas constant
T =
temperature
For pressure 1 to 5 Bar and temperatures 250 to 1000
Kelvin (-50 to 700 Celsius), quite far from critical point, the assumption is
true within 1%[2]
∆P = Pa g ∆h (1/To – 1/Ti)
/ R
Where :
Pa
= Pressure outside
To
= Absolute temperature outside (Kelvin)
Ti
= Absolute temperature of gas inside the building / chimney (Kelvin)
Substituting value for Standard Atmosphere at ground
level and gravitation:
∆P = 101,325 x 9.807 / 287 (1/To – 1/Ti)
x ∆h = 3474[3] (1/To
– 1/Ti) x ∆h
Flow rate can be evaluated, by manipulating the equation at White[4] p.15
Q = Cd A (∆P/ρ)1/2
Cd
= discharge coefficient
A =
Cross section of gas flow = Internal diameter of chimney of opening of building
Q = C A (2 g ∆h (Ti- To)/Ti
)1/2
∆h is height of chimney or the elevation above
neutral plane (NLP)
Typical value for C is 0.6 to 0.7 [5]
