Stack Draft Pressure (Chimney Effect)

A chimney works because two columns of fluid of different densities sit side by side. Outside there is a column of cold, dense air of height $h$; inside there is a column of hot, light flue gas of the same height. The hydrostatic pressure at the base of each is $\rho g h$, and the difference between them is the draft: $\Delta p = h g (\rho_a - \rho_g)$. A 30 m stack with ambient air at 1.2 kg/m³ and flue gas at 0.7 kg/m³ develops $30 \times 9.80665 \times 0.5 = 147$ Pa, which is 0.59 inches of water column on a manometer. There is no fan in that sentence anywhere — the pressure is manufactured by gravity acting on a density difference, which is why a natural-draft appliance works during a power failure.

The densities are usually not measured but computed, and the ideal gas law is all you need: $\rho = PM/RT$, which for air at ordinary pressure collapses to the useful shortcut $\rho \approx 353/T$ with T in kelvin. That gives 1.20 kg/m³ at 20 °C and 0.70 kg/m³ at 232 °C, which is where the example numbers came from. Flue gas is not air, but its molar mass sits within a couple of percent of air's for ordinary combustion products, so the shortcut is good enough for draft work. The temperature to use is the MEAN gas temperature over the height of the stack, not the temperature at the breeching, and on an uninsulated exterior chimney those two can differ by a hundred degrees. Using the hot inlet temperature over-states the draft, which is the classic way a chimney gets sized too small.

What the equation gives is THEORETICAL draft, and a real chimney never delivers it. Friction along the flue, the entry loss at the breeching, the exit loss at the tip and every elbow in between all consume part of it, and the gas has to be accelerated to exit velocity out of what is left. A common working figure is that available draft is 70 to 80 percent of theoretical, and a tall narrow flue can be worse. That is also why lengthening a chimney has diminishing returns: the driving pressure grows with the first power of height while the friction loss grows with it too, and beyond a point the extra height buys almost nothing.

The same equation, with no changes at all, explains the stack effect in a building. Warm indoor air is the light column, winter outdoor air is the heavy one, and a 60 m tower on a −20 °C day develops something like 200 Pa across its full height. That is what makes ground-floor lobby doors hard to open, drives infiltration in at the bottom and out at the top, and puts a neutral pressure plane somewhere around mid-height where the difference reverses. It is also the mechanism behind cold-flue backdraft: at start-up the gas inside is the same density as the air outside, the draft is zero, and the chimney will not pull until it has warmed through. Any appliance that has to light against a cold exterior masonry chimney is fighting exactly this, and it is why induced-draft fans exist.