Factory Chimney Draft

What is modelled

Hot gas is lighter than the same volume of cold outside air, so a column of it in a chimney is pushed up by the unbalanced weight of the air outside. That pressure difference, the draft, drives the gas through the grate, flues and damper and out of the top. The gas cools on the way up through the brick wall, which lowers the draft.

Equations

• Draft Δp = g ∫0H (ρair − ρgas(z)) dz, with ρ = p / (R T); without cooling Δp = g H (p/R)(1/Ta − 1/Tg).
• Losses Δp = (Σζ + f H / D) m² / (2 ρ A²).
• Cooling dT/dz = −(U π D / (m cp)) (T − Ta).
• Best base temperature for flow Tgas = 2 Tair (kelvin).

Checks run in the page

• Numerical draft against the closed form.
• Cooling by Runge-Kutta and by an energy balance on the wall.
• The best gas temperature found by scanning against twice the air temperature.
• Draft equal to losses at the operating point.

Honest simplifications

Constant air density with height at ambient temperature, ideal gas with the properties of air, one friction factor, one lumped resistance, steady flow, no wind and no inversion layers, and combustion products treated as hot air. It is a teaching model of natural draught, not a boiler or emissions design. The 3D page shows the whole quarter; here only the chimney physics is modelled.

• Press Cold winter morning and see the draft rise because the air outside is denser.
• Press Damper nearly closed: the draft is the same but the flow collapses.
• Raise the gas temperature above the best value and see the flow stop rising.