Stairwell Stack Effects in High-Rise Buildings During Power Outages: A Buoyancy Model, Smoke-Transit Times, and a Sized Passive Venting Design

SIMULATED, NOT MEASURED. A closed-form stack-effect model (buoyancy pressure vs shaft height, temperature difference, and leakage area) is applied to high-rise stairwells during power outages in two cases: a heatwave blackout and a winter fire. Smoke entering an unpressurised shaft transits it in seconds: 7.3 s for a 60 m shaft and 11.6 s for a 150 m shaft (smoke at 120 C, shaft air at 20 C, fire floor at 25% of height). A sealed concrete shaft heats slowly in a heatwave (0.327 C per hour; 0.163 C in 30 minutes), but an open shaft reaches 37.7 C within 30 minutes as reverse stack effect drives 38 C outdoor air through it with a time constant of about 7.5 minutes. Winter stack pressure grows at 1.101 Pa per metre (66.1 Pa at 60 m, 110.1 Pa at 100 m, 165.2 Pa at 150 m), and the resultant force on a ground-floor door exceeds a 100 N limit above a shaft height of 96.1 m. A passive design sized at a stated design condition (outdoor 32 C, shaft limit 40 C, six air changes per hour of smoke dilution, 30-minute evacuation) requires a shaft-top vent and matched inlet of 0.33 m2 for a 30 m building ($7,230 installed), 0.47 m2 for 60 m ($9,416), 0.61 m2 for 100 m ($12,139), and 0.74 m2 for 150 m ($15,581), under stated price assumptions, plus a maximum door undercut of 11.0 mm (total door leakage at most 0.0119 m2, holding leakage to 0.05 m3/s per floor at 25 Pa). Failure regimes are stated at full size: passive-only protection cannot hold above about 96 m in winter door-force conditions, wind above 6.6 m/s overcomes the design stack pressure of a 60 m shaft (94.8 Pa at 15 m/s), and no passive vent can cool a shaft with 38 C outdoor air at peak heatwave temperatures. Nothing described has been built, installed, or hardware-tested.