Stairwell Pressurization Airflow and Door Force

Which are the two halves of the same design and pull against each other. A pressurized stairwell holds a positive pressure difference against the floors so smoke cannot enter, and the air it takes is an orifice problem: every gap in the enclosure -- door undercuts and edge gaps, construction leakage, penetrations -- passes flow proportional to the SQUARE ROOT of the pressure difference, with 2610 the flow coefficient in customary units. That square root matters, because doubling the design pressure does not double the fan, it multiplies it by 1.41. The second equation is the constraint that actually decides the design. Pressure across a closed door acts on the whole leaf, and the moment it produces has to be overcome at the knob, which is a short lever arm from the hinges. The code caps total opening force at 30 lbf and the door closer alone already eats 10 to 15 of it, so on a 3 by 7 door there is only so much pressure left, and the usable window between holding smoke back and letting a person out is narrow -- typically 0.10 to 0.25 in. w.g. A stairwell with 2.5 sq ft of leakage at 0.15 in. w.g. takes 2,527 cfm and opens at 18.9 lbf with a 10 lbf closer; push it to 0.25 for more smoke margin and the fan grows only 29% while the door force reaches 24.9 lbf, and with a 15 lbf closer it would be at the limit. The door, not the fan, caps the design pressure. A screen, never a stamp: the smoke-control design, its commissioning test, and a qualified engineer govern.

airflow_cfm = 2610 x leakage_area_sqft x sqrt(pressure_inwg); door_force_lbf = closer_force + 5.2 x door_width_ft x door_area_sqft x pressure_inwg / (2 x (door_width_ft - knob_setback_ft)); max_pressure_inwg = (force_limit - closer_force) x 2 x (W - d) / (5.2 x W x A).

Stairwell pressurization airflow from the orifice relation Q = 2610 x A x sqrt(dP) in customary units (cfm, sq ft, in. w.g.), and door opening force from the pressure moment about the hinges taken at the knob's lever arm, by name. The 30 lbf total opening-force cap is the International Building Code / NFPA 92 limit, cited by name and not reproduced. A screen, never a stamp; the smoke-control design, its commissioning test, and a qualified engineer govern.

Orifice flow and the door moment balance are public physics. The leakage area, design pressure, door geometry, and closer force are the designer's own values; the opening-force limit is entered.

Estimate. AHJ and licensed professional govern.

Field names used by the API: leakage_area_sqft, pressure_inwg, door_width_ft, door_height_ft, knob_setback_in, closer_force_lbf, force_limit_lbf, airflow_cfm, door_force_lbf, max_pressure_inwg

• Orifice flow Q = 2610 x A x sqrt(dP), cfm from sq ft and in. w.g.; flow goes as the SQUARE ROOT of pressuresmoke-control design practice
• Opening-force cap 30 lbf total, of which the closer alone typically takes 10 to 15IBC / NFPA 92
• The door governs the usable design window is roughly 0.10 to 0.25 in. w.g., set by door force rather than by fan capacitysmoke-control design practice