Atrium Smoke Control: Design Fire and Exhaust Trade-off
A four-story atrium in a mixed-use building is 60 ft high with a 100 ft by 60 ft plan (about 360,000 ft³, 10,200 m³). The performance-based smoke control design assumes a single 2,500 kW fire in a cluster of retail kiosks with mobile merchandise carts and provides 60,000 cfm of roof exhaust. The report labels the growth "fast" but does not document the fuel package, and the exhaust is justified only as 10 air changes per hour. The architect wants to cut exhaust to 35,000 cfm to save shaft space, and the AHJ has asked you to review the design before the atrium opens.
1. Using t-squared growth, calculate the time to reach 2,500 kW for slow, medium, fast, and ultrafast growth and explain what the result says about the report's design fire.
Read the worked answer
Use Q = αt², so t = √(Q/α). With Q = 2,500 kW:
| Growth | α (kW/s²) | Time to 2,500 kW |
|---|---|---|
| Slow | 0.00293 | √(2,500/0.00293) ≈ 924 s ≈ 15.4 min |
| Medium | 0.0117 | √(2,500/0.0117) ≈ 462 s ≈ 7.7 min |
| Fast | 0.0469 | √(2,500/0.0469) ≈ 231 s ≈ 3.9 min |
| Ultrafast | 0.1876 | √(2,500/0.1876) ≈ 115 s ≈ 1.9 min |
The label matters far less than the fuel package. A cluster of retail kiosks with mobile carts is not automatically a "fast" fire; cart contents, height, and spacing can produce growth from medium to ultrafast. The report should justify the α from the actual commodity and arrangement, state whether 2,500 kW is a peak or a steady value, and show how the fire is expected to be controlled. If the kiosks can produce an ultrafast fire, 2,500 kW is reached in under 2 minutes, leaving little time for detection, notification, and smoke layer management.
2. Estimate the plume mass flow at 2,500 kW when the smoke layer is 6 ft deep and compare it with 60,000 cfm. What does that comparison tell you?
Read the worked answer
Use the axisymmetric plume relation M = 0.071 Qc^(1/3) z^(5/3), with z = 6 ft ≈ 1.83 m and Qc ≈ 0.7 × 2,500 = 1,750 kW:
- Qc^(1/3) ≈ 12.05
- z^(5/3) ≈ 2.74
- M ≈ 0.071 × 12.05 × 2.74 ≈ 2.3 kg/s
At roughly 1.0 m³/kg for hot smoke, that is about 2.3 m³/s, or roughly 5,000 cfm entering the layer. The 60,000 cfm exhaust is therefore more than an order of magnitude above the plume rate at that layer depth. That does not prove the design is wrong, but it shows the design is not mass-flow-limited at the assumed fire. The governing issues become make-up air, pressure differences across doors, ceiling-jet mixing, and whether the assumed fire is realistic. The report should show a smoke-filling analysis or CFD, not an air-change rate.
3. Advise on the 35,000 cfm reduction and list the verification steps you would require.
Read the worked answer
NFPA 92 does not set a minimum air-change rate; exhaust must be justified by the design fire, the required smoke layer, and tenability. On the plume estimate alone, 35,000 cfm is still several times the plume flow at a 6 ft layer, so the reduction is not automatically unacceptable. But it cannot be approved from an ACH argument.
Require:
- A documented design fire with fuel package, growth rate, peak, and sprinkler interaction.
- A smoke-filling or CFD analysis at 35,000 cfm showing the layer stays above the design height for the required egress time.
- Make-up air at least equal to exhaust, with a path that does not create unacceptable door forces or velocities.
- Analysis of pressure differences at atrium boundaries, including elevator and stair doors.
- Sensitivity cases for a larger or faster fire and for partial exhaust failure.
- A clear statement that the 60,000 cfm value was never a code minimum and that the reduced value is tied to the analysis.
If the fire is upgraded to ultrafast or the make-up air is inadequate, reject the reduction.