Tools › Building Systems › Fire Protection › Fire Dynamics Calculations › Example
NUREG-1805 Example 2-1: hot gas layer temperature and smoke layer height in a naturally ventilated room (MQH, Yamana and Tanaka)
| Tool | Fire Dynamics Calculations |
| Source | Iqbal, N., and Salley, M. H. (2004). Fire Dynamics Tools (FDTs): Quantitative Fire Hazard Analysis Methods for the U.S. Nuclear Regulatory Commission Fire Protection Inspection Program. NUREG-1805, U.S. Nuclear Regulatory Commission, Washington, DC. Chapter 2, Example Problem 2.16.1-1, pp. 2-29 to 2-40 (re-solved in NUREG-1805 Supplement 1, Vol. 2, 2013, pp. A-3 to A-20). |
| Level | Professional |
Problem
A compartment 15 ft wide, 15 ft long and 10 ft high has a single vent 4 ft wide and 6 ft tall whose top is 6 ft above the floor. A steady 500 kW fire burns away from the walls; the ambient air is at 77 °F. Find the hot gas layer temperature and the smoke layer height 2 minutes after ignition when the interior lining is (a) 1 ft thick concrete and (b) 1 in gypsum board.
Inputs to Enter
- Compartment 15 × 15 × 10 ft, vent 4 × 6 ft with its top at 6 ft, natural ventilation (MQH)
- Lining (a) concrete: kρc 2.9 (kW/m²-K)²-s, k 0.0016 kW/m-K, c 0.75 kJ/kg-K, ρ 2,400 kg/m³, 12 in thick; (b) gypsum board: 0.18, 0.00017, 1.1, 960, 1 in thick (NUREG-1805 Table 2-3)
- Heat release rate 500 kW, time after ignition 2 min, ambient 77 °F, c_p 1.0 kJ/kg-K
Answers
- A_v = 1.2192 × 1.8288 = 2.2297 m², A_T = 2(4.572²) + 4(3.048 × 4.572) − 2.2297 = 95.32 m²; concrete t_p = (2400 × 0.75/0.0016)(0.1524/2)² = 26,129 s > 120 s, so h_k = √(2.9/120) = 0.1555 kW/m²-K
- ΔT_g = 6.85 [500²/(2.2297 × √1.8288 × 95.32 × 0.1555)]^(1/3) = 121.6 K; T_g = 147 °C (296 °F) (printed 147 °C / 296 °F)
- Gypsum board 1 in: t_p = 1,002 s > 120 s, h_k = √(0.18/120) = 0.0387; ΔT_g = 193.3 K; T_g = 218 °C (425 °F) (printed 218 / 425)
- Smoke layer (Yamana and Tanaka): ρ_g = 353/419.8 = 0.841 kg/m³, k = 0.0904; z = [2 × 0.0904 × 500^(1/3) × 120/(3 × 20.90) + 3.048^(−2/3)]^(−3/2) = 0.17 m, below the vent top, so the credited height is the vent top 1.83 m (6.00 ft) with the handbook's 'smoke exiting vent' caution (printed 6.00 ft for both linings)
Notes
The tool's default inputs are case (a); press Submit, then choose Gypsum board with a 1 in thickness for case (b). The handbook's equations are images in the PDF; the tool implements the Supplement 1 spreadsheet 02.1 and reproduces its cached values to six figures. Every printed example of chapters 2, 3, 5, 6, 9, 10 to 13 and 18 is reproduced by test_fire_dynamics.php (427 checks) with an independent numpy re-implementation in References/Fire-Dynamics/checks/.