Smoke control systems (NFPA 92)

modified2026-07-21statusfinished

NFPA 92 Standard for Smoke Control Systems §4.4 & §5.5 — atrium plume mass flow, exhaust sizing, and stairwell/door pressurization checks, in one reference.

Index

Axisymmetric plume mass flow
Balcony spill & window plume
Volumetric smoke exhaust & density correction
Plugholing limit
Stairwell pressurization airflow
Door opening force

Each relation set below includes a Voici¹1Voici compiles a notebook to a static, serverless dashboard — mocked here as a static page, since this pipeline has no Jupyter kernel to run against. dashboard: a matplotlib-styled chart with the live calculator input marked as a red point on the curve.

1.1 · Axisymmetric plume mass flow

[1.1] Governing equations

$$\dot{m}_p = 0.071\,\dot{Q}_c^{1/3} z^{5/3} + 0.0018\,\dot{Q}_c \quad (z \ge z_l)$$

$$z_l = 0.166\,\dot{Q}_c^{2/5}$$

$\dot{m}_p$ smoke mass flow (kg/s), $\dot{Q}_c$ convective HRR (kW), $z$ clear layer height (m). Source: NFPA 92 §5.5, SFPE Handbook.

FIG. 01 — axisymmetric plume geometry: virtual origin z_l, clear height z

reference photo — atrium fire plume / smoke layer (NFPA 92 Fig. 5.5.1 or similar)

REF. — drop in a real photo here to validate FIG. 01 against

Heat release rate Q̇ (MW) Convective fraction χc Clear layer height z (m)

—

import numpy as np, matplotlib.pyplot as plt
z = np.linspace(0.5, 20, 200)
mp = 0.071*Qc**(1/3)*z**(5/3) + 0.0018*Qc
plt.plot(z, mp); plt.scatter([z_input],[mp_input], color='red', zorder=3)

FIG. 02 — plume mass flow ṁp vs. clear height z, current z marked in red

1.2 · Balcony spill & window plume

[1.2] Governing equation

$$\dot{m}_p = 0.36\left(z+z_b\right)^{1/3} W \dot{Q}_c^{1/3}$$

$W$ balcony width (m), $z$ height above balcony (m), $z_b$ balcony height above fire source (m). Source: NFPA 92 §5.5.

FIG. 03 — smoke spilling under a balcony/overhang into an atrium void

reference photo — balcony spill plume / atrium void opening

REF. — drop in a real photo here to validate FIG. 03 against

Balcony width W (m) Convective HRR Q̇c (kW) Height above balcony z (m) Balcony height z_b (m)

—

import numpy as np, matplotlib.pyplot as plt
z = np.linspace(0.2, 10, 200)
mp = 0.36*(z+zb)**(1/3)*W*Qc**(1/3)
plt.plot(z, mp); plt.scatter([z_input],[mp_input], color='red', zorder=3)

FIG. 04 — spill-plume mass flow vs. height above balcony z, current z marked in red

1.3 · Volumetric smoke exhaust & density correction

[1.3] Governing equations

$$T_s = T_0 + \frac{\dot{Q}_c}{\dot{m}_p c_p},\quad \rho_s = \rho_0\frac{T_0}{T_s},\quad V_e = \frac{\dot{m}_p}{\rho_s}$$

$c_p \approx 1.0\ \text{kJ/kg·K}$. Converts smoke mass flow to fan volumetric duty. Source: NFPA 92 §5.5.

Smoke mass flow ṁp (kg/s) Convective HRR Q̇c (kW) Ambient T0 (°C) Ambient density ρ0 (kg/m³)

Smoke temp Ts	—
Smoke density ρs	—
Volumetric rate Ve	—

1.4 · Plugholing limit

[1.4] Governing equation

$$V_{\text{max}} = 3.3\,\gamma\, d^{5/2}\left(\frac{T_s-T_0}{T_0}\right)^{1/2}$$

$\gamma$ location factor (1.0 center of layer, 0.5 near a wall/perimeter). Prevents clean air pull-through at a single exhaust inlet. Source: NFPA 92 §5.5, NFPA 204.

FIG. 05 — smoke layer depth d at a single point extract; plugholing draws clean air through the layer

reference photo — smoke exhaust inlet / plugholing vortex at ceiling vent

REF. — drop in a real photo here to validate FIG. 05 against

Smoke layer depth d (m) Smoke temperature Ts (°C) Ambient T0 (°C) Location factor γ

—

import numpy as np, matplotlib.pyplot as plt
d = np.linspace(0.1, 3, 200)
Vmax = 3.3*gamma*d**(5/2)*np.sqrt((Ts-T0)/T0)
plt.plot(d, Vmax); plt.scatter([d_input],[Vmax_input], color='red', zorder=3)

FIG. 06 — plugholing limit V_max vs. smoke layer depth d, current d marked in red

1.5 · Stairwell pressurization airflow

[1.5] Governing equation

$$Q = C\,A_e\sqrt{\frac{2\Delta P}{\rho}}$$

Target overpressure 0.05–0.10 in. w.g. (12–25 Pa) per NFPA 92 §4.4. $A_e$ total leakage area, $C$ flow/discharge coefficient (~0.6 for cracks). Source: NFPA 92 §4.4.

FIG. 07 — stairwell pressurization: supply air leaks through door/crack area at target ΔP

reference photo — stairwell pressurization fan / egress stair door

REF. — drop in a real photo here to validate FIG. 07 against

Leakage area Ae (m²) Target pressure ΔP (Pa) Flow coefficient C Air density ρ (kg/m³)

—

import numpy as np, matplotlib.pyplot as plt
dP = np.linspace(5, 75, 200)
Q = C*Ae*np.sqrt(2*dP/rho)
plt.plot(dP, Q); plt.scatter([dP_input],[Q_input], color='red', zorder=3)

FIG. 08 — supply airflow Q vs. target pressure ΔP, current ΔP marked in red

1.6 · Door opening force

[1.6] Governing equation

$$F = F_{dc} + \frac{W\cdot A\cdot\Delta P}{2(W-d)}$$

Egress doors must open at $F \le 133\,\text{N}$ (30 lbf) per NFPA 101. $F_{dc}$ closer force, $W$ door width, $A$ door area, $d$ knob offset from hinge edge. Source: NFPA 92 §4.4, NFPA 101.

FIG. 09 — pressure differential across an egress door increases the force needed to swing it open

reference photo — egress door closer / knob with pressure-differential test rig

REF. — drop in a real photo here to validate FIG. 09 against

Door closer force Fdc (N) Door width W (m) Door area A (m²) Knob offset d (m) Pressure differential ΔP (Pa)

—

import numpy as np, matplotlib.pyplot as plt
dP = np.linspace(1, 75, 200)
F = Fdc + (W*A*dP)/(2*(W-d))
plt.plot(dP, F); plt.axhline(133, ls='--'); plt.scatter([dP_input],[F_input], color='red', zorder=3)

FIG. 10 — opening force F vs. pressure differential ΔP, current ΔP marked in red (133 N / 30 lbf limit shown as amber gridline)