Fire-induced pressure

Fire-induced pressure is the change in gas pressure that a fire produces inside a room or building, measured relative to the pressure outside it. Heat from the fire makes the gases expand, and the expansion drives gas out of the room through every available opening. Hot gases are also lighter than the surrounding air, and this buoyancy creates pressure differences that grow with height. In fire experiments, measured pressures range from about 10 Pa in an open compartment fire to about 800 Pa in a closed room that only leaks.

In a perfectly sealed room the rise would be far larger: a constant 100 kW fire in a closed room of 34 m³ would raise the pressure by about 12 kPa within 10 seconds. Real rooms leak, so such values are rarely reached, but even small pressure differences push smoke through cracks and gaps into adjoining spaces. Fire-induced pressure therefore matters for smoke movement, for the force needed to open doors and for the design of smoke control by pressurisation.

Expansion and buoyancy

The ideal gas law describes how the temperature, volume, pressure and amount of a gas are related. When a gas is heated at constant pressure, its volume grows and its density falls. When the amount of gas and the volume stay the same, the pressure rises instead. For air and smoke at about atmospheric pressure, the density follows from the simple relation $\rho \approx 353/T$, with $T$ in kelvin. This gives about 1.2 kg/m³ at 20 °C and 0.75 kg/m³ at 200 °C.

A fire therefore tries to expand the gas it heats. If the room has no space for the extra volume, the surplus gas is pushed out through all available openings. Van Rossum notes that this happens very strongly around the moment of flashover, when smoke is pressed through seams, cracks and holes. Klote names stack effect, buoyancy, expansion, wind and the heating, ventilating and air conditioning (HVAC) system as the main forces that move smoke in buildings. Of these, buoyancy and expansion are produced by the fire itself, while stack effect also occurs without a fire whenever the air inside a building is warmer or colder than outside.

Buoyancy appears because hot smoke weighs less than the same volume of cold air. In a still gas, the pressure at a point depends on the weight of the gas above it, so over a height $\mathrm{\Delta }h$ the pressure changes by roughly $\rho g\mathrm{\Delta }h$. Inside a hot room the pressure therefore falls more slowly with height than outside, and the inside pressure exceeds the outside pressure in the upper part of the room. The level at which both pressures are equal is called the neutral plane. Below it air tends to flow in, and above it smoke tends to flow out.

The buoyancy pressure grows with the height above the neutral plane and with the difference between the inverse absolute temperatures outside and inside the fire room. Klote expresses the pressure difference between a fire compartment and its surroundings as: $$\mathrm{\Delta }P=K_s(\frac{1}{T_0}-\frac{1}{T_F})h$$

Symbol	Description	Unit
$\mathrm{\Delta }P$	pressure difference between fire compartment and surroundings	Pa
$K_s$	coefficient, 3460 in SI units	Pa·K/m
$T_0$	absolute temperature of the surroundings	K
$T_F$	absolute temperature of the fire compartment	K
$h$	height above the neutral plane	m

For a fire compartment at 800 °C, the pressure difference 1.52 m above the neutral plane is about 13 Pa. In a series of full-scale tests cited by Klote, the largest difference measured across the wall of the burn room at the ceiling was 16 Pa. Much larger values require tall fire compartments: at 700 °C, the difference 10.7 m above the neutral plane is about 88 Pa. Klote describes such a case as an extremely large fire, beyond what smoke control systems can resist.

Pressure rise in a closed room

If a room were sealed completely, a relatively small fire would raise the pressure until a window, door or wall burst. NUREG-1805, a set of hand calculation methods of the United States Nuclear Regulatory Commission (NRC), quotes a simple estimate for this case from Karlsson and Quintiere. The relative pressure rise equals the heat released since ignition, divided by the product of the room volume, the air density, the specific heat of air at constant volume and the absolute air temperature: $$\frac{P-P_a}{P_a}=\frac{\dot{Q}t}{V{\rho }_a{c}_v{T}_a}$$

Symbol	Description	Unit
$P$	compartment pressure	Pa or atm
$P_a$	initial atmospheric pressure	Pa or atm
$\dot{Q}$	heat release rate of the fire	kW
$t$	time after ignition	s
$V$	compartment volume	m³
${\rho }_a$	ambient air density	kg/m³
$c_v$	specific heat of air at constant volume, 0.71 to 0.85	kJ/(kg·K)
$T_a$	ambient air temperature	K

The method assumes a constant heat release rate and a constant specific heat. It also neglects the mass of the burning fuel and the small pressure differences over the height of the room. Because the heat released grows with time, the predicted pressure keeps rising for as long as the fire burns.

Worked example: a sealed pump room

NUREG-1805 applies the method to a closed pump room of 3.05 m by 3.66 m by 3.05 m, with a volume of 33.98 m³. A fire with a constant heat release rate of 100 kW burns for 10 s. The ambient air is at 298 K, with a density of 1.18 kg/m³ and $c_v$ = 0.71 kJ/(kg·K).

The heat released is 100 × 10 = 1,000 kJ. The denominator is 33.98 × 1.18 × 0.71 × 298, or about 8,480 kJ. The ratio is therefore 0.118, and multiplying by an atmospheric pressure of 101 kPa gives a rise of about 11.9 kPa. After only 1 s the same calculation gives about 1.2 kPa. NUREG-1805 concludes that the pressure in a closed compartment rises to a large value in a very short time.

Such values are rarely reached in buildings, because cracks around windows and doors and other gaps keep the pressure and its rate of rise small. Truly sealed rooms occur mainly in special cases, such as certain compartments on ships. Failure of a compartment by fire pressure is described as extremely rare, because the vast majority of compartments leak. The quick rise to leakage-limited values is used to justify the constant pressure assumption that is usual for fires in leaky rooms.

Pressure in a leaky room

Leakage changes the result completely. As the pressure rises, gas is forced out through the gaps, and the outflow increases until it balances the expansion. A validation report by the NRC and the Electric Power Research Institute (EPRI) writes the average pressure in a closed and ventilated compartment as a balance of two terms. The first term is the net heating of the gas, which raises the pressure. The second term is the net volume of gas supplied by ventilation minus the gas lost through leaks: $$\frac{\mathrm{d}p}{\mathrm{d}t}=\frac{\gamma -1}{V}(\dot{Q}-{\dot{Q}}_{\mathrm{l}\mathrm{o}\mathrm{s}\mathrm{s}})+\frac{\gamma p}{V}(\dot{V}-{\dot{V}}_{\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{k}})$$

The leakage flow behaves like flow through an orifice, in which the overpressure accelerates the gas through the leakage area: $${\dot{V}}_{\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{k}}=A_{\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{k}}\sqrt{\frac{2(p-p_{\mathrm{\infty }})}{{\rho }_{\mathrm{\infty }}}}$$

The pressure stops rising when the leakage removes exactly the volume created by expansion and supplied by the fans. Setting the rate of change to zero gives an estimate of the maximum overpressure: $${(p-p_{\mathrm{\infty }})}_{\mathrm{m}\mathrm{a}\mathrm{x}}\cong \frac{{\rho }_{\mathrm{\infty }}}{2}{\left(\frac{(\gamma -1)(\dot{Q}-{\dot{Q}}_{\mathrm{l}\mathrm{o}\mathrm{s}\mathrm{s}})+\gamma p_{\mathrm{\infty }}\dot{V}}{\gamma p_{\mathrm{\infty }}{A}_{\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{k}}}\right)}^2$$

Symbol	Description	Unit
$p$	average compartment pressure	Pa
$p_{\mathrm{\infty }}$	ambient pressure	Pa
$\gamma$	ratio of specific heats, about 1.4	–
$V$	compartment volume	m³
$\dot{Q}$	heat release rate (in watts when $p$ is in pascals)	W
${\dot{Q}}_{\mathrm{l}\mathrm{o}\mathrm{s}\mathrm{s}}$	sum of heat losses to the walls	W
$\dot{V}$	net ventilation rate into the compartment	m³/s
${\dot{V}}_{\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{k}}$	leakage rate out of the compartment	m³/s
$A_{\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{k}}$	leakage area	m²
${\rho }_{\mathrm{\infty }}$	ambient air density	kg/m³

The fraction inside the brackets has the unit of a velocity: it is the speed at which the expanded gas must leave through the leakage area. The maximum overpressure is the pressure needed to drive the gas at that speed. The room volume does not appear in the result, although a larger room takes longer to reach it. The overpressure scales with the inverse square of the leakage area, so ten times more leakage gives about one hundredth of the pressure.

Worked example: a small room with leaks

NUREG-1805 states that adding 100 kW to a 60 m³ room with an opening of 0.01 m² causes a steady pressure rise of about 1,000 Pa within several seconds. The estimate above can be checked by hand, with no fan flow and no heat losses. The expansion term $(\gamma -1)\dot{Q}/(\gamma p_{\mathrm{\infty }})$ gives 0.4 × 100,000 / (1.4 × 101,325) = 0.28 m³ of extra gas volume every second. Pushing this volume through 0.01 m² requires a speed of 28.2 m/s. With an air density of 1.2 kg/m³, the overpressure is 0.6 × 28.2² ≈ 480 Pa.

Real gaps do not pass the full flow of their geometric area. Emmons gives a flow coefficient of about 0.60 for orifices, and Van Rossum describes the same effect as a contraction factor that reduces the effective area of an opening. With an effective area of 0.6 × 0.01 = 0.006 m², the speed becomes 47.0 m/s and the overpressure about 1,330 Pa. The two results bracket the value of about 1,000 Pa quoted by NUREG-1805. Both ignore heat losses to the walls, which would lower the pressure in a real room.

Quintiere gives a second case, a 100 kW fire in a 40 m³ room with a vent of 0.1 m². The pressure rises by roughly 10 Pa above the ambient 100,000 Pa in less than 0.01 s. The opening is ten times larger than in the NUREG-1805 case, and the overpressure is about one hundred times smaller, as the inverse-square scaling predicts. Quintiere also notes that a fall in the heat release rate makes the pressure drop below ambient. Cycling between heating and cooling explains the breathing effect of fires in closed buildings.

Openings and buoyant flow

A room with a normal door or window behaves differently from a leaky closed room. At the start, the fire plume carries hot gas to the ceiling, and expansion pushes some gas out of the opening. As the fire grows, the buoyant outflow of hot gas through the upper part of the opening exceeds the expansion. The pressure at the floor of the fire room then falls below atmospheric, and outside air flows in at the bottom while smoke leaves through the upper part. From that moment the vent flow is driven mainly by buoyancy. Klote states that the pressure difference due to expansion across open doors or windows is negligible, while in a tightly sealed fire compartment it may be important.

Expansion still shows in the size of the flows. If the small added mass of the fuel is neglected, the volume flow of smoke leaving the room divided by the volume flow of air entering equals the ratio of their absolute temperatures. For smoke at 700 °C the ratio is 3.32, so 1.5 m³/s of incoming air leaves as 4.98 m³/s of smoke. Emmons describes the same balance for a building: the net outflow only accommodates the expansion, but the hot outflow by volume may be 2.5 times the inflow.

The pressure differences behind these flows are tiny compared with the atmospheric pressure. In a room 2.5 m high, the difference in atmospheric pressure between floor and ceiling is 28.84 Pa, only 0.00028 of the atmospheric pressure. A buoyant room fire can nevertheless drive gas velocities of up to 7.00 m/s through its openings. Because the pressure changes so little, its effect on gas density is negligible, and the density can be found from the temperature alone.

Doors and leakage paths

A fire anywhere in a building raises the local pressure and pushes air through all pathways that lead to the outside. With an open window in the room of origin and little wind, little flow passes through the rest of the building. Without an open window, the flow moves towards cracks and leaks wherever they are. The buoyancy pressure of the fire also drives smoke through leakage paths in the walls and around the doors of the fire compartment. Where the ceiling leaks, smoke reaches the floor above, although the effect weakens with distance as the smoke cools.

Closed doors are therefore important leakage paths. A door of 0.9 m by 2.1 m with an average crack width of 3.2 mm has a leakage area of about 0.020 m². Elevator doors have measured leakage areas of 0.051 to 0.065 m² per door. In New Zealand, C/VM2 (second edition, 2025) requires that a fire door without smoke seals be modelled with a 10 mm gap over its full height. A smoke control door is modelled with a 10 mm gap under the door only, and other fire and smoke separations are taken as airtight. Non-fire-rated walls leak 0.1 % of their area when lined and 0.5 % when they are unlined external walls.

In Australia, the Fire Safety Verification Method handbook of the Australian Building Codes Board (ABCB) describes a reference scenario without sprinklers. The fire reaches flashover, and smoke leaks around the fire door into a stair, possibly preventing evacuation from the floors above. The accompanying data sheets cite the Australian standard AS 6905. For a single-leaf smoke door, it allows no more than 40 m³/h at medium temperature and 25 Pa, after exposure to 200 °C for at least 30 minutes.

Pressure differences also affect the people who must open doors. The force needed is the sum of the force to overcome the door closer and the force to overcome the pressure on the door leaf. The pressure part grows with the door area and the pressure difference, and it shrinks as the knob moves further from the hinges. Klote gives: $$F=F_{\mathrm{d}\mathrm{c}}+\frac{k_{d}WA\mathrm{\Delta }P}{2(W-d)}$$

Symbol	Description	Unit
$F$	total door opening force	N
$F_{\mathrm{d}\mathrm{c}}$	force to overcome the door closer	N
$k_d$	coefficient, 1.00 in SI units	–
$W$	door width	m
$A$	door area	m²
$\mathrm{\Delta }P$	pressure difference across the door	Pa
$d$	distance from the knob to the knob-side edge of the door	m

For a door 2.13 m high and 0.91 m wide, with 75 Pa across it and a closer force of 53 N, the total opening force is 133 N. The closer accounts for 53 N of this, so the pressure difference adds about 80 N. Klote cites the Life Safety Code of the United States National Fire Protection Association (NFPA 101). It limits the force to open any door in a means of egress to 133 N.

Measurement and modelling

In fire experiments, compartment pressure is measured with sensitive pressure transducers. The NRC and EPRI validation experiments used transducers with a range of about 1,000 Pa and an accuracy of 0.5 % of full scale. This gave an uncertainty of about ±5 Pa. The measured pressures ranged from about 10 Pa, typical of an open compartment, to about 800 Pa, typical of a closed compartment with leakage.

A zone model such as CFAST (Consolidated Fire and Smoke Transport) calculates a single pressure for each compartment from the conservation of mass and energy and the ideal gas law. For a closed compartment without mass flows, the CFAST pressure equation reduces to $\mathrm{d}P/\mathrm{d}t=(\gamma -1)({\dot{q}}_l+{\dot{q}}_u)/V$, where the two heat terms belong to the lower and upper gas layers. The pressure reacts to changes much faster than the other variables, which makes the equations stiff and calls for special numerical solvers. The Fire Dynamics Simulator (FDS) treats each closed room or isolated volume as a pressure zone with its own background pressure. This captures a fire in a closed compartment and the effect of ventilation systems. Gaps around windows and doors and openings for services are modelled as equivalent ducts between pressure zones.

In the NRC and EPRI validation study, the overpressures predicted by FDS were about as accurate as the measurements. The report attributes this to the global conservation of mass and energy in FDS. The zone models found it harder to predict the pressure at a specific point, because they assume that pressure varies only with height. CFAST overpredicted the pressure more than the zone model MAGIC. Because FDS assumes flow speeds far below the speed of sound, it should not be used for the rapid discharge of pressure vessels.

Use in design and limitations

Fire-induced pressure sets the minimum pressure difference that a smoke control system must maintain across its boundaries. Klote suggests 20 to 25 Pa for a boundary that may face an intense fire next to a door, slightly more than the 16 Pa measured in full-scale tests. For smoke at 400 °C from a remote fire, the buoyancy pressure 1.53 m above the neutral plane is about 10 Pa, for which Klote suggests 15 to 20 Pa. In sprinklered buildings, where the water spray cools the smoke, the suggested range is 5 to 10 Pa. The upper limit is set by the door opening force, which must not become excessive.

The estimates in this article rest on simplifying assumptions. Empirical correlations for room pressure apply only in the simplest room geometries. Leakage areas are uncertain: C/VM2 notes that the actual amount of leakage is never known and asks for a reasonable estimate in models. Klote reports that actual leakage areas are believed to depend mainly on workmanship rather than on construction materials. The calculated pressure is also sensitive to its inputs. Random sampling of typical values of 1,000 kW, 1 m³/s and 0.06 m² gave a relative standard uncertainty of 21 % in the overpressure.

Wind can easily exceed the pressures produced by the fire. A wind of 15.6 m/s produces about 117 Pa on a windward wall with a pressure coefficient of 0.8. A broken window on the windward side can then force smoke throughout the fire floor and even to other floors.

See also

• Neutral plane
• Hot gas layer
• Smoke filling
• Smoke explosion

References

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• Stroup, D., Lindeman, A., McGrattan, K., Peacock, R., Overholt, K., Joglar, F., LeStrange, S., & Montanez, S. (2016). Verification and validation of selected fire models for nuclear power plant applications: Supplement 1 (NUREG-1824, Supplement 1; EPRI 3002002182). U.S. Nuclear Regulatory Commission, Office of Nuclear Regulatory Research; Electric Power Research Institute.
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