Vent flow: Difference between revisions

Latest revision as of 17:19, 2 November 2026

Vent flow is the flow of gas through an opening in the boundary of a room or building during a fire. Emmons calls any opening through which gas can flow out of the fire room a vent. Vents include open doors, open or broken windows, ventilation ducts and the cracks around closed doors and windows.^[1] Gas moves only when it is pushed, and the only forces acting on it are pressure and gravity.^[1] In a room fire, vent flows carry hot smoke out of the room and bring in the fresh air that keeps the fire burning.^[2]

Vent flows are calculated with the methods of hydraulics, corrected by a flow coefficient that is found by experiment.^[1] For a door or window, the flow is driven mainly by the difference in density between hot smoke inside and cool air outside. Hot gas then leaves through the upper part of the opening and air enters through the lower part.^[2] Vent flows set the depth of the smoke layer in a room with an open door, limit the air supply of a fully developed fire and carry smoke through a building.^[3]^[4]^[5]

Pressure-driven flow through openings

When a pressure difference exists across an opening, gas is pushed through it. For a gas of constant density, the velocity, the volume flow and the mass flow follow from the pressure difference.^[1] The volume flow through an opening of area $A$ is: $\dot{V} = C A \sqrt{\frac{2 Δ p}{ρ}}, \dot{m} = C A \sqrt{2 ρ Δ p}$

Symbol	Description	Unit
$\dot{V}$	volume flow through the opening	m³/s
$\dot{m}$	mass flow through the opening	kg/s
$C$	flow coefficient	–
$A$	area of the opening	m²
$Δ p$	pressure difference across the opening	Pa
$ρ$	density of the gas flowing through the opening	kg/m³

The flow coefficient corrects for effects such as viscosity, an uneven velocity across the opening and the shape of the edges.^[6] At a sharp-edged opening the flow separates from the edge and contracts to about 0.6 of the opening area. Emmons therefore gives a coefficient of about 0.60 for orifices, such as most fire vents, and 0.98 for rounded nozzles.^[1]^[2] The coefficient depends on the Reynolds number, but in most fire applications this number is about one million, and these fixed values can be used.^[2] Klote uses the same relation for leakage paths around doors and through walls, with a coefficient generally between 0.6 and 0.7.^[7] In Australia, the data sheets of the Fire Safety Verification Method use 0.65 for leakage paths.^[8]

Klote shows how small these flows can be. A closed door with a crack area of 0.01 m² leaks about 0.013 m³/s at a pressure difference of 2.5 Pa. At 75 Pa the leakage rises to 0.073 m³/s, because the flow grows with the square root of the pressure difference.^[7]^[9] Klote adds that this square-root law is reasonable for all flow paths except extremely narrow cracks.^[7] In the early stage of a fire, the expansion of heated gas drives such flows through all openings, before buoyancy takes over.^[2]

Buoyant flow through doors and windows

In a door or window, the pressure difference changes with height. Inside a hot room the pressure falls more slowly with height than outside, because the hot gas is lighter. The difference in buoyancy between the two gas columns therefore produces a pressure difference that grows from the bottom to the top of the opening.^[2]^[10] Below a certain height the outside pressure is higher and air flows in. Above it the inside pressure is higher and smoke flows out. The height where the two pressures are equal and the velocity is zero is the neutral plane.^[11]

Left: room with hot layer and door, smoke out above and air in below. Right: inside and outside pressure lines crossing at the neutral plane. — Pressure inside and outside a fire room with an open door: above the neutral plane smoke flows out, below it air flows in. Based on Emmons (2002), pp. 2-34 and 2-36.

The density of the gases follows from their temperature through the ideal gas law. For fire gases, which consist mostly of air, Emmons gives ρ = 352.8/T kg/m³, with the temperature in kelvin.^[12] The pressure itself changes so little that its effect on density can be neglected.^[12] The pressure differences involved are tiny. 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. Yet buoyant flows in a room fire can reach velocities of up to 7.00 m/s.^[12]

If the room contains a uniform hot layer above a cool lower layer, the outflow can be calculated directly. The velocity at a height $y$ above the neutral plane and the total mass flow out are:^[13] $V_{u} = {(2 g \frac{ρ_{a} - ρ}{ρ} y)}^{1 / 2}, {\dot{m}}_{u} = \frac{\sqrt{8}}{3} C b \sqrt{g ρ (ρ_{a} - ρ)} {(h_{v} - h_{n})}^{3 / 2}$

Symbol	Description	Unit
$V_{u}$	outflow velocity at height $y$ above the neutral plane	m/s
${\dot{m}}_{u}$	mass flow out of the opening	kg/s
$C$	flow coefficient for buoyant flow, 0.68	–
$b$	width of the opening	m
$g$	acceleration due to gravity	m/s²
$ρ$ , $ρ_{a}$	density of the hot layer and of the ambient air	kg/m³
$h_{v}$	height of the top of the opening above the sill	m
$h_{n}$	height of the neutral plane above the sill	m

The flow coefficient of 0.68 was measured in experiments with kerosene and water, two liquids that do not mix. Emmons advises using this value and expecting errors of about ±10 % in flow calculations.^[13] The International Fire Engineering Guidelines (IFEG) give the same formula, with the constant √8/3 written as 0.943 and a default coefficient of 0.68.^[14]

For a preflashover fire with a typical door or window, Walton and Thomas place the neutral plane and the interface at mid-height of the opening. This approximation applies once the room has filled with smoke and the flows in and out are established.^[4] The IFEG note that the neutral plane usually lies close to the smoke layer interface. Above about 200 °C, and with a low interface, it does not fall below about 0.44 times the height of the opening.^[14]

Worked example

Emmons applies the two-layer formula to test data from a steady burner fire at the United States National Bureau of Standards. The doorway was 1.83 m high and 0.737 m wide, the ambient temperature was 294.3 K, and the outflow measured with velocity probes was 0.588 kg/s.^[15] From the measured temperature profile, the neutral plane was placed at 1.00 m, where the steep temperature rise in the doorway begins. The lower temperature was 308 K, and the average of 1/T over the doorway was 2.875 × 10⁻³ K⁻¹.^[15]

The hot layer temperature follows from the condition that the two-layer model has the same average density as the real flow.^[13] This gives about 412 K, so the hot layer density is 352.8 / 412 = 0.856 kg/m³. The ambient density is 352.8 / 294.3 = 1.199 kg/m³.^[15] The outflow is then 0.943 × 0.68 × 0.737 × √(9.81 × 0.856 × 0.343) × 0.83^1.5, or about 0.61 kg/s. This is about 3 % higher than the measured value.^[15] At the top of the doorway, 0.83 m above the neutral plane, the outflow velocity is about 2.6 m/s.

Chart of height in a doorway against outflow velocity: zero at 1.0 m, rising along a square-root curve to about 2.6 m/s at 1.83 m. — Outflow velocity in the doorway of the worked example, from the two-layer formula. Based on Emmons (2002), pp. 2-37–2-39.

Air supply and the ventilation factor

Near and after flashover, the interface between the hot and cool layers lies close to the floor. The flow through the opening then reaches a maximum for a given gas temperature.^[4] Above about 150 °C the inflow hardly depends on temperature and is proportional to $A_{0} \sqrt{H_{0}}$ , where $A_{0}$ is the area and $H_{0}$ the height of the opening.^[4] Rockett calculated the constant as 0.40 to 0.61 kg/(s·m^5/2), depending on the discharge coefficient. Thomas and Heselden estimated 0.5, the value most often used, which gives an air inflow of 0.5 $A_{0} \sqrt{H_{0}}$ kg/s.^[4]

Line chart: air inflow rises in proportion to the ventilation factor; a band between 0.40 and 0.61 times with a central line at 0.5. — Air inflow of a room near or after flashover against the ventilation factor of its opening. Based on Walton and Thomas (2002), p. 3-174.

The product $A_{0} \sqrt{H_{0}}$ is called the ventilation factor. Kawagoe first used this kind of analysis for fully developed fires, and wood fires in rooms with small windows were found to burn at a rate of about 0.09 $A_{0} \sqrt{H_{0}}$ kg/s.^[4] For most fuels, about 3,000 kJ of heat is released for each kilogram of air consumed. The largest heat release rate that the inflowing air can support is therefore about 1,500 $A_{0} \sqrt{H_{0}}$ kW.^[16] For the doorway of the worked example, the ventilation factor is 1.349 × √1.83 ≈ 1.82 m^5/2. This gives an air inflow of about 0.91 kg/s and a stoichiometric heat release rate of about 2.7 MW.

Openings can also change during a fire. In New Zealand, C/VM2 (second edition, 2025) assumes that exterior windows without fire-resisting glazing break and become fully open at the sooner of two moments. One is when the average upper layer temperature reaches 500 °C, and the other is when the fire becomes limited by ventilation.^[17] The same document treats open doors used for escape as half their width in smoke flow calculations, because people passing through obstruct the flow.^[18]^[17]

Flows between rooms and through horizontal vents

When smoke reaches a second room, there may be a hot layer on both sides of a connecting opening. The pressure profiles then depend on four gas densities and four heights, and the opening can carry up to four flow layers separated by up to three neutral planes.^[19] In the common case of a fire room next to the open air, there is a single neutral plane somewhat above the hot layer interface in the fire room.^[19] A zone model calculates such flows layer by layer, with a linear pressure variation within each layer.^[19]

The zone model CFAST (Consolidated Fire and Smoke Transport) divides each wall opening into horizontal segments. Each segment is bounded by the sill, the top of the opening, the layer interfaces on either side or the neutral plane. The flow in each segment follows from Bernoulli's equation with an orifice coefficient of 0.7.^[20] Hot gas that flows into the cool lower layer of the next room is treated as a spill plume that entrains air as it rises.^[21] Van Rossum notes that a high opening in a façade can act as a supply, an exhaust or both, depending on its position relative to the neutral plane.^[22]

Flows through horizontal openings, such as holes in a ceiling or roof, are much less well understood. Emmons gives formulas of unknown accuracy, which he describes as better than nothing.^[15]^[23] For a 1 m vent with a density ratio of 4 to 1, the buoyancy effect amounts to 8.6 Pa and produces a velocity of about 4 m/s.^[15] Near zero net flow, the boundary between the hot and cold gas becomes unstable, and gas flows up and down at the same time.^[15] The IFEG name two observed phenomena: puffing, which is closely related to the combustion process in the fire room, and exchange flow, which occurs when the arrangement of the gases across the vent is unstable. They also give a simple formula with a default discharge coefficient of 0.61.^[24] CFAST uses a correlation by Cooper with a coefficient of 0.68 plus an exchange flow term.^[25]

Effective areas and leakage networks

The area that counts in a flow calculation is often smaller than the opening itself. Van Rossum calls the effective area of an opening its aerodynamic area. It equals the actual area multiplied by a contraction factor, for example 0.65 for a vent hatch, because eddies at the edges and obstacles disturb the flow.^[26] Manufacturers give this aerodynamic free area for their products. Louvres and screens further reduce the flow area of a vent.^[26]^[27] For an open stairwell door, Klote recommends a flow area of half the geometric area of the doorway, based on measurements by Cresci.^[27]

A building behaves as a network of such openings, comparable to a system of pipes and orifices.^[5] A layer of hot gas moves along the ceilings of connected spaces and rises through the first stairwell or ceiling opening it meets.^[5] Klote combines leakage paths into effective areas, in the same way as electrical resistances. Paths in parallel simply add up, so leaks of 0.10, 0.05 and 0.05 m² act as one opening of 0.20 m².^[28] For paths in series, the effective area is:^[28] $A_{e} = {(\sum_{i = 1}^{n} \frac{1}{A_{i}^{2}})}^{- 1 / 2}$ where $A_{e}$ is the effective area and $A_{i}$ are the individual areas in m². Two equal paths of 0.02 m² in series give 0.014 m², and paths of 0.02 m² and 0.2 m² in series give 0.0199 m².^[28] When one of two openings in series is much larger than the other, the effective area is approximately that of the smaller one.^[28]

Leakage paths in parallel add up (left); in series the smallest opening controls the flow (right). Based on Klote (2002), p. 4-283.

In smoke exhaust design, Van Rossum notes that the exhaust capacity by volume should exceed the supply capacity, and the more so the hotter the smoke.^[22] A single exhaust point with too much capacity can also draw clean air from below a thin smoke layer, an effect called plugholing.^[26] Remedies include more exhaust points with a smaller capacity each, a deeper smoke layer, and guiding the air so that the suction acts horizontally on the layer.^[26]

Measurement and accuracy

Vent flows in fire tests are measured with rows of pressure probes and thermocouples in the opening. Bidirectional probes give velocities within 10 % for flow directions up to 50 degrees from the probe axis.^[12] Simpler methods use the pressure difference at one height, the visible bottom of the outflow or an assumed two-layer profile, at the cost of accuracy.^[11]^[13] Emmons notes that a fire close to the opening has unknown effects on the flow.^[12]

The achievable accuracy differs strongly between cases. Flow through nozzles and orifices in a calibrated pipe can be calculated to about 2 %. For vents in vertical walls with limited circulation inside the fire room, the best methods of measurement may get 5 % accuracy. In real fires the induced circulations are often severe and unknown, so errors of 10 % or more must be expected.^[23] The accuracy for horizontal vents is completely unknown.^[23] The IFEG add that hand calculations of smoke spread beyond the room of fire origin are more difficult and therefore rarely used. Their results are also more uncertain than those for the room of fire origin.^[14]

Vent flows nevertheless control important results of fire models. The United States Nuclear Regulatory Commission (NRC) and the Electric Power Research Institute (EPRI) carried out a validation study of fire models. Most of its experiments in which the smoke layer depth was predicted had at least one open door or window. In those experiments the depth was largely set by the height of the opening and was relatively insensitive to the heat release rate.^[3] NUREG-1805 describes the same process: the hot layer descends within the opening until the inflow and outflow of the layer balance.^[29]

Notes

↑ ^1.0 ^1.1 ^1.2 ^1.3 ^1.4 Emmons (2002), p. 2-32.
↑ ^2.0 ^2.1 ^2.2 ^2.3 ^2.4 ^2.5 Emmons (2002), p. 2-34.
↑ ^3.0 ^3.1 Stroup et al. (2016), p. 3-35.
↑ ^4.0 ^4.1 ^4.2 ^4.3 ^4.4 ^4.5 Walton and Thomas (2002), p. 3-174.
↑ ^5.0 ^5.1 ^5.2 Emmons (2002), p. 2-41.
↑ Emmons (2002), p. 2-33.
↑ ^7.0 ^7.1 ^7.2 Klote (2002), p. 4-280.
↑ Australian Building Codes Board (2020a), Data Sheet C5, p. 149.
↑ Klote (2002), p. 4-281.
↑ Van Rossum (2027), §3.2.
↑ ^11.0 ^11.1 Emmons (2002), p. 2-36.
↑ ^12.0 ^12.1 ^12.2 ^12.3 ^12.4 Emmons (2002), p. 2-35.
↑ ^13.0 ^13.1 ^13.2 ^13.3 Emmons (2002), p. 2-37.
↑ ^14.0 ^14.1 ^14.2 National Research Council of Canada et al. (2005), p. 2.5-6.
↑ ^15.0 ^15.1 ^15.2 ^15.3 ^15.4 ^15.5 ^15.6 Emmons (2002), p. 2-39.
↑ Walton and Thomas (2002), p. 3-184.
↑ ^17.0 ^17.1 Ministry of Business, Innovation and Employment (2025b), p. 16.
↑ Ministry of Business, Innovation and Employment (2025b), p. 15.
↑ ^19.0 ^19.1 ^19.2 Emmons (2002), p. 2-38.
↑ Peacock et al. (2026), p. 19.
↑ Peacock et al. (2026), pp. 20–21.
↑ ^22.0 ^22.1 Van Rossum (2027), §9.3 (How a zone model works).
↑ ^23.0 ^23.1 ^23.2 Emmons (2002), p. 2-40.
↑ National Research Council of Canada et al. (2005), p. 2.5-7.
↑ Peacock et al. (2026), p. 21.
↑ ^26.0 ^26.1 ^26.2 ^26.3 Van Rossum (2027), §6.8.
↑ ^27.0 ^27.1 Klote (2002), p. 4-282.
↑ ^28.0 ^28.1 ^28.2 ^28.3 Klote (2002), p. 4-283.
↑ Iqbal and Salley (2004), p. 2-8.

References

Australian Building Codes Board. (2020a). Data sheets: Fire Safety Verification Method (Handbook annex, Print version 1.1).
Emmons, H. W. (2002). Vent flows. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 2-32–2-41). National Fire Protection Association; Society of Fire Protection Engineers.
Iqbal, N., & 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, Office of Nuclear Reactor Regulation.
Klote, J. H. (2002). Smoke control. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 4-274–4-291). National Fire Protection Association; Society of Fire Protection Engineers.
Ministry of Business, Innovation and Employment. (2025b). Verification Method C/VM2: Framework for fire safety design (2nd ed.).
National Research Council of Canada, International Code Council, Department of Building and Housing, & Australian Building Codes Board. (2005). International fire engineering guidelines (2005 ed.). Australian Building Codes Board.
Peacock, R. D., McGrattan, K. B., Forney, G. P., & Reneke, P. A. (2026). CFAST – Consolidated Fire and Smoke Transport: Vol. 1. Technical reference guide (Version 7, NIST Technical Note 1889v1). National Institute of Standards and Technology. https://doi.org/10.6028/NIST.TN.1889v1
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.
Van Rossum, E. (2027). Introduction to Fire Safety Engineering. Fire Safety Academy.
Walton, W. D., & Thomas, P. H. (2002). Estimating temperatures in compartment fires. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 3-171–3-188). National Fire Protection Association; Society of Fire Protection Engineers.

[EM-2-32-1] 1.0 ^1.1 ^1.2 ^1.3 ^1.4 Emmons (2002), p. 2-32.

[EM-2-34-2] 2.0 ^2.1 ^2.2 ^2.3 ^2.4 ^2.5 Emmons (2002), p. 2-34.

[ST-3-35-3] 3.0 ^3.1 Stroup et al. (2016), p. 3-35.

[WT-3-174-4] 4.0 ^4.1 ^4.2 ^4.3 ^4.4 ^4.5 Walton and Thomas (2002), p. 3-174.

[EM-2-41-5] 5.0 ^5.1 ^5.2 Emmons (2002), p. 2-41.

[EM-2-33-6] Emmons (2002), p. 2-33.

[KL-4-280-7] 7.0 ^7.1 ^7.2 Klote (2002), p. 4-280.

[ABCB-C5-8] Australian Building Codes Board (2020a), Data Sheet C5, p. 149.

[KL-4-281-9] Klote (2002), p. 4-281.

[VR-3.2-10] Van Rossum (2027), §3.2.

[EM-2-36-11] 11.0 ^11.1 Emmons (2002), p. 2-36.

[EM-2-35-12] 12.0 ^12.1 ^12.2 ^12.3 ^12.4 Emmons (2002), p. 2-35.

[EM-2-37-13] 13.0 ^13.1 ^13.2 ^13.3 Emmons (2002), p. 2-37.

[IFEG-2.5-6-14] 14.0 ^14.1 ^14.2 National Research Council of Canada et al. (2005), p. 2.5-6.

[EM-2-39-15] 15.0 ^15.1 ^15.2 ^15.3 ^15.4 ^15.5 ^15.6 Emmons (2002), p. 2-39.

[WT-3-184-16] Walton and Thomas (2002), p. 3-184.

[MBIE-16-17] 17.0 ^17.1 Ministry of Business, Innovation and Employment (2025b), p. 16.

[MBIE-15-18] Ministry of Business, Innovation and Employment (2025b), p. 15.

[EM-2-38-19] 19.0 ^19.1 ^19.2 Emmons (2002), p. 2-38.

[PE-19-20] Peacock et al. (2026), p. 19.

[PE-20-21] Peacock et al. (2026), pp. 20–21.

[VR-9.3-22] 22.0 ^22.1 Van Rossum (2027), §9.3 (How a zone model works).

[EM-2-40-23] 23.0 ^23.1 ^23.2 Emmons (2002), p. 2-40.

[IFEG-2.5-7-24] National Research Council of Canada et al. (2005), p. 2.5-7.

[PE-21-25] Peacock et al. (2026), p. 21.

[VR-6.8-26] 26.0 ^26.1 ^26.2 ^26.3 Van Rossum (2027), §6.8.

[KL-4-282-27] 27.0 ^27.1 Klote (2002), p. 4-282.

[KL-4-283-28] 28.0 ^28.1 ^28.2 ^28.3 Klote (2002), p. 4-283.

[IS-2-8-29] Iqbal and Salley (2004), p. 2-8.

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@@ Line 29: / Line 29: @@
 == Buoyant flow through doors and windows ==
 In a door or window, the pressure difference changes with height. Inside a hot room the pressure falls more slowly with height than outside, because the hot gas is lighter. The difference in [[buoyancy]] between the two gas columns therefore produces a pressure difference that grows from the bottom to the top of the opening.<ref name="EM-2-34" /><ref name="VR-3.2">Van Rossum (2027), §3.2.</ref> Below a certain height the outside pressure is higher and air flows in. Above it the inside pressure is higher and smoke flows out. The height where the two pressures are equal and the velocity is zero is the [[neutral plane]].<ref name="EM-2-36">Emmons (2002), p. 2-36.</ref>
+[[File:fse-vent-flow-v2.svg|thumb|upright=1.5|alt=Left: room with hot layer and door, smoke out above and air in below. Right: inside and outside pressure lines crossing at the neutral plane.|Pressure inside and outside a fire room with an open door: above the neutral plane smoke flows out, below it air flows in. Based on Emmons (2002), pp. 2-34 and 2-36.]]
 The density of the gases follows from their temperature through the [[ideal gas law]]. For fire gases, which consist mostly of air, Emmons gives ρ = 352.8/''T'' kg/m³, with the temperature in kelvin.<ref name="EM-2-35">Emmons (2002), p. 2-35.</ref> The pressure itself changes so little that its effect on density can be neglected.<ref name="EM-2-35" /> The pressure differences involved are tiny. 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. Yet buoyant flows in a room fire can reach velocities of up to 7.00 m/s.<ref name="EM-2-35" />
@@ Line 63: / Line 64: @@
 The hot layer temperature follows from the condition that the two-layer model has the same average density as the real flow.<ref name="EM-2-37" /> This gives about 412 K, so the hot layer density is 352.8 / 412 = 0.856 kg/m³. The ambient density is 352.8 / 294.3 = 1.199 kg/m³.<ref name="EM-2-39" /> The outflow is then 0.943 × 0.68 × 0.737 × √(9.81 × 0.856 × 0.343) × 0.83<sup>1.5</sup>, or about 0.61 kg/s. This is about 3 % higher than the measured value.<ref name="EM-2-39" /> At the top of the doorway, 0.83 m above the neutral plane, the outflow velocity is about 2.6 m/s.
+[[File:fse-vent-flow-v3.svg|thumb|upright=1.5|alt=Chart of height in a doorway against outflow velocity: zero at 1.0 m, rising along a square-root curve to about 2.6 m/s at 1.83 m.|Outflow velocity in the doorway of the worked example, from the two-layer formula. Based on Emmons (2002), pp. 2-37–2-39.]]
 == Air supply and the ventilation factor ==
 Near and after flashover, the interface between the hot and cool layers lies close to the floor. The flow through the opening then reaches a maximum for a given gas temperature.<ref name="WT-3-174" /> Above about 150 °C the inflow hardly depends on temperature and is proportional to <math>A_0 \sqrt{H_0}</math>, where <math>A_0</math> is the area and <math>H_0</math> the height of the opening.<ref name="WT-3-174" /> Rockett calculated the constant as 0.40 to 0.61 kg/(s·m<sup>5/2</sup>), depending on the discharge coefficient. Thomas and Heselden estimated 0.5, the value most often used, which gives an air inflow of 0.5 <math>A_0 \sqrt{H_0}</math> kg/s.<ref name="WT-3-174" />
+[[File:fse-vent-flow-v4.svg|thumb|upright=1.5|alt=Line chart: air inflow rises in proportion to the ventilation factor; a band between 0.40 and 0.61 times with a central line at 0.5.|Air inflow of a room near or after flashover against the ventilation factor of its opening. Based on Walton and Thomas (2002), p. 3-174.]]
 The product <math>A_0 \sqrt{H_0}</math> is called the [[ventilation factor]]. Kawagoe first used this kind of analysis for fully developed fires, and wood fires in rooms with small windows were found to burn at a rate of about 0.09 <math>A_0 \sqrt{H_0}</math> kg/s.<ref name="WT-3-174" /> For most fuels, about 3,000 kJ of heat is released for each kilogram of air consumed. The largest heat release rate that the inflowing air can support is therefore about 1,500 <math>A_0 \sqrt{H_0}</math> kW.<ref name="WT-3-184">Walton and Thomas (2002), p. 3-184.</ref> For the doorway of the worked example, the ventilation factor is 1.349 × √1.83 ≈ 1.82 m<sup>5/2</sup>. This gives an air inflow of about 0.91 kg/s and a stoichiometric heat release rate of about 2.7 MW.
@@ Line 76: / Line 79: @@
 The zone model [[CFAST]] (Consolidated Fire and Smoke Transport) divides each wall opening into horizontal segments. Each segment is bounded by the sill, the top of the opening, the layer interfaces on either side or the neutral plane. The flow in each segment follows from Bernoulli's equation with an orifice coefficient of 0.7.<ref name="PE-19">Peacock et al. (2026), p. 19.</ref> Hot gas that flows into the cool lower layer of the next room is treated as a spill plume that entrains air as it rises.<ref name="PE-20">Peacock et al. (2026), pp. 20–21.</ref> Van Rossum notes that a high opening in a façade can act as a supply, an exhaust or both, depending on its position relative to the neutral plane.<ref name="VR-9.3">Van Rossum (2027), §9.3 (How a zone model works).</ref>
-Flows through horizontal openings, such as holes in a ceiling or roof, are much less well understood. Emmons gives formulas of unknown accuracy, which he describes as better than nothing.<ref name="EM-2-39" /><ref name="EM-2-40">Emmons (2002), p. 2-40.</ref> For a 1 m vent with a density ratio of 4 to 1, the buoyancy effect amounts to 8.6 Pa and produces a velocity of about 4 m/s.<ref name="EM-2-39" /> Near zero net flow, the boundary between the hot and cold gas becomes unstable, and gas flows up and down at the same time.<ref name="EM-2-39" /> The IFEG describe this exchange flow and a pulsating flow called puffing, and give a simple formula with a default discharge coefficient of 0.61.<ref name="IFEG-2.5-7">National Research Council of Canada et al. (2005), p. 2.5-7.</ref> CFAST uses a correlation by Cooper with a coefficient of 0.68 plus an exchange flow term.<ref name="PE-21">Peacock et al. (2026), p. 21.</ref>
+Flows through horizontal openings, such as holes in a ceiling or roof, are much less well understood. Emmons gives formulas of unknown accuracy, which he describes as better than nothing.<ref name="EM-2-39" /><ref name="EM-2-40">Emmons (2002), p. 2-40.</ref> For a 1 m vent with a density ratio of 4 to 1, the buoyancy effect amounts to 8.6 Pa and produces a velocity of about 4 m/s.<ref name="EM-2-39" /> Near zero net flow, the boundary between the hot and cold gas becomes unstable, and gas flows up and down at the same time.<ref name="EM-2-39" /> The IFEG name two observed phenomena: puffing, which is closely related to the combustion process in the fire room, and exchange flow, which occurs when the arrangement of the gases across the vent is unstable. They also give a simple formula with a default discharge coefficient of 0.61.<ref name="IFEG-2.5-7">National Research Council of Canada et al. (2005), p. 2.5-7.</ref> CFAST uses a correlation by Cooper with a coefficient of 0.68 plus an exchange flow term.<ref name="PE-21">Peacock et al. (2026), p. 21.</ref>
 == Effective areas and leakage networks ==
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 A building behaves as a network of such openings, comparable to a system of pipes and orifices.<ref name="EM-2-41" /> A layer of hot gas moves along the ceilings of connected spaces and rises through the first stairwell or ceiling opening it meets.<ref name="EM-2-41" /> Klote combines leakage paths into effective areas, in the same way as electrical resistances. Paths in parallel simply add up, so leaks of 0.10, 0.05 and 0.05 m² act as one opening of 0.20 m².<ref name="KL-4-283">Klote (2002), p. 4-283.</ref> For paths in series, the effective area is:<ref name="KL-4-283" />
 <math display="block">A_e = \left( \sum_{i=1}^{n} \frac{1}{A_i^2} \right)^{-1/2}</math>
-where <math>A_e</math> is the effective area and <math>A_i</math> are the individual areas in m². Two equal paths of 0.02 m² in series give 0.014 m², and paths of 0.02 m² and 0.2 m² in series give 0.0199 m².<ref name="KL-4-283" /> The smallest opening in a chain therefore controls the flow.
+where <math>A_e</math> is the effective area and <math>A_i</math> are the individual areas in m². Two equal paths of 0.02 m² in series give 0.014 m², and paths of 0.02 m² and 0.2 m² in series give 0.0199 m².<ref name="KL-4-283" /> When one of two openings in series is much larger than the other, the effective area is approximately that of the smaller one.<ref name="KL-4-283" />
+[[File:fse-vent-flow-v5.svg|thumb|upright=1.5|alt=Left: three openings side by side in one wall add up to 0.20 square metres. Right: two openings in a row give an effective area close to the smaller one.|Leakage paths in parallel add up (left); in series the smallest opening controls the flow (right). Based on Klote (2002), p. 4-283.]]
 In smoke exhaust design, Van Rossum notes that the exhaust capacity by volume should exceed the supply capacity, and the more so the hotter the smoke.<ref name="VR-9.3" /> A single exhaust point with too much capacity can also draw clean air from below a thin smoke layer, an effect called [[plugholing]].<ref name="VR-6.8" /> Remedies include more exhaust points with a smaller capacity each, a deeper smoke layer, and guiding the air so that the suction acts horizontally on the layer.<ref name="VR-6.8" />
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 Vent flows in fire tests are measured with rows of pressure probes and thermocouples in the opening. Bidirectional probes give velocities within 10 % for flow directions up to 50 degrees from the probe axis.<ref name="EM-2-35" /> Simpler methods use the pressure difference at one height, the visible bottom of the outflow or an assumed two-layer profile, at the cost of accuracy.<ref name="EM-2-36" /><ref name="EM-2-37" /> Emmons notes that a fire close to the opening has unknown effects on the flow.<ref name="EM-2-35" />
-The achievable accuracy differs strongly between cases. Flow through nozzles and orifices in a calibrated pipe can be calculated to about 2 %. For openings in vertical walls, the best laboratory measurements reach about 5 %, but errors of 10 % or more must be expected in real fires because of strong circulation in the room.<ref name="EM-2-40" /> The accuracy for horizontal vents is completely unknown.<ref name="EM-2-40" /> The IFEG add that hand calculations of smoke spread beyond the room of fire origin are rarely used, because they are more difficult and more uncertain.<ref name="IFEG-2.5-6" />
+The achievable accuracy differs strongly between cases. Flow through nozzles and orifices in a calibrated pipe can be calculated to about 2 %. For vents in vertical walls with limited circulation inside the fire room, the best methods of measurement may get 5 % accuracy. In real fires the induced circulations are often severe and unknown, so errors of 10 % or more must be expected.<ref name="EM-2-40" /> The accuracy for horizontal vents is completely unknown.<ref name="EM-2-40" /> The IFEG add that hand calculations of smoke spread beyond the room of fire origin are more difficult and therefore rarely used. Their results are also more uncertain than those for the room of fire origin.<ref name="IFEG-2.5-6" />
-Vent flows nevertheless control important results of fire models. In the validation study of the United States Nuclear Regulatory Commission (NRC) and the Electric Power Research Institute (EPRI), most experiments had at least one open door or window. The smoke layer depth was largely set by the height of that opening and was relatively insensitive to the heat release rate.<ref name="ST-3-35" /> NUREG-1805 describes the same process: the hot layer descends within the opening until the inflow and outflow of the layer balance.<ref name="IS-2-8">Iqbal and Salley (2004), p. 2-8.</ref>
+Vent flows nevertheless control important results of fire models. The United States Nuclear Regulatory Commission (NRC) and the Electric Power Research Institute (EPRI) carried out a validation study of fire models. Most of its experiments in which the smoke layer depth was predicted had at least one open door or window. In those experiments the depth was largely set by the height of the opening and was relatively insensitive to the heat release rate.<ref name="ST-3-35" /> NUREG-1805 describes the same process: the hot layer descends within the opening until the inflow and outflow of the layer balance.<ref name="IS-2-8">Iqbal and Salley (2004), p. 2-8.</ref>
 == See also ==