Line plume - Revision history

Jan: Add 3 watermarked SVG illustrations from the Expert visual plan

2026-11-02T16:18:28Z

Add 3 watermarked SVG illustrations from the Expert visual plan

← Older revision		Revision as of 17:18, 2 November 2026
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	The first form is the free line plume. It rises above a line fire, or above a line-like source of hot smoke, that is far enough from walls to draw in air freely on both sides.<ref name="Cooper-3-231" /> Cooper applies it, for example, to smoke that spills over the free edge of a balcony.<ref name="Cooper-3-231" /><ref name="Cooper-3-232">Cooper (2002b), p. 3-232.</ref> The second form is the near-wall line plume, which can draw in air on one side only.<ref name="Cooper-3-231" /> It occurs above a line fire against a wall, or when smoke from a fire in an adjacent room enters a space through a wide opening and rises along the wall above it.<ref name="Cooper-3-231" />		The first form is the free line plume. It rises above a line fire, or above a line-like source of hot smoke, that is far enough from walls to draw in air freely on both sides.<ref name="Cooper-3-231" /> Cooper applies it, for example, to smoke that spills over the free edge of a balcony.<ref name="Cooper-3-231" /><ref name="Cooper-3-232">Cooper (2002b), p. 3-232.</ref> The second form is the near-wall line plume, which can draw in air on one side only.<ref name="Cooper-3-231" /> It occurs above a line fire against a wall, or when smoke from a fire in an adjacent room enters a space through a wide opening and rises along the wall above it.<ref name="Cooper-3-231" />
			[[File:fse-line-plume-v1.svg\|thumb\|upright=1.5\|alt=Three plumes: round, drawing air from all sides; flat line plume, from both long sides; line plume against a wall, from one side.\|A round (axisymmetric) plume, a free line plume and a near-wall line plume, with the sides from which each draws in air. Based on Cooper (2002b), pp. 3-230 to 3-231, and Milke (2002b), p. 4-299.]]

	In the ''Introduction to Fire Safety Engineering'', a line plume is smoke that flows out of an adjacent room under a ceiling edge or other construction and rises into a larger space.<ref name="VR-6.7" /> Its cross-section is more oval than the round section of an ordinary plume.<ref name="VR-6.7" /> A plume that emerges from under a balcony or gallery also has an oval shape, and the book calls this a line plume too.<ref name="VR-9.3" /> In the SFPE Handbook, Milke treats this case separately as the [[balcony spill plume]], with its own entrainment equation.<ref name="Milke-4-301" /> Cooper, in the same handbook, applies the free line plume equation to it.<ref name="Cooper-3-231" />		In the ''Introduction to Fire Safety Engineering'', a line plume is smoke that flows out of an adjacent room under a ceiling edge or other construction and rises into a larger space.<ref name="VR-6.7" /> Its cross-section is more oval than the round section of an ordinary plume.<ref name="VR-6.7" /> A plume that emerges from under a balcony or gallery also has an oval shape, and the book calls this a line plume too.<ref name="VR-9.3" /> In the SFPE Handbook, Milke treats this case separately as the [[balcony spill plume]], with its own entrainment equation.<ref name="Milke-4-301" /> Cooper, in the same handbook, applies the free line plume equation to it.<ref name="Cooper-3-231" />
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	== Worked example ==		== Worked example ==
	Cooper applies the free line plume equation to smoke that spills from under a balcony.<ref name="Cooper-3-231" /> A fire with a total heat release rate of 5 MW burns on 4 m² of floor, 3 m below a balcony with a width of 3 m.<ref name="Cooper-3-231" /> The convective part is taken as 65% of the total, or 3.25 MW.<ref name="Cooper-3-231" /> The round plume above the fire reaches the underside of the balcony with a mass flow of about 12.0 kg/s.<ref name="Cooper-3-232" /> Cooper assumes that the smoke then flows to the edge of the balcony without significant extra entrainment or heat loss and rises from it as a line plume.<ref name="Cooper-3-231" /> Its length is estimated at 1.5 times the width of the balcony, which is 4.5 m.<ref name="Cooper-3-232" />		Cooper applies the free line plume equation to smoke that spills from under a balcony.<ref name="Cooper-3-231" /> A fire with a total heat release rate of 5 MW burns on 4 m² of floor, 3 m below a balcony with a width of 3 m.<ref name="Cooper-3-231" /> The convective part is taken as 65% of the total, or 3.25 MW.<ref name="Cooper-3-231" /> The round plume above the fire reaches the underside of the balcony with a mass flow of about 12.0 kg/s.<ref name="Cooper-3-232" /> Cooper assumes that the smoke then flows to the edge of the balcony without significant extra entrainment or heat loss and rises from it as a line plume.<ref name="Cooper-3-231" /> Its length is estimated at 1.5 times the width of the balcony, which is 4.5 m.<ref name="Cooper-3-232" />
			[[File:fse-line-plume-v2.svg\|thumb\|upright=1.5\|alt=Cross-section: a fire plume hits the underside of a balcony, flows to its edge and rises as a line plume from an imaginary source 1.7 m below the edge.\|Smoke from a 5 MW fire spills from under a 3 m balcony and rises as a line plume; the calculation uses an imaginary line source 1.7 m below the balcony edge. Based on Cooper (2002b), pp. 3-231 to 3-232.]]

	The convective heat release rate per metre of this equivalent line source is 3,250 kW divided by 4.5 m, or 722 kW/m.<ref name="Cooper-3-232" /> At the balcony edge, the line plume must carry the same mass as the round plume, 12.0 kg/s spread over 4.5 m, or 2.7 kg/(m·s).<ref name="Cooper-3-232" /> Solving the free line plume equation for the height difference places an imaginary line source 1.7 m below the balcony edge:		The convective heat release rate per metre of this equivalent line source is 3,250 kW divided by 4.5 m, or 722 kW/m.<ref name="Cooper-3-232" /> At the balcony edge, the line plume must carry the same mass as the round plume, 12.0 kg/s spread over 4.5 m, or 2.7 kg/(m·s).<ref name="Cooper-3-232" /> Solving the free line plume equation for the height difference places an imaginary line source 1.7 m below the balcony edge:
	<math display="block">z_\mathrm{bal} - z_\mathrm{source} = \frac{2.7}{0.18 \times 722^{1/3}} = 1.7\ \mathrm{m}</math>		<math display="block">z_\mathrm{bal} - z_\mathrm{source} = \frac{2.7}{0.18 \times 722^{1/3}} = 1.7\ \mathrm{m}</math>
	The design level for the smoke layer lies 3 m above the balcony, so 4.7 m above this imaginary source.<ref name="Cooper-3-232" /> The line plume there carries 0.18 × 4.7 × 722<sup>1/3</sup> = 7.6 kg/(m·s), or 34.2 kg/s over the full length.<ref name="Cooper-3-232" /> For comparison, Cooper estimates that the same fire burning in the open, away from the balcony, would supply 26.0 kg/s at the same height.<ref name="Cooper-3-232" /> The spill over the balcony edge therefore increases the smoke flow into the upper layer by 31%, from 26 to 34 kg/s.<ref name="Cooper-3-232" /> A smoke exhaust system that holds the smoke layer at this level must remove at least this mass flow.<ref name="Milke-4-299" />		The design level for the smoke layer lies 3 m above the balcony, so 4.7 m above this imaginary source.<ref name="Cooper-3-232" /> The line plume there carries 0.18 × 4.7 × 722<sup>1/3</sup> = 7.6 kg/(m·s), or 34.2 kg/s over the full length.<ref name="Cooper-3-232" /> For comparison, Cooper estimates that the same fire burning in the open, away from the balcony, would supply 26.0 kg/s at the same height.<ref name="Cooper-3-232" /> The spill over the balcony edge therefore increases the smoke flow into the upper layer by 31%, from 26 to 34 kg/s.<ref name="Cooper-3-232" /> A smoke exhaust system that holds the smoke layer at this level must remove at least this mass flow.<ref name="Milke-4-299" />
			[[File:fse-line-plume-v3.svg\|thumb\|upright=1.5\|alt=Line chart: above the balcony the line plume mass flow rises faster than that of the same 5 MW fire burning in the open.\|Plume mass flow against height for the same 5 MW fire burning in the open and as a line plume spilling from a balcony at 3 m. Based on Cooper (2002b), pp. 3-231 to 3-232.]]

	Cooper's energy balance gives the average temperature of the plume gases as they enter the smoke layer. It equals the convective heat release rate divided by the plume mass flow and the specific heat of air.<ref name="Cooper-3-234">Cooper (2002b), p. 3-234.</ref> The calculation uses the specific heat of air of 1.0 kJ/(kg·K) given in the book.<ref name="VR-6.7" /> The line plume then reaches the design level about 95 K above ambient, and the plume of the fire in the open about 125 K. The extra entrainment of the line plume thus gives more smoke at a lower temperature, as the Australian handbook also notes.<ref name="Australian-98" />		Cooper's energy balance gives the average temperature of the plume gases as they enter the smoke layer. It equals the convective heat release rate divided by the plume mass flow and the specific heat of air.<ref name="Cooper-3-234">Cooper (2002b), p. 3-234.</ref> The calculation uses the specific heat of air of 1.0 kJ/(kg·K) given in the book.<ref name="VR-6.7" /> The line plume then reaches the design level about 95 K above ambient, and the plume of the fire in the open about 125 K. The extra entrainment of the line plume thus gives more smoke at a lower temperature, as the Australian handbook also notes.<ref name="Australian-98" />

Mark: FSE wiki: corrections after independent fact-check (written by Claude Opus 5.5)

2026-11-01T23:29:34Z

FSE wiki: corrections after independent fact-check (written by Claude Opus 5.5)

Mark: New FSE wiki article: Line plume (written by Claude Opus 5.5)

2026-11-01T22:23:40Z

New FSE wiki article: Line plume (written by Claude Opus 5.5)

New page

A '''line plume''' is a buoyant plume of hot gas that rises from a long, narrow source, such as a line of burning material or smoke spilling from a wide opening.<ref name="Cooper-3-230">Cooper (2002b), p. 3-230.</ref><ref name="Cooper-3-231">Cooper (2002b), p. 3-231.</ref> Instead of the round column above a compact fire, it forms a flat, wedge-like sheet that draws in air along its two long sides.<ref name="Cooper-3-231" /> The ''Introduction to Fire Safety Engineering'' describes a line plume as smoke that leaves an adjacent room under a ceiling edge, or under a balcony or gallery, and rises into a larger space.<ref name="VR-6.7">Van Rossum (2027), §6.7.</ref><ref name="VR-9.3">Van Rossum (2027), §9.3 (How a zone model works).</ref>

Because the perimeter of its cross-section is large compared with its area, a line plume mixes in more fresh air than an ordinary round plume.<ref name="VR-6.7" /> Its mass flow per unit length grows in proportion to the height above the source and to the cube root of the heat release rate per unit length.<ref name="Cooper-3-231" /> Near the source, a line plume therefore carries much more smoke than a round plume of the same fire.<ref name="Milke-4-301">Milke (2002b), p. 4-301.</ref> This matters in smoke control for atria and malls, where the plume mass flow at the smoke layer sets the exhaust rate that the system must provide.<ref name="Milke-4-299">Milke (2002b), p. 4-299.</ref> The two-dimensional, wedge-like shape lasts only up to a height of about the length of the source.<ref name="Cooper-3-231" />

== Forms of line plumes ==
Any [[fire plume]] forms because hot combustion gases are less dense than the surrounding air and therefore rise.<ref name="VR-6.7" /> The standard plume equations describe an axisymmetric plume above a fire away from walls, which draws in air around its whole perimeter.<ref name="Milke-4-299" /> Cooper adds two plume models for line-like fires, which are described by an effective length.<ref name="Cooper-3-230" /> For such fires, the heat release rate and the plume mass flow are expressed per metre of length.<ref name="Cooper-3-230" />

The first form is the free line plume. It rises above a line fire, or above a line-like source of hot smoke, that is far enough from walls to draw in air freely on both sides.<ref name="Cooper-3-231" /> Cooper applies it, for example, to smoke that spills over the free edge of a balcony.<ref name="Cooper-3-231" /><ref name="Cooper-3-232">Cooper (2002b), p. 3-232.</ref> The second form is the near-wall line plume, which can draw in air on one side only.<ref name="Cooper-3-231" /> It occurs above a line fire against a wall, or when smoke from a fire in an adjacent room enters a space through a wide opening and rises along the wall above it.<ref name="Cooper-3-231" />

The book describes the second situation from the point of view of the space that receives the smoke. Smoke flows out of an adjacent room under a ceiling edge or other construction and then rises into a larger space.<ref name="VR-6.7" /> Its cross-section is more oval than the round section of an ordinary plume.<ref name="VR-6.7" /> A plume that emerges from under a balcony or gallery has the same oval shape, and the book also calls this a line plume.<ref name="VR-9.3" /> The SFPE Handbook treats this case separately as the [[balcony spill plume]], with its own entrainment equation.<ref name="Milke-4-301" />

The flames of a line fire also follow their own rules. For a line fire against a wall, NUREG-1805 gives a flame height that grows with the heat release rate per unit length to the power 2/3.<ref name="IS-4-2">Iqbal and Salley (2004), p. 4-2.</ref> With a heat release rate of 100 kW per metre, this correlation gives a flame height of about 0.37 m.<ref name="IS-4-2" /> For a fire that spreads over the full height of a wall surface, the same source gives a coefficient twice as large.<ref name="IS-4-2" />

== Entrainment and smoke production ==
As hot gases rise in a plume, cold air from the surroundings is mixed into the flow.<ref name="VR-6.7" /> This [[entrainment]] increases the mass flow of the plume with height, so the smoke delivered to a smoke layer consists mostly of entrained air.<ref name="Milke-4-299" /> For an axisymmetric plume, the mass flow grows with the height to the power 5/3.<ref name="Milke-4-298">Milke (2002b), p. 4-298.</ref> This dependence follows from the work of Heskestad, whose equation for the [[Heskestad plume]] is used in NFPA 92B for malls, atria and large areas.<ref name="Milke-4-299" />

For a free line plume, Cooper gives a simpler relation: the mass flow per metre grows linearly with height. It also grows with the cube root of the convective heat release rate per metre.<ref name="Cooper-3-231" /> For a near-wall line plume, the reflection principle applies. The heat release rate per metre is doubled to represent the mirror image behind the wall, and the resulting mass flow is halved.<ref name="Cooper-3-231" /> The axisymmetric plume above the flames is given for comparison.<ref name="Milke-4-298" />
<math display="block">\dot{m}'_\mathrm{line} = 0.18\,(z - z_\mathrm{fire})\,\dot{Q}'^{1/3}_\mathrm{conv} \qquad \text{(free line plume)}</math>
<math display="block">\dot{m}'_\mathrm{line} = \frac{0.18}{2}\,(z - z_\mathrm{fire})\,\left(2\dot{Q}'_\mathrm{conv}\right)^{1/3} \qquad \text{(near-wall line plume)}</math>
<math display="block">\dot{m} = 0.071\,\dot{Q}_\mathrm{c}^{1/3}\,(z - z_\mathrm{o})^{5/3} + 0.002\,\dot{Q}_\mathrm{c} \qquad \text{(axisymmetric plume)}</math>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>\dot{m}'_\mathrm{line}</math> || mass flow in the line plume per metre of length || kg/(m·s)
|-
| <math>\dot{m}</math> || mass flow in the axisymmetric plume || kg/s
|-
| <math>\dot{Q}'_\mathrm{conv}</math> || convective heat release rate per metre of source length || kW/m
|-
| <math>\dot{Q}_\mathrm{c}</math> || convective heat release rate || kW
|-
| <math>z</math> || height above the floor or reference level || m
|-
| <math>z_\mathrm{fire}</math> || height of the base of the line source || m
|-
| <math>z_\mathrm{o}</math> || height of the virtual origin of the axisymmetric plume || m
|}

The difference in the height terms has a large effect. If the height above the source doubles, the line plume carries twice as much mass, but the first term of the axisymmetric equation grows by a factor of about 3.2.<ref name="Cooper-3-231" /><ref name="Milke-4-298" /> Close to the source, the line plume therefore produces far more smoke. Further up, the round plume catches up, and the two become comparable at greater heights.<ref name="Milke-4-301" /> For the balcony spill plume, the handbook estimates that this happens when the height above the balcony is about 12.5 times the width of the plume.<ref name="Milke-4-301" />

The near-wall equation gives about 63% of the mass flow of a free line plume with the same heat release rate per metre. Doubling the heat release rate raises the flow by the cube root of 2, and halving the result then leaves this fraction.<ref name="Cooper-3-231" /> Cooper notes that this estimate assumes small heat losses from the plume to the wall.<ref name="Cooper-3-231" /> The same mirror-image idea is used for a round plume against a wall, which behaves like half of a plume with twice the heat release rate.<ref name="VR-6.7" /><ref name="Milke-4-300">Milke (2002b), p. 4-300.</ref>

== Worked example ==
Cooper applies the free line plume equation to smoke that spills from under a balcony.<ref name="Cooper-3-231" /> A fire with a total heat release rate of 5 MW burns on 4 m² of floor, 3 m below a balcony with a width of 3 m.<ref name="Cooper-3-231" /> The convective part is taken as 65% of the total, or 3.25 MW.<ref name="Cooper-3-231" /> The round plume above the fire reaches the underside of the balcony with a mass flow of about 12.0 kg/s.<ref name="Cooper-3-232" /> Cooper assumes that the smoke then flows to the edge of the balcony without significant extra entrainment or heat loss and rises from it as a line plume.<ref name="Cooper-3-231" /> Its length is estimated at 1.5 times the width of the balcony, which is 4.5 m.<ref name="Cooper-3-232" />

The convective heat release rate per metre of this equivalent line source is 3,250 kW divided by 4.5 m, or 722 kW/m.<ref name="Cooper-3-232" /> At the balcony edge, the line plume must carry the same mass as the round plume, 12.0 kg/s spread over 4.5 m, or 2.7 kg/(m·s).<ref name="Cooper-3-232" /> Solving the free line plume equation for the height difference places an imaginary line source 1.7 m below the balcony edge:
<math display="block">z_\mathrm{bal} - z_\mathrm{source} = \frac{2.7}{0.18 \times 722^{1/3}} = 1.7\ \mathrm{m}</math>
The design level for the smoke layer lies 3 m above the balcony, so 4.7 m above this imaginary source.<ref name="Cooper-3-232" /> The line plume there carries 0.18 × 4.7 × 722<sup>1/3</sup> = 7.6 kg/(m·s), or 34.2 kg/s over the full length.<ref name="Cooper-3-232" /> For comparison, the axisymmetric plume equation gives about 27.3 kg/s at the same height of 6 m above the fire. This assumes that the virtual origin lies at the base of the fire.<ref name="Milke-4-298" /> The spill over the balcony edge therefore increases the smoke flow at the design level by about a quarter. A smoke exhaust system that holds the smoke layer at this level must remove at least this mass flow.<ref name="Milke-4-299" />

Cooper's energy balance gives the average temperature of the plume gases as they enter the smoke layer. It equals the convective heat release rate divided by the plume mass flow and the specific heat of air.<ref name="Cooper-3-234">Cooper (2002b), p. 3-234.</ref> With a specific heat of 1.0 kJ/(kg·K), the line plume reaches the design level about 95 K above ambient and the round plume about 119 K.<ref name="VR-6.7" /> The extra entrainment of the line plume thus gives more smoke at a lower temperature, as the Australian handbook also notes.<ref name="Australian-98" />

== Use in smoke control design ==
In [[atrium smoke control]], the smoke layer stops descending when the exhaust rate equals the rate at which the plume supplies smoke to the layer.<ref name="Milke-4-299" /> The required exhaust capacity therefore depends directly on the type of plume.<ref name="Milke-4-299" /> A line plume that forms under a balcony or gallery can increase the volume of smoke for a given fire.<ref name="Australian-98">Australian Building Codes Board (2020b), p. 98.</ref> The same fire placed in the centre of the atrium gives a hotter and more concentrated plume with less volume.<ref name="Australian-98" />

The handbook to the Australian Fire Safety Verification Method illustrates this with an example of a large enclosure with overhanging projections and escape routes above floor level.<ref name="Australian-97">Australian Building Codes Board (2020b), p. 97.</ref> Because the worst fire position could not be found by reasoning alone, design fires had to be evaluated at several positions.<ref name="Australian-98" /> One of these positions lies under horizontal projections where line plumes may form. There the larger smoke volume may affect more escape routes in less time, although temperatures and concentrations of toxic species are lower.<ref name="Australian-98" />

In vent design, the flow out of the ceiling vents must match the plume mass flow at the chosen height of the smoke layer.<ref name="Cooper-3-234" /> Cooper's design procedure lists the free and near-wall line plume equations among the plume models that can supply this mass flow.<ref name="Cooper-3-235">Cooper (2002b), p. 3-235.</ref> For a near-wall line plume, the plume also loses heat to the wall it touches.<ref name="Cooper-3-234" />

Zone models reproduce the same effect for smoke that flows between rooms. In the zone model CFAST, hot gas that leaves the upper layer of one room and enters the lower layer of the next rises into the upper layer as a spill plume.<ref name="Peacock-20">Peacock et al. (2026), p. 20.</ref> Its entrainment follows a correlation of Poreh and co-workers, in which the mass flow grows with the width of the opening to the power 2/3.<ref name="Peacock-20" /> The book points out that a fire in a room next to an atrium, such as a shop in a covered mall, is often the governing scenario.<ref name="VR-9.3" /> The smoke then passes through more mixing steps and forms a larger volume.<ref name="VR-9.3" /> A calculation with only one room is then not realistic if the adjacent room is not separated by fire- and smoke-resisting construction.<ref name="VR-9.3" />

== Limits and uncertainty ==
The line plume equations hold only near the source. Cooper states that a line plume cannot keep its two-dimensional, wedge-like shape much beyond a height above the source equal to its length.<ref name="Cooper-3-231" /> At greater heights, the mass flow is better estimated with an axisymmetric plume equation and an effective fire diameter.<ref name="Cooper-3-231" /> The near-wall equation is limited in the same way and also requires that heat losses to the wall stay small.<ref name="Cooper-3-231" />

Line plume sub-models in fire models have not always been tested against experiments. In the 2007 validation study NUREG-1824, the line plume model of the zone model MAGIC was not evaluated, while its axisymmetric plume model was.<ref name="Joglar-6-10">Joglar et al. (2007), p. 6-10.</ref> The axisymmetric model predicted plume temperatures within the experimental uncertainty of 14% in one test series.<ref name="Joglar-6-10" />

The constants in these correlations come from experiments, and published values differ. For the spill plume in CFAST, the suggested values of the entrainment constant range from 0.44 to 0.66.<ref name="Peacock-21">Peacock et al. (2026), p. 21.</ref> The constant used in CFAST, 0.44, lies at the low end of this range. The balcony spill plume equation in the SFPE Handbook rests on small-scale experiments with a single opening and a walkway.<ref name="Milke-4-301" /> Its use is questionable when the smoke reaches the atrium through a long corridor and loses heat on the way.<ref name="Milke-4-301" />

The length of an equivalent line source is often uncertain as well. In Cooper's balcony example, the spill length was expected to lie between one and two times the width of the balcony, and 1.5 times was chosen.<ref name="Cooper-3-232" /> Because the mass flow scales with the length to the power 2/3 for a given total heat release rate, such choices change the result noticeably. The Australian example therefore evaluates several fire positions instead of one assumed worst case.<ref name="Australian-98" />

== See also ==
* [[Thomas plume]]
* [[Virtual origin]]
* [[Flame height]]
* [[Turbulence]]

== Notes ==
<references />

== References ==
* Australian Building Codes Board. (2020b). ''Handbook: Fire Safety Verification Method'' (Print version 1.1).
* Cooper, L. Y. (2002b). Smoke and heat venting. 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. 3-219–3-242). 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.
* Joglar, F., Gautier, B., Gay, L., & Texeraud, J. (2007). ''Verification and validation of selected fire models for nuclear power plant applications: Vol. 6. MAGIC'' (NUREG-1824; EPRI 1011999). U.S. Nuclear Regulatory Commission, Office of Nuclear Regulatory Research; Electric Power Research Institute.
* Milke, J. A. (2002b). Smoke management in covered malls and atria. 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. 4-292–4-310). National Fire Protection Association; Society of Fire Protection Engineers.
* 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
* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.

[[Category:Fire Dynamics]]

← Older revision		Revision as of 00:29, 2 November 2026
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	A '''line plume''' is a buoyant plume of hot gas that rises from a long, narrow source, such as a line of burning material or smoke spilling from a wide opening.<ref name="Cooper-3-230">Cooper (2002b), p. 3-230.</ref><ref name="Cooper-3-231">Cooper (2002b), p. 3-231.</ref> Instead of the round column above a compact fire, it forms a flat, wedge-like sheet that draws in air along its two long sides.<ref name="Cooper-3-231" /> The ''Introduction to Fire Safety Engineering'' describes a line plume as smoke that leaves an adjacent room under a ceiling edge, or under a balcony or gallery, and rises into a larger space.<ref name="VR-6.7">Van Rossum (2027), §6.7.</ref><ref name="VR-9.3">Van Rossum (2027), §9.3 (How a zone model works).</ref>		A '''line plume''' is a buoyant plume of hot gas that rises from a long, narrow source, such as a line of burning material or smoke spilling from a wide opening.<ref name="Cooper-3-230">Cooper (2002b), p. 3-230.</ref><ref name="Cooper-3-231">Cooper (2002b), p. 3-231.</ref><ref name="IS-9-2">Iqbal and Salley (2004), p. 9-2.</ref> Instead of the round column above a compact fire, it forms a flat, wedge-like sheet that draws in air along its two long sides.<ref name="Cooper-3-231" /> The ''Introduction to Fire Safety Engineering'' describes a line plume as smoke that leaves an adjacent room under a ceiling edge, or under a balcony or gallery, and rises into a larger space.<ref name="VR-6.7">Van Rossum (2027), §6.7.</ref><ref name="VR-9.3">Van Rossum (2027), §9.3 (How a zone model works).</ref>

	Because the perimeter of its cross-section is large compared with its area, a line plume mixes in more fresh air than an ordinary round plume.<ref name="VR-6.7" /> Its mass flow per unit length grows in proportion to the height above the source and to the cube root of the heat release rate per unit length.<ref name="Cooper-3-231" /> Near the source, a line plume therefore carries much more smoke than a round plume of the same fire.<ref name="Milke-4-301">Milke (2002b), p. 4-301.</ref> This matters in smoke control for atria and malls, where the plume mass flow at the smoke layer sets the exhaust rate that the system must provide.<ref name="Milke-4-299">Milke (2002b), p. 4-299.</ref> The two-dimensional, wedge-like shape lasts only up to a height of about the length of the source.<ref name="Cooper-3-231" />		Because the perimeter of its cross-section is large compared with its area, a line plume mixes in more fresh air than an ordinary round plume.<ref name="VR-6.7" /> Its mass flow per unit length grows in proportion to the height above the source and to the cube root of the heat release rate per unit length.<ref name="Cooper-3-231" /> Near the source, a line plume therefore carries much more smoke than a round plume of the same fire, as Milke shows for the balcony spill plume.<ref name="Milke-4-301">Milke (2002b), p. 4-301.</ref> This matters in smoke control for atria and malls, where the plume mass flow at the smoke layer sets the exhaust rate that the system must provide.<ref name="Milke-4-299">Milke (2002b), p. 4-299.</ref> The two-dimensional, wedge-like shape lasts only up to a height of about the length of the source.<ref name="Cooper-3-231" />

	== Forms of line plumes ==		== Forms of line plumes ==
	Any [[fire plume]] forms because hot combustion gases are less dense than the surrounding air and therefore rise.<ref name="VR-6.7" /> The standard plume equations describe an axisymmetric plume above a fire away from walls, which draws in air around its whole perimeter.<ref name="Milke-4-299" /> Cooper adds two plume models for line-like fires, which are described by an effective length.<ref name="Cooper-3-230" /> For such fires, the heat release rate and the plume mass flow are expressed per metre of length.<ref name="Cooper-3-230" />		Any [[fire plume]] forms because hot combustion gases are less dense than the surrounding air and therefore rise.<ref name="VR-6.7" /> The standard plume equations describe an axisymmetric plume above a fire away from walls, which draws in air around its whole perimeter.<ref name="Milke-4-299" /> Cooper adds two plume models for line-like fires, which are described by an effective length.<ref name="Cooper-3-230" /> For such fires, the heat release rate and the plume mass flow are expressed per metre of length.<ref name="Cooper-3-230" /> NUREG-1805 also names the line plume as a separate category, formed above a long and narrow burner that allows air to be drawn in from two sides.<ref name="IS-9-2" /> Its examples of line fires include flame spread over flammable wall linings, a balcony spill plume, a long sofa, a row of town houses and the advancing front of a forest fire.<ref name="IS-9-2" />

	The first form is the free line plume. It rises above a line fire, or above a line-like source of hot smoke, that is far enough from walls to draw in air freely on both sides.<ref name="Cooper-3-231" /> Cooper applies it, for example, to smoke that spills over the free edge of a balcony.<ref name="Cooper-3-231" /><ref name="Cooper-3-232">Cooper (2002b), p. 3-232.</ref> The second form is the near-wall line plume, which can draw in air on one side only.<ref name="Cooper-3-231" /> It occurs above a line fire against a wall, or when smoke from a fire in an adjacent room enters a space through a wide opening and rises along the wall above it.<ref name="Cooper-3-231" />		The first form is the free line plume. It rises above a line fire, or above a line-like source of hot smoke, that is far enough from walls to draw in air freely on both sides.<ref name="Cooper-3-231" /> Cooper applies it, for example, to smoke that spills over the free edge of a balcony.<ref name="Cooper-3-231" /><ref name="Cooper-3-232">Cooper (2002b), p. 3-232.</ref> The second form is the near-wall line plume, which can draw in air on one side only.<ref name="Cooper-3-231" /> It occurs above a line fire against a wall, or when smoke from a fire in an adjacent room enters a space through a wide opening and rises along the wall above it.<ref name="Cooper-3-231" />

	~~The book describes~~ the ~~second situation from the point of view of the space~~ that ~~receives the smoke. Smoke~~ flows out of an adjacent room under a ceiling edge or other construction and ~~then~~ rises into a larger space.<ref name="VR-6.7" /> Its cross-section is more oval than the round section of an ordinary plume.<ref name="VR-6.7" /> A plume that emerges from under a balcony or gallery has ~~the same~~ oval shape, and the book ~~also~~ calls this a line plume.<ref name="VR-9.3" /> ~~The~~ SFPE Handbook treats this case separately as the [[balcony spill plume]], with its own entrainment equation.<ref name="Milke-4-301" />		In the ''Introduction to Fire Safety Engineering'', a line plume is smoke that flows out of an adjacent room under a ceiling edge or other construction and rises into a larger space.<ref name="VR-6.7" /> Its cross-section is more oval than the round section of an ordinary plume.<ref name="VR-6.7" /> A plume that emerges from under a balcony or gallery also has an oval shape, and the book calls this a line plume too.<ref name="VR-9.3" /> In the SFPE Handbook, Milke treats this case separately as the [[balcony spill plume]], with its own entrainment equation.<ref name="Milke-4-301" /> Cooper, in the same handbook, applies the free line plume equation to it.<ref name="Cooper-3-231" />

	The flames of a line fire also follow their own rules. For a line fire against a wall, NUREG-1805 gives a flame height that grows with the heat release rate per unit length to the power 2/3.<ref name="IS-4-2">Iqbal and Salley (2004), p. 4-2.</ref> With a heat release rate of 100 kW per metre, this correlation gives a flame height of about 0.37 m.<ref name="IS-4-2" /> For a fire ~~that spreads over~~ the ~~full height of~~ a wall ~~surface~~, ~~the same source~~ gives a coefficient twice ~~as large~~.<ref name="IS-4-2" />		The flames of a line fire also follow their own rules. For a line fire against a wall, NUREG-1805 gives a flame height that grows with the heat release rate per unit length to the power 2/3.<ref name="IS-4-2">Iqbal and Salley (2004), p. 4-2.</ref> With a heat release rate of 100 kW per metre, this correlation gives a flame height of about 0.37 m.<ref name="IS-4-2" /> For a wall fire, in which the fire source lies on the floor against a wall, NUREG-1805 gives a coefficient of 0.034, twice that for a line fire against a wall.<ref name="IS-4-2" /><ref name="IS-4-3">Iqbal and Salley (2004), p. 4-3.</ref>

	== Entrainment and smoke production ==		== Entrainment and smoke production ==
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	The convective heat release rate per metre of this equivalent line source is 3,250 kW divided by 4.5 m, or 722 kW/m.<ref name="Cooper-3-232" /> At the balcony edge, the line plume must carry the same mass as the round plume, 12.0 kg/s spread over 4.5 m, or 2.7 kg/(m·s).<ref name="Cooper-3-232" /> Solving the free line plume equation for the height difference places an imaginary line source 1.7 m below the balcony edge:		The convective heat release rate per metre of this equivalent line source is 3,250 kW divided by 4.5 m, or 722 kW/m.<ref name="Cooper-3-232" /> At the balcony edge, the line plume must carry the same mass as the round plume, 12.0 kg/s spread over 4.5 m, or 2.7 kg/(m·s).<ref name="Cooper-3-232" /> Solving the free line plume equation for the height difference places an imaginary line source 1.7 m below the balcony edge:
	<math display="block">z_\mathrm{bal} - z_\mathrm{source} = \frac{2.7}{0.18 \times 722^{1/3}} = 1.7\ \mathrm{m}</math>		<math display="block">z_\mathrm{bal} - z_\mathrm{source} = \frac{2.7}{0.18 \times 722^{1/3}} = 1.7\ \mathrm{m}</math>
	The design level for the smoke layer lies 3 m above the balcony, so 4.7 m above this imaginary source.<ref name="Cooper-3-232" /> The line plume there carries 0.18 × 4.7 × 722<sup>1/3</sup> = 7.6 kg/(m·s), or 34.2 kg/s over the full length.<ref name="Cooper-3-232" /> For comparison, the ~~axisymmetric plume equation gives about 27~~.3 kg/s at the same height ~~of 6 m above the fire. This assumes that the virtual origin lies at the base of the fire~~.<ref name="~~Milke~~-4-~~298~~" /> The spill over the balcony edge therefore increases the smoke flow at the ~~design level~~ by ~~about a quarter~~. A smoke exhaust system that holds the smoke layer at this level must remove at least this mass flow.<ref name="Milke-4-299" />		The design level for the smoke layer lies 3 m above the balcony, so 4.7 m above this imaginary source.<ref name="Cooper-3-232" /> The line plume there carries 0.18 × 4.7 × 722<sup>1/3</sup> = 7.6 kg/(m·s), or 34.2 kg/s over the full length.<ref name="Cooper-3-232" /> For comparison, Cooper estimates that the same fire burning in the open, away from the balcony, would supply 26.0 kg/s at the same height.<ref name="Cooper-3-232" /> The spill over the balcony edge therefore increases the smoke flow into the upper layer by 31%, from 26 to 34 kg/s.<ref name="Cooper-3-232" /> A smoke exhaust system that holds the smoke layer at this level must remove at least this mass flow.<ref name="Milke-4-299" />

	Cooper's energy balance gives the average temperature of the plume gases as they enter the smoke layer. It equals the convective heat release rate divided by the plume mass flow and the specific heat of air.<ref name="Cooper-3-234">Cooper (2002b), p. 3-234.</ref> ~~With a~~ specific heat of 1.0 kJ/(kg·K), the line plume reaches the design level about 95 K above ambient and the ~~round~~ plume about ~~119~~ K.~~<ref name="VR-6.7" />~~ The extra entrainment of the line plume thus gives more smoke at a lower temperature, as the Australian handbook also notes.<ref name="Australian-98" />		Cooper's energy balance gives the average temperature of the plume gases as they enter the smoke layer. It equals the convective heat release rate divided by the plume mass flow and the specific heat of air.<ref name="Cooper-3-234">Cooper (2002b), p. 3-234.</ref> The calculation uses the specific heat of air of 1.0 kJ/(kg·K) given in the book.<ref name="VR-6.7" /> The line plume then reaches the design level about 95 K above ambient, and the plume of the fire in the open about 125 K. The extra entrainment of the line plume thus gives more smoke at a lower temperature, as the Australian handbook also notes.<ref name="Australian-98" />

	== Use in smoke control design ==		== Use in smoke control design ==
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	== Limits and uncertainty ==		== Limits and uncertainty ==
	The line plume equations hold only near the source. Cooper states that a line plume cannot keep its two-dimensional, wedge-like shape much beyond a height above the source equal to its length.<ref name="Cooper-3-231" /> At greater heights, the mass flow ~~is better~~ estimated with ~~an axisymmetric plume equation~~ and an effective fire diameter.<ref name="Cooper-3-231" /> The near-wall equation is limited in the same way and also requires that heat losses to the wall stay small.<ref name="Cooper-3-231" />		The line plume equations hold only near the source. Cooper states that a line plume cannot keep its two-dimensional, wedge-like shape much beyond a height above the source equal to its length.<ref name="Cooper-3-231" /> At greater heights, the mass flow would perhaps be best estimated with Cooper's pool fire equations and an effective fire diameter.<ref name="Cooper-3-231" /> The near-wall equation is limited in the same way and also requires that heat losses to the wall stay small.<ref name="Cooper-3-231" />

	~~Line~~ plume ~~sub-models in fire models have not always been tested against experiments~~. In the ~~2007 validation study NUREG-1824,~~ the ~~line plume model of~~ the ~~zone model MAGIC was not evaluated, while its axisymmetric plume model was~~.<ref name="~~Joglar~~-6-10">~~Joglar et al.~~ (~~2007~~), p. 6-10.</ref> ~~The axisymmetric model predicted~~ plume ~~temperatures within~~ the ~~experimental uncertainty~~ of ~~14% in one test series~~.<ref name="~~Joglar~~-6-10" />		Different methods can give very different results for the same case. As an alternative solution to his balcony example, Cooper applies a spill plume equation from another reference, with a constant of 0.39 and the total heat release rate of the fire below the balcony.<ref name="Cooper-3-232" /><ref name="Cooper-3-233">Cooper (2002b), p. 3-233.</ref> It gives 68 kg/s, about 2.0 times his line plume estimate and about 2.6 times the estimate for the fire in the open.<ref name="Cooper-3-233" /> Milke's balcony spill plume equation has the same form with a constant of 0.36.<ref name="Milke-4-301" /> It rests on small-scale experiments with a single opening and a walkway.<ref name="Milke-4-301" /> Its use is questionable when the smoke reaches the atrium through a long corridor and loses heat on the way.<ref name="Milke-4-301" />

	The constants in these correlations come from experiments, and published values differ. For the spill plume in CFAST, the suggested values of the entrainment constant range from 0.44 to 0.66.<ref name="Peacock-21">Peacock et al. (2026), p. 21.</ref> The constant used in CFAST, 0.44, lies at the low end of this range. The balcony spill plume equation in the SFPE Handbook rests on small-scale experiments with a single opening and a walkway.<ref name="Milke-4-301" /> Its use is questionable when the smoke reaches the atrium through a long corridor and loses heat on the way.<ref name="Milke-4-301" />		In the 2007 validation study NUREG-1824, the line plume model of the zone model MAGIC was not evaluated, while its axisymmetric plume model was.<ref name="Joglar-6-10">Joglar et al. (2007), p. 6-10.</ref> The axisymmetric model predicted plume temperatures within the experimental uncertainty of 14% in one test series.<ref name="Joglar-6-10" /> The constants in these correlations come from experiments, and published values differ. For the spill plume in CFAST, the suggested values of the entrainment constant range from 0.44 to 0.66.<ref name="Peacock-21">Peacock et al. (2026), p. 21.</ref> The constant used in CFAST, 0.44, lies at the low end of this range.

	The length of an equivalent line source is ~~often~~ uncertain as well. In Cooper's balcony example, the spill length was expected to lie between one and two times the width of the balcony, and 1.5 times was chosen.<ref name="Cooper-3-232" /> ~~Because~~ the ~~mass flow scales~~ with ~~the~~ length ~~to the power 2/~~3 ~~for a given total heat release rate~~, ~~such choices change~~ the ~~result noticeably~~. The Australian example ~~therefore~~ evaluates several fire positions instead of one assumed worst case.<ref name="Australian-98" />		The length of an equivalent line source is uncertain as well. In Cooper's balcony example, the spill length was expected to lie between one and two times the width of the balcony, and 1.5 times was chosen.<ref name="Cooper-3-232" /> Recalculating the example with a spill length of 3, 4.5 or 6 m gives about 28.6, 33.8 or 38.4 kg/s at the design level.<ref name="Cooper-3-232" /> The Australian example evaluates several fire positions instead of one assumed worst case.<ref name="Australian-98" />

	== See also ==		== See also ==