Buoyancy

Buoyancy is the upward force that arises from pressure differences around a body or fluid region immersed in another fluid. For a submerged body, Archimedes' principle relates this force to the weight of the displaced fluid. In fire safety, the term usually concerns hot combustion products that are less dense than surrounding air and therefore rise.

This upward movement drives fire plumes and contributes to smoke accumulation near ceilings. It also produces pressure differences across openings and within tall buildings. Buoyancy therefore links fire temperatures with smoke transport, ventilation flows and the exposure of spaces away from the fire.

Buoyancy is not the same as convection. It is a driving force, while convection is heat transfer associated with moving gas or liquid. Buoyant motion can transport energy and combustion products, but wind, fans and other pressure differences can change the resulting flow.

Pressure, displacement and density

Pressure in a static fluid changes with height because of the weight of fluid above. A submerged body experiences different pressures on its upper and lower surfaces. The vertical difference between the resulting pressure forces produces an upward buoyant force.

Density contrast produces buoyancy in hot fire gases. Based on Kandola (2002), pp. 1-4–1-5 and Van Rossum (2027), §3.2.

Archimedes' principle states that the lifting force equals the weight of the displaced fluid volume. If this force exceeds the body's weight, the body rises or floats. If it is smaller, the body sinks. Equilibrium requires the appropriate balance of forces and, for rotational stability, a suitable relationship between the centres of gravity and buoyancy.

The centre of buoyancy is located at the centroid of the displaced fluid volume. This geometric result helps explain why shape and orientation affect stability. It is separate from the centre of gravity, where the body's weight acts.

For hot gases, a simple displaced-body picture becomes part of a wider flow. The heated region is not a sealed object moving through still air. It expands, mixes and exchanges heat while pressure and density vary around it. The same density principle nevertheless explains the upward driving force.

Density differences, rather than temperature alone, provide the direct mechanical contrast. Heating usually lowers gas density at approximately constant pressure, but composition and pressure also affect density. A complete flow assessment therefore avoids treating temperature as a direct velocity or force without the intervening physics.

Heating and the ideal-gas relationship

The Ideal gas law connects pressure, volume, temperature and amount of gas. At approximately constant pressure, heating allows a given mass of gas to occupy more volume, reducing its density. If volume cannot change freely, pressure can instead increase. These alternatives shape different enclosure scenarios.

Absolute temperature in kelvin is required for this relationship. Van Rossum gives an approximation for air density near atmospheric pressure, yielding about 1.2 kg/m³ at 20 °C and 0.75 kg/m³ at 200 °C. The example shows why hot combustion products tend to rise through cooler air.

These values are not a general smoke-density table. Real smoke contains entrained air and combustion products whose temperature and composition change. The approximation is useful for illustrating density, but an engineering calculation needs conditions appropriate to the actual gas.

A simple pressure calculation

A column of gas has weight, so its pressure decreases with height. Two columns with different densities have different rates of pressure decrease. If their pressures are equal at a reference height, a pressure difference develops above or below that level. Van Rossum gives the following approximation for uniform warm and cool columns.

$$\rho \approx \frac{353}{T},\mathrm{\Delta }p\approx gh({\rho }_c-{\rho }_h)$$

Symbol	Description	Unit
$\rho$	Approximate air density near atmospheric pressure	kg/m³
$T$	Absolute gas temperature	K
$\mathrm{\Delta }p$	Warm-column pressure minus cool-column pressure above an equal-pressure reference level	Pa
$g$	Gravitational acceleration	m/s²
$h$	Height above the reference level	m
${\rho }_c,{\rho }_h$	Cool and hot column densities	kg/m³

The coefficient 353 is used with temperature in kelvin to obtain density in kilograms per cubic metre. It incorporates the assumed gas properties and atmospheric pressure. The pressure expression assumes each column has approximately constant density over the height considered. It describes the buoyant contribution before wind, ventilation and flow resistance are included.

For an illustrative calculation, consider air columns at Van Rossum's example temperatures of 20 °C and 200 °C. Choose a height of 3 m above a level where their pressures are equal. This height is an example assumption, not a prescribed building dimension. Using 9.8 m/s² for gravitational acceleration follows the value in the 2005 International Fire Engineering Guidelines.

The temperatures become 293.15 K and 473.15 K, giving densities of approximately 1.20 kg/m³ and 0.746 kg/m³. Keeping the unrounded densities in the calculation gives about 13.5 Pa. At the upper level, pressure in the hotter column exceeds pressure in the cooler column. The difference arises because pressure falls less rapidly with height in the less dense gas.

$$\mathrm{\Delta }p\approx 9.8\times 3\times (\frac{353}{293.15}-\frac{353}{473.15})\approx 13.5\mathrm{P}\mathrm{a}$$

This result is a pressure estimate, not a smoke velocity or exhaust capacity. Turning pressure into a flow rate also requires the opening geometry and flow resistance. An actual building's equal-pressure level depends on its openings and other driving forces. The chosen reference level cannot simply be assumed for every room or shaft.

Heating also causes expansion. When a room cannot accommodate the increased gas volume, gas is pushed through available openings. Van Rossum notes that this can become pronounced around flashover, forcing hot gases through seams, cracks and holes as well as larger vents.

Expansion and buoyancy should be distinguished. Expansion results from increasing gas volume or pressure, while buoyancy results from density contrasts and gravity. Both can act during the same fire and contribute to flow through different parts of an opening.

Fire plumes and entrainment

A Fire plume is the rising flow of hot combustion products above a fire. Buoyancy drives the upward motion, and turbulence draws surrounding air into the plume. The plume widens and becomes more diluted as its mass flow increases.

Buoyancy drives plume rise and upper-layer formation. Based on Van Rossum (2027), §6.7 and Australian Building Codes Board et al. (2005), p. 2.5-2.

This air entrainment can greatly exceed the mass flow of burned fuel. The 2005 International Fire Engineering Guidelines note that some smoke-development methods consequently neglect the fuel mass flow in comparison. Heat release from the fuel still establishes the buoyant source, so neglecting its mass is not the same as neglecting the fire.

The plume transports heat as well as combustion products. Its temperature and concentration decline through dilution and heat exchange, while the total volume of affected gas increases. A relatively small fire can therefore create a large smoke flow.

Plume geometry affects entrainment. The 2005 guidelines describe axisymmetric models for fires away from walls, where air can enter from all sides. Walls, corners and obstructions alter this symmetry and require suitable models rather than an unmodified free-plume assumption.

Different plume regions can also behave differently. The guidelines refer to persistent-flame, intermittent-flame and buoyant-plume regions in one modelling approach. A single velocity or temperature should therefore not be assumed to represent the entire height from fuel surface to ceiling.

Hot layers and stratification

When a rising plume reaches the top of an enclosure, smoke spreads beneath the ceiling and can form a Hot gas layer. Sufficient temperature contrast between the plume and room air supports a stratified situation, with hotter gas above cooler gas. Weak contrast and strong mixing can instead produce more homogeneous conditions.

The layer accumulates mass and energy supplied by the plume. Its depth and temperature influence radiation to lower objects, heat transfer to boundaries and flow through openings. Buoyancy therefore affects the enclosure even after the initial vertical rise has ended.

The upper layer is not composed only of products generated directly by combustion. Entrained air forms much of its volume, and this dilution changes density and composition. Layer buoyancy depends on the resulting mixture, not on flame temperature alone.

At an opening, the Neutral plane marks the height around which the pressure relationship changes and flow can reverse direction. The 2005 guidelines explain that its location is often near, but not identical to, the smoke-layer interface. A lower smoke interface therefore does not necessarily place the neutral plane at the same height.

Neutral-plane and layer-interface positions should therefore not be treated as interchangeable definitions. One concerns pressure-driven flow, while the other describes a smoke concentration or thermal region. Their relationship depends on the enclosure and opening conditions.

Stack effect and vertical shafts

Stack effect is buoyancy-induced pressure difference caused by temperature differences between the inside and outside of a building, particularly over tall vertical spaces. Elevator shafts, stairwells and service ducts can provide routes for the resulting vertical smoke movement.

Stack effect and neutral-plane exchange shape smoke movement. Based on Australian Building Codes Board et al. (2005), p. 2.5-6.

A chimney can strengthen vertical flow by limiting horizontal mixing. Van Rossum notes that the effect can also occur without a chimney wherever density differences act over height. Architectural form changes the flow but does not create the underlying thermal principle.

Stack effect can move smoke in directions that a local plume description would not predict. It can draw gas upwards through remote shafts or contribute to exchange through openings at different heights. The direction depends on inside-outside temperature and pressure distributions.

Wind adds another pressure field, and mechanical systems can add or remove air at selected locations. These forces can strengthen, weaken or reverse buoyancy-driven flow. A smoke assessment based only on hot gas rising in still air can therefore miss important paths.

Openings themselves modify flow. Discharge coefficients, effective area and unsteady exchange can affect how much gas crosses. The 2005 guidelines note puffing and exchange flow through horizontal vents, demonstrating that an opening is not a simple passive hole in every configuration.

Buoyancy and convective heat transfer

Convection uses the moving gas to transport energy. Buoyancy supplies one means of motion, while forced convection uses external influences such as wind or fans. In many fires both occur together as mixed convection.

The convective energy carried by a flow depends on its temperature, density, specific heat and volume flow. Buoyancy influences these variables indirectly by driving entrainment and transport. It does not by itself specify the watts delivered to a surface.

At walls and ceilings, boundary-layer flow controls heat exchange between gas and solid. The same buoyant movement that brings hot gas to a surface therefore produces a second heat-transfer problem at that surface. Plume transport and surface heat flux require different analyses.

Smoke movement includes the wider result of buoyancy, expansion, wind and equipment acting through the building. It includes gas composition and visibility as well as heat. Buoyancy is fundamental to many smoke scenarios, but it is only one component of the complete pressure and transport model.

Buoyancy and smoke management

Smoke-management methods work with or against the pressure and density conditions created by fire. The 2005 International Fire Engineering Guidelines identify natural ventilation, zone pressurisation, extraction, dilution and containment as broad approaches. Each changes the flow path or the accumulation of smoke in a different way.

Natural ventilation uses openings to release hot smoke and admit replacement air. Buoyancy can provide much of the driving force, but vent location and area determine how that force produces flow. Wind can alter the intended direction and must be considered where it affects the system.

Zone pressurisation establishes a pressure difference intended to keep selected spaces clear of smoke. This approach can oppose buoyancy-driven movement across a boundary. Its effect depends on maintaining the required pressure relationship when doors, vents and other openings change state.

Extraction removes smoke and its transported energy from the building. It can reduce accumulation while also changing the pressure field and air entrainment into the fire region. The exhaust flow and make-up air therefore have to be considered together with the buoyant source.

Dilution adds air to reduce smoke concentration, but it changes the total gas flow and does not remove the fire's heat source. Containment instead limits the region through which smoke can travel. Both approaches still require an account of buoyancy at openings and within vertical spaces.

These methods demonstrate why buoyancy is not simply a reason for smoke to rise unimpeded. It is one force within a designed and changing system. Effective analysis identifies the intended pressure and flow pattern, then tests whether fire, wind and equipment can maintain or disturb it.

Engineering use and uncertainty

Buoyancy-informed models estimate plume mass flow, smoke production, layer conditions and vent flow. Their inputs include heat release rate, geometry, gas properties and opening arrangements. Results must be tied to the model's applicable fire size and position.

A free-plume result should not be transferred automatically to a wall or corner fire. Likewise, a stratified-layer model should not be used where mixing has removed the assumed layer. Checking these physical assumptions is as necessary as selecting correct numerical values.

Time changes the force and the flow. Heat release rate, smoke temperature, vent state and mechanical-system operation can all vary. A steady buoyancy calculation can represent selected conditions but does not establish the complete sequence of smoke spread.

Rising hot gas does not mean every particle moves only upwards. Turbulence, obstacles, wind and pressure differences create horizontal and downward components. A building-scale assessment follows the resulting flow field rather than relying on the simplified image of a vertical column.

Field interpretation needs corresponding measurements of temperature, pressure and flow. Temperature helps establish density, pressure differences help establish driving force and opening conditions reveal the resulting transport. None of these observations alone describes the entire buoyant system.

See also

• Vent flow

References

• Atreya, A. (2002). Convection heat transfer. In P. J. DiNenno (Ed.), SFPE handbook of fire protection engineering (3rd ed., pp. 1-44–1-72). National Fire Protection Association.
• Australian Building Codes Board, National Research Council of Canada, International Code Council, & Department of Building and Housing New Zealand. (2005). International fire engineering guidelines (2005 ed.). Australian Building Codes Board.
• Kandola, B. S. (2002). Introduction to mechanics of fluids. In P. J. DiNenno (Ed.), SFPE handbook of fire protection engineering (3rd ed., pp. 1-1–1-26). National Fire Protection Association.
• Van Rossum, E. (2027). Introduction to Fire Safety Engineering. Fire Safety Academy.