Fire Protection & Fire Dynamics formula solvers

Categories — 60 of them, 1488 solvers in all

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A H M P T V

Alpert Ceiling Jet Temperature (far field)

\Delta T = \dfrac{5.38 \, (\dot{Q}/r)^{2/3}}{H}

Fire Protection & Fire DynamicsRonald Alpert's 1972 correlation for the gas temperature in the thin, fast layer that spreads radially under a ceiling when a plume strikes it. This is the far-field form, for a radius greater than about 0.18 of the ceiling height — the region where sprinklers and heat detectors actually sit.

Alpert Ceiling Jet Velocity (far field)

u = \dfrac{0.195 \, \dot{Q}^{1/3} H^{1/2}}{r^{5/6}}

Fire Protection & Fire DynamicsThe companion to Alpert's temperature correlation: how fast the ceiling jet is moving at a given radius. Velocity is what carries heat into a detector element, so it is half of any response-time calculation — the other half being the temperature the gas is at.

Heat Release Rate from Fuel Area

\dot{Q} = \dot{m}'' \, \Delta H_c \, A_f \, \chi

Fire Protection & Fire DynamicsThe fire size a burning surface can actually deliver: mass leaving the fuel per unit area per second, times the heat that mass carries, times the area alight, times the fraction that burns completely. This is the fuel-controlled ceiling that a growth curve has to be checked against.

Heskestad Flame Height

L_f = 0.235 \, \dot{Q}^{2/5} - 1.02 \, D

Fire Protection & Fire DynamicsGunnar Heskestad's correlation for the mean height of the luminous flame above a fire of known size and base diameter. Two terms: the heat release rate lifts the flame, and the base diameter pulls the tip down, because a wide fire entrains air along its whole perimeter and burns out sooner.

MQH Hot Gas Layer Temperature

\Delta T_g = 6.85 \left( \dfrac{\dot{Q}^{2}}{A_0 \sqrt{H_0} \; h_k A_T} \right)^{1/3}

Fire Protection & Fire DynamicsMcCaffrey, Quintiere and Harkleroad's 1981 correlation for how hot the upper layer gets in a naturally ventilated compartment fire. It balances what the fire puts in against what the opening carries out and what the boundaries absorb, and it is the workhorse hand calculation of enclosure fire analysis.

Plume Centreline Temperature Rise

\Delta T_0 = 25.0 \, \dfrac{\dot{Q}_c^{2/3}}{(z - z_0)^{5/3}}

Fire Protection & Fire DynamicsHow hot the gases are on the axis of a buoyant plume, a stated height above the fire. Heskestad's far-field solution: the convective part of the fire drives the column, and the temperature rise falls off as the 5/3 power of the height above the plume's virtual origin.

Point Source Radiant Heat Flux

\dot{q}'' = \dfrac{\chi_r \, \dot{Q}}{4 \pi R^{2}}

Fire Protection & Fire DynamicsThe simplest radiation model in fire protection: treat the fire as a point radiating a fixed fraction of its heat release rate equally in all directions, and the flux at a target falls off as the inverse square of the distance. Crude, quick, and the first thing anyone reaches for when asked how far away is far enough.

t-Squared Fire Growth

\dot{Q} = \alpha \, t^{2}

Fire Protection & Fire DynamicsThe design fire curve every performance-based analysis starts from: heat release rate grows as the square of the time since ignition. One coefficient sets how fast, and the four named rates — slow, medium, fast, ultra-fast — are just four values of it.

Thomas Flashover Correlation

\dot{Q}_{fo} = 7.8 \, A_T + 378 \, A_0 \sqrt{H_0}

Fire Protection & Fire DynamicsPhilip Thomas's 1981 estimate of the heat release rate at which flashover becomes likely in a compartment: one term for the heat the boundaries absorb, one for the heat the opening carries away. It is a screening figure, and flashover is a transition rather than a threshold.

Ventilation-Limited Burning Rate (Kawagoe)

\dot{m} = 0.5 \, A_0 \sqrt{H_0}

Fire Protection & Fire DynamicsKunio Kawagoe's 1958 result, and one of the oldest quantitative facts in fire science: in a fully developed compartment fire the fuel burns at a rate set by the opening, not by the fuel. Half a kilogram of wood per second for every square metre of opening times the square root of its height.