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Smoke Layer Filling — Zukoski
The time until the base of the smoke layer descends to a given height in a compartment, against a t² fire, using Zukoski's plume correlation.
The compartment
Zero is valid. z is measured upward from the fire base, not from the floor.
The time returned is the time until the base of the layer reaches that height.
The layer density is derived from it by the ideal gas law.
The fire
Needed to calculate the flame height, which is the lower bound of the plume correlation's validity.
Energy split
χ_r and χ_c are the same physical quantity seen from its two ends, so only one value is entered and the other follows from it. That way one project cannot hold two contradictory values for the same split — and it is the same value the radiation calculator asks for.
Fuel-dependent. The tool supplies no value and assumes no 0.7.
Required. The tool does not supply this value, and a result resting on a value with no source is marked as undocumented.
Validity range and assumptions
Validity range
The conditions that determine whether the correlation applies. Crossing them changes the state of the result.
- The plume correlation describes the region above the flame tip, where the gas rises and entrains air rather than burning. The tool calculates the flame height by Heskestad at every step — the fire grows, so the flame does too — and if the layer reaches the flame tip the calculation stops and no time is shown. That is not a warning but the absence of an answer.
Calculation assumptions
What was assumed in order to calculate. These are the tool's decisions, not the source's.
- z is measured above the virtual origin of the plume, which may lie above or below the fuel surface. The tool measures from the fire base — that is an approximation. Locating the virtual origin requires a correlation and a source we do not hold, so it is not corrected for here.
- A two-zone model, one compartment: no openings and no leakage — nothing leaves; a floor area constant with height; a well-mixed upper layer with a sharp interface.
- The layer density is held constant through the integration and taken as the ambient density at the temperature entered. A real layer is hotter and therefore less dense, and the same mass occupies a greater volume in it than the calculation assumes.
- There is no growth limit: Q̇ = α·t² for as long as the calculation runs. The layer descending to the floor is not a physical scenario — the fire would have been starved of air before then, and the assumptions above are the first to break.
The equation
ṁ_p = 0.071 · Q̇_c^(1/3) · z^(5/3) · A · dz/dt = − ṁ_p / ρ
- ṁ_p [kg/s]
- Plume mass flow
- Q̇_c [kW]
- Convective heat release rate
- z [m]
- Height above the fire base
- A [m²]
- Compartment floor area
- ρ [kg/m³]
- Layer density
- t_g [s]
- Growth time
- D [m]
- Fire base diameter — for the flame tip check
Zukoski — SFPE Handbook 5th ed.
Result
Missing dataA value is missing that you can supply here and now.
No result was calculated. The details are below.
To complete the calculation the following are missing:
- Energy split χ
Source of the equations
Zukoski — smoke plume mass flow; Heskestad — flame height. SFPE Handbook of Fire Protection Engineering, 5th ed.
The integration is numerical (RK4) with a calculation horizon of 3,600 s. The horizon is a computational bound, not a physical limit.
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