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Flame Height — Heskestad
Calculates flame height from heat release rate and fire base diameter, using the correlation L = 0.235·Q̇^(2/5) − 1.02·D.
The fire
This can be taken from the pool fire calculator or the t² fire growth calculator, or entered from elsewhere.
Validity range
Validity range
The conditions that determine whether the correlation applies. Crossing them changes the state of the result.
- The correlation was fitted to flames that are tall relative to their base — an L/D ratio above roughly 1. Below that ratio a value is shown with a warning: the trend is meaningful, the accuracy is not.
- When the 1.02·D term exceeds the 0.235·Q̇^(2/5) term the expression returns a non-positive value. A negative flame height is not a shorter flame; it is a sign that the correlation is outside its range — and in that case no number is shown at all.
Model limits
What the model does not describe, even within its validity range. These always hold.
- The correlation describes a flame burning freely, with no significant wind and no ceiling. A low ceiling or a cross wind changes the flame height and is not accounted for.
There are no material constants here
Unlike the pool fire calculator, this correlation consumes no property of any material. Q̇ and D describe the fire itself, and the coefficients 0.235 and 1.02 are part of Heskestad's correlation. So there are no source fields here.
The equation
L = 0.235 · Q̇^(2/5) − 1.02 · D
8.22 / 2
- L [m]
- Flame height
- Q̇ [kW]
- Heat release rate
- D [m]
- Fire base diameter
Heskestad — SFPE Handbook 5th ed., Fire Plumes, Flame Height and Air Entrainment
Result
ResultThe calculation completed within the model's range of validity.
- Flame height L
- 8.22 m
- Height-to-diameter ratio L/D
- 4.11
- The heat-release term — 0.235 · Q̇^(2/5)0.235 · 12,584^(2/5)10.26 m
- The diameter term — 1.02 · D1.02 · 22.04 m
- Flame height — L = 0.235·Q̇^(2/5) − 1.02·D10.26 − 2.048.22 m
- Height-to-diameter ratio — L/D8.22 / 24.11
Source of the equation
Heskestad, SFPE Handbook of Fire Protection Engineering, 5th ed. — the chapter "Fire Plumes, Flame Height, and Air Entrainment".
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