Various textbooks such as Quintiere’s Principles of Fire Behavior and Drysdale’s Principles of Fire dynamics cite the 1949 work of Hottel and Hawthorn e on jet flame lengths. These books show graphical presentations of a series of flames issuing from a nozzle. The flames grow shorter as they morph into the turbulent state and then remain constant in length as the gas flow increases. In the case of Quintire at least, the flames also appear to remain constant in diameter as opposed to their actual conical shape.

Hottel worked with city gas, a material rarely encountered today. Perhaps his work was accurate for this particular gas and geometry (1/8-inch orifice, flow range 0.0 -- 250 feet/sec), but the results are misleading with respect to most flame jets. The results do not comport with the brief but learned treatise in the SFPE Handbook.

Sugawa and Sagai conducted numerous experiments with propane jets and published the results in a paper entitled “Flame Length and Width Produced by Ejected Propane from a Pipe,” which can be found at the NIST web site. The authors correlated flame length and width with Q*, finding the values proportional to (Q*)^1/3 over a wide range of flow rates and nozzle diameters. Unfortunately, there is a typographical error in their equation for deriving Q* which may lead to confusion for those who want to plug and play.

The defined relationship between Q* and Q can be combined with the derived relationship between flame length (L) and Q* into a handy general equation for jet flame length hand calculations:

L = 0.79Q^1/3*D^1/6

Where Q = HRR (kW), D = Diameter of nozzle (m) and L = average flame length (m).

Other relationships have been derived by other authors, but the above should give a reasonable approximation if I did the math correctly.