Average Flame Height (Heskestad)Pool-fire flame height away from walls

What this calculates

This spreadsheet estimates the average height of a pool fire flame based on its heat release rate and diameter. It can also give an approximate idea of flame height for non-pool fires, and could be used “backwards” to determine a heat release rate based on the flame height and diameter observed at a fire.

How to use it

Enter the heat release rate of the fire in cell D5. Enter the diameter of the fire in cell D6.

Variables

L
Average flame height [m]
Q
Heat release rate [kW]
D
Diameter of pool fire [m]

Equations

$$ L = 0.23 \, Q^{2/5} - 1.02 \, D $$Heskestad flame height (Quintiere eq. 7-9)

Discussion

There are some limitations to the use of this equation. This is equation is not good for jet fires, nor for very large pool fires (tank farms, industrial applications, etc.). It does not account for wall or corner effects on flame height. It is useful for many applications in compartment fires though.

Worked example

Example 1

A pool of gasoline 6 feet across is set on fire in the middle of a parking lot on a calm day with no wind. It has a heat release rate of 6300 kW, what is the height of that fire?

Enter 6300 in cell D5 and 6 in cell D6. The height of the flame is shown as 5.75 meters (cell D8) or the equivalent height of 18.85 feet (cell D9).

Example 2

Using multiple spreadsheets…a pool of gasoline 5 feet across is set on fire in the middle of a parking lot on a calm day with no wind. What is the height of the fire?

This time the problem has not specified a heat release rate, so it needs to be calculated first using the HRR spreadsheet, and will require some unit conversion.

First, the diameter of the fire is 5 feet, but we want an area of the fire in square meters. Divide 5/2 to get a radius of 2.5 feet, divide 2.5/3.28 to get that in meters, which comes to a radius of 0.762m. The area of a circle is πr2, with a radius of 0.762 meters that would give an area of 1.83 m2.

Go to the HRR sheet, choose gasoline from the pull-down menu and enter an area of 1.83 in cell C8. The heat release rate shown in cell C10 should be 4,398 kW, which we can round to 4,400 kW.

Go to the Flame Height spreadsheet, enter a heat release rate of 4400 in cell D5 and a diameter of 5 in cell D6. The answer should be a flame height of 5.04 meters, or 16.53 feet (round to 5 meters or 16.5 feet).

Example 3

A witness saw a fire on a sofa in the middle of the living room. The flames were just touching the ceiling, which was 8’ off the ground. The base of the fire was about the size of the sofa cushion, which was 2’ wide x 2’ wide. What was the heat release rate of the fire when the witness saw it?

The first step is to figure out the diameter that we want to use for the “pool fire”.

Technically the most accurate way would be to take our 2’ x 2’ square cushion and find an equivalent diameter for a circular cushion with the same area. We could do that using the equation , which gives a diameter of 2.26’. For a rough calculation it wouldn’t be unreasonable to just assume 2’ for the sake of simplicity and a quick answer. Just remember that if you are right on the line and/or it is an important calculation then you should consider this.

For the sake of this example, let’s use 2’ for the diameter. Enter 2 into cell D6.

Now we want to find the heat release rate at which the average flame height is 8’. So, start trying numbers in cell D5 until the value in cell D9 is close to 8. The answer should be close to 650 kW. If we had used the diameter of 2.26’, the answer would be more like 690 kW.

References

  1. Heskestad, G., method as reported in Quintiere, Principles of Fire Behavior, Ch. 7, eq. 7-9.