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The Iowa Rate of Flow Formula
The formula
| Gpm x t = (Vol/200) |
was named by Royer & Nelson “The Gallonage Formula”. We have renamed this formula the “Royer-Nelson Formula”. This is not the formula that became widely known as “The Iowa Rate of Flow Formula”. The Iowa formula can be derived easily from the Royer-Nelson formula. From the research done by Royer-Nelson, they determined that almost all structure fires could be controlled by using fog nozzles in less than 30 seconds. Keith Royer recommended that this fact be used to determine the capability of a fire department to handle its structure fires. So taking the time of 30 seconds (0.5 minute) and substituting into the Royer-Nelson formula gives
| Gpm x 0.5 = (Vol/200) |
Dividing both sides of the equation by 0.5 gives
| Gpm x (0.5/200) = (Vol/0.5) |
Simplify by dividing and multiplying
| Gpm x 1 = (Vol/100) |
| Gpm = (Vol/100) |
This is the equation known as The Iowa r.o.f. formula. This equation must be interpreted very carefully. The time factor has disappeared from the left side of the equation, and dividing by time on the right produces a different fraction: Vol/100. What has happened is that time has been eliminated from both sides of the equation. V/200 was the product of Gpm x t. Now Vol/100 is only Gpm. So the Iowa Formula is a simple statement that Gpm = Gpm, that and nothing more. No longer are the expressions a product of Gpm x t.
The key to eliminating the confusion is the realization that the Iowa Formula is valid only for a time of 30 seconds. Mathematics has created a notation that helps solve our problem and makes everything clear The solution is to use subscript notation.
Subscript notation uses smaller numerals or letters written below and to the right of a given numeral or expression. Thus the Iowa r.o.f. written as follows is read as: “Gpm for 30 seconds”. This notation serves as a reminder that the Iowa formula is valid only for a time of 30 seconds.
| Gpm30s = (Vol/100) |
This is the way the Iowa Formula should be written The Iowa r.o.f. formula should not be compared with any other r.o.f formula with a different time. This second equation should be called the Royer Nelson 30 second formula.
The Iowa r.o.f. formula has universally been misused by ignoring the time of 30 seconds and by using it to apply to the volume of the entire structureThere is a second error that has been made universally in the use of the Iowa r.o.f. formula. The volume of the entire structure should not be used, only the volume of the largest open area of the structure. Keith Royer believed that it would be a rare occurrence that a large building with many rooms would be fully involved before the arrival of a fire department in less than ten minutes. So the fire department’s capability should be measured by the largest open area of that structure. The Iowa r.o.f. formula has universally been misused by ignoring the time of 30 seconds and by using it to apply to the volume of the entire structure. Also Keith Royer strongly recommended that the 30 second formula primarily should be used for pre planning.
