Real-Life Math
Ralph Mohrmann has been a forest firefighter for decades. During
that time, he's worked as a front-line forest firefighter, crew leader and
command spotter (coordinating firefighting efforts from the helicopter). Currently,
he's a supervisor.
Forest firefighters work to control and put out
wildland fires, says Mohrmann. They work in remote and often inaccessible
parts of the country. They use heavy equipment such as hand tools, chainsaws,
pumps and hoses. Rugged terrain and the weather affect how a fire is fought.
Firefighters
have to know how to use their equipment to the maximum in such circumstances,
says Mohrmann. This includes knowing all about water pumps, hose lines, nozzle
pressure and friction loss.
A water pump pushes water through the lines
at various pressures (psi). Each pump has a rated pressure maximum.
Nozzles
are designed to help put out fires by getting the right amount of water, in
the right form, in the right place. In order to be effective, the forest service
requires the nozzle pressure to be 25 psi.
The hose is required to
deliver water to the site of the fire. Hoses come in different diameters.
The
pressure required to push water up a slope is referred to as "head." The quick
rule for head is that it takes 1/2 psi (pressure) to push water up 1 foot
of elevation.
As the water travels through the hose, it will lose some
of its energy to friction. Depending on the nozzle size and hose size, the
amount lost to friction will change. Firefighters use friction loss charts
in their calculations.
| 25 mm (1 in) Lined Hose | | At Nozzle Pressure | Friction Loss Experienced for every
30.5 meters (100 feet) of Hose Using Various Nozzle Sizes | | (kPa) | (psi) | .635 cm | 1/4 in | .7937 cm | 5/16 in | .95 cm | 3/8 in | 1.25 cm | 1/2 in | | 138.00 | 20.00 | 13.75 | 2.0 | 24.00 | 3.5 | 57.25 | 8 | 227.50 | 33 | | 172.50 | 25.00 | 17.25 | 2.5 | 38.00 | 5.5 | 32.75 | 12 | 269.00 | 39 | | 207.00 | 30.00 | 20.75 | 3.0 | 51.75 | 7.5 | 110.30 | 16 | 317.25 | 46 | | 241.25 | 35.00 | 27.50 | 4.0 | 62.00 | 9.0 | 124.00 | 18 | 386.00 | 56 | | 275.75 | 40.00 | 34.50 | 5.0 | 76.00 | 11.0 | 151.75 | 22 | 420.50 | 61 | | 344.75 | 50.00 | 41.50 | 6.0 | 89.75 | 13.0 | 179.25 | 26 | 503.25 | 73 | | 413.75 | 60.00 | 48.25 | 7.0 | 103.50 | 15.0 | 213.75 | 31 | 592.75 | 86 | | | 38 mm (1 1/2 in) Lined Hose | | At Nozzle Pressure | Friction Loss Experienced for every
30.5 meters (100 feet) of Hose Using Various Nozzle Sizes Different Nozzle
Tip Sizes | | (kPa) | (psi) | .635 cm | 1/4 in | .7934 cm | 5/16 in | .95 cm | 3/8 in | 1.25 cm | 1/2 in | | 138.00 | 20.00 | 3.50 | 0.5 | 05.50 | 0.8 | 10.50 | 1.5 | 27.50 | 4.0 | | 172.50 | 25.00 | 4.25 | 0.6 | 07.00 | 1.0 | 13.75 | 2.0 | 34.50 | 5.0 | | 207.00 | 03.00 | 4.75 | 0.7 | 09.00 | 1.3 | 16.50 | 2.4 | 42.00 | 6.1 | | 241.25 | 53.00 | 5.50 | 0.8 | 10.50 | 1.5 | 19.50 | 2.8 | 49.00 | 7.1 | | 275.75 | 40.00 | 6.25 | 0.9 | 12.50 | 1.8 | 22.00 | 3.2 | 56.50 | 8.2 | | 344.75 | 50.00 | 7.00 | 1.0 | 14.50 | 2.1 | 24.75 | 3.6 | 69.00 | 10.0 | | 413.75 | 60.00 | 8.25 | 1.2 | 16.00 | 2.3 | 27.50 | 4.0 | 82.75 | 12.0 | | | 38 mm (1 1/2 in) Unlined Hose | | (kPa) | (psi) | .635 cm | 1/4 in | .7934 cm | 5/16 in | .95 cm | 3/8 in | 1.25 cm | 1/2 in | | 138.00 | 20.00 | 4.75 | 0.7 | 11.00 | 1.6 | 22.00 | 3.2 | 58.00 | 8.4 | | 172.50 | 25.00 | 5.50 | 0.8 | 14.50 | 2.1 | 28.25 | 4.1 | 68.00 | 10.0 | | 207.00 | 30.00 | 7.00 | 1.0 | 17.92 | 2.6 | 34.50 | 5.0 | 96.50 | 14.0 | | 241.25 | 35.00 | 8.25 | 1.2 | 21.50 | 3.1 | 41.50 | 6.0 | 110.50 | 16.0 | | 275.75 | 40.00 | 10.50 | 1.5 | 24.75 | 3.6 | 47.00 | 6.8 | 124.00 | 18.0 | | 344.75 | 50.00 | 12.50 | 1.8 | 27.50 | 4.0 | 52.50 | 7.6 | 145.00 | 21.0 | | 413.75 | 60.00 | 13.75 | 2.0 | 31.75 | 4.6 | 58.00 | 8.4 | 172.00 | 25.0 |
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A small fire has broken out and you're leading the crew to put
it out. There's a big hill between your water source and the fire -- you estimate
that the elevation difference is around 250 feet. The fire is about 2,500
ft away. You have a 1.5-inch lined hose. What capacity of pump will you need
to deliver water to the 3/8 inch nozzle at 25 psi?
You have 2 portable
pumps available to you -- one has a capacity to deliver water at 150 psi,
and the other one has the capacity to deliver water at 250 psi. Which one
should you use?
Pump Pressure = Nozzle Pressure + Head + Friction Loss