The Practice Item That Doesn't Add Up
During a recruit study session at the academy, the instructor hands out a practice written item built from a real company run sheet. Engine 12 carries a 500-gallon booster tank. Its hose bed holds 250 feet of 3½-inch supply line in 50-foot sections and 350 feet of 1¾-inch attack line in 50-foot sections. The department's rule of thumb is that a 3½-inch line loses about 2 psi per 100 feet at 500 gpm. The scenario: a two-story garden apartment with fire showing from a second-floor window. The hydrant sits 180 feet from where the engineer will stop the engine. The officer wants a 200-foot attack line to the front door and a 150-foot line to the rear stairwell, both flowing 150 gpm at the nozzle. The engine will not have a supply line connected until roughly 45 seconds after the attack lines are charged. A classmate raises his hand and says, "Tank water gives us 3.3 minutes per line, so with two lines we have 6.6 minutes."
1. How many 50-foot sections does the scenario require for the supply lay and both attack lines, and are the hose beds sufficient? Show the arithmetic, and give the friction loss in a 200-foot supply line at 500 gpm.
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Supply lay. 180 ft ÷ 50 ft = 3.6, so 4 sections (200 ft). That leaves 20 ft of slack and one 50-ft section still on a 250-ft bed.
Attack lines. Front 200 ft + rear 150 ft = 350 ft = 7 sections. The bed carries exactly 350 ft, so the answer to "is it sufficient?" is yes - with zero margin.
Friction loss. At the stated rule of thumb, 2 psi per 100 ft at 500 gpm: 200 ft ÷ 100 = 2; 2 × 2 psi = 4 psi.
Judgment. Exactly enough is not the same as enough. If one 50-ft length is damaged, or the rear line needs 50 more feet because of a fence line or a stairwell turn, the crew is short at the worst moment. Options, in order of preference: confirm the rear access distance before stretching; keep a spare 1¾-inch section available from the ready load; or shorten the rear line and reposition the engine if rear access allows it. The engineer should also resist adding 100 ft of supply "for safety" - 300 ft of 3½-inch line adds 2 psi of loss and 50 ft of coupled hose to drain and repack for no real gain, and every extra length is another coupling to fail.
2. Using the 500-gallon tank and 150 gpm per line, compute how long the tank lasts with both lines flowing. The supply line will not be connected until about 45 seconds after the lines are charged. What should the officer and engineer do, and why?
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The math. Combined flow = 150 + 150 = 300 gpm. 500 gal ÷ 300 gpm = 1.67 minutes, or 1 minute 40 seconds to run the tank dry.
The timeline. If both nozzles open at time zero, the supply connection is complete at about 0:45, leaving roughly 55 seconds of tank water while the pump takes suction and a charged, confirmed supply reaches the lines. That margin is thin. A missing hydrant cap, a bad thread, a dry main, or a hydrant that has to be flushed erases it, and the crew is inside a burning building with no water.
Reasonable plan. (1) The engineer makes the hydrant and lays the supply first if the layout allows it, or at minimum has the connection made before the officer calls for water. (2) Both lines are stretched, but the nozzles stay closed until the supply is confirmed and charged. (3) If fire conditions force an immediate attack, flow one line at 150 gpm - that is 3 minutes 20 seconds of tank water - and charge the second line when the hydrant is on line.
The point of the exercise. Booster-tank water buys seconds, not minutes. The tank is a buffer for the stretch, not a water supply, and any plan that assumes otherwise is a plan to run dry at the door of the fire room.
3. A classmate argues that the tank gives 3.3 minutes per line, so two lines give 6.6 minutes. Identify the reasoning error and explain how you would correct it without simply giving him the answer.
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The error. Time does not double when a second line is added. Both nozzles draw from the same 500 gallons at the same moment, so the flows add (150 + 150 = 300 gpm) and the time divides (500 ÷ 300 ≈ 1.67 min). The classmate computed the duration for one line, then added a second identical duration as though the lines ran one after another. That is a sequencing error, not an arithmetic slip, and it is the kind of error that looks right because the first number he produced (3.3) is correct for a different question.
How to correct it without handing over the answer. Draw the tank as a box labeled 500 gal with two arrows leaving it, each labeled 150 gpm, and ask: "How fast is the box emptying?" Then have him rework it with one line at 150 gpm and one at 100 gpm - the answer is 2 minutes - and check that he added flows rather than times. Finally, ask what the number means on the fireground: under two minutes of water, which is exactly why the hydrant connection comes before the charge.
Why this matters beyond the item. The same trap shows up in air management - adding durations instead of combining consumption rates - so the correction is worth more than the point on the exam.