Firefighter Math Applications Questions and Answers Flashcards

A fire engine pump is supplying water at 150 psi engine pressure through 200 feet of 2.5-inch hose with a friction loss of 15 psi per 100 feet. What is the nozzle pressure?

Answer: 120 psi

Friction loss = 15 psi × 2 (for 200 ft) = 30 psi; nozzle pressure = 150 − 30 = 120 psi.

A storage tank is cylindrical with a diameter of 10 feet and a height of 8 feet. Approximately how many gallons does it hold? (1 cu ft ≈ 7.48 gal)

Answer: 4,712 gallons

Volume = π × r² × h = 3.14 × 25 × 8 ≈ 628 cu ft; 628 × 7.48 ≈ 4,697 ≈ 4,712 gal.

A hose line flows 200 gpm. How many minutes will it take to empty a 3,000-gallon tank?

Answer: 15 minutes

Time = 3,000 ÷ 200 = 15 minutes.

Friction loss in a 1.75-inch hose is 25 psi per 100 feet. A pumper must supply a nozzle pressure of 100 psi through 300 feet of hose. What pump discharge pressure is required?

Answer: 175 psi

Friction loss = 25 × 3 = 75 psi; pump pressure = 100 + 75 = 175 psi.

A ladder truck's aerial ladder is extended 85 feet at a 70° angle. Approximately how high does the tip reach vertically? (sin 70° ≈ 0.94)

Answer: 80 feet

Vertical height = 85 × sin 70° = 85 × 0.94 ≈ 79.9 ≈ 80 feet.

A room measures 20 ft × 15 ft × 9 ft. What is its volume in cubic feet?

Answer: 2,700 cu ft

Volume = 20 × 15 × 9 = 2,700 cubic feet.

If a pumper delivers 750 gpm and the hydrant can supply 1,200 gpm, how many additional gallons per minute are available from the hydrant beyond what the pumper uses?

Answer: 450 gpm

Remaining supply = 1,200 − 750 = 450 gpm.