FCTC Firefighter Math Applications Questions and Answers

Question 1

An engine company is operating two attack lines at a residential fire. The first line is a 1.75-inch hose flowing 150 gallons per minute (GPM). The second line is a 2.5-inch hose flowing 250 GPM. What is the total flow rate, in GPM, that the pump operator must supply to maintain pressure for both lines?

Accepted Answer

400 GPM

Answer

To find the total flow rate required from the pump, simply add the flow rates of each individual hoseline being supplied. In this case, 150 GPM (Line 1) + 250 GPM (Line 2) equals a total of 400 GPM.

Question 2

A firefighter is operating a 2.5-inch hoseline that is 300 feet long and is flowing 250 GPM. Using a common fireground rule of thumb that estimates friction loss in 2.5-inch hose at this flow rate to be approximately 15 psi per 100 feet, what is the TOTAL estimated friction loss for the entire hoseline?

Accepted Answer

45 psi

Answer

The rule of thumb states a friction loss of 15 psi for every 100 feet of hose. Since the total length is 300 feet, you multiply the friction loss per section by the number of sections (300 feet / 100 feet = 3 sections). Therefore, 15 psi/section * 3 sections = 45 psi total friction loss.

Question 3

You are the pump operator supplying an attack line to the 5th floor of an apartment building. The firefighting crew is using a standard fog nozzle that requires 100 psi nozzle pressure. The friction loss in the 200 feet of 1.75-inch hose is calculated to be 40 psi. You must also account for head loss, which is approximately 5 psi for each floor above the fire engine. What is the correct Pump Discharge Pressure (PDP)?

Accepted Answer

160 psi

Answer

The formula for Pump Discharge Pressure is PDP = Nozzle Pressure (NP) + Total Friction Loss (FL) + Elevation (Head) Loss. Head loss is 5 psi per floor above the engine, so for the 5th floor, it's 4 floors up (5-1=4), which is 4 * 5 psi = 20 psi. Therefore, PDP = 100 psi (NP) + 40 psi (FL) + 20 psi (Head Loss) = 160 psi.

Question 4

A hazardous materials incident has occurred in a sealed warehouse room. To properly ventilate the space, you must first calculate its total volume. The room measures 40 feet long, 30 feet wide, and has a ceiling height of 20 feet. What is the volume of the room in cubic feet?

Accepted Answer

24,000 cubic feet

Answer

The volume of a rectangular space is calculated by multiplying its length by its width by its height. In this scenario, the calculation is 40 ft (Length) x 30 ft (Width) x 20 ft (Height) = 24,000 cubic feet.

Question 5

A 3,000-gallon water tender is being used in a shuttle operation to supply water to a rural fire scene. The total time for one complete cycle (drive to the scene, dump the water, return to the fill site, and refill the tank) is 20 minutes. How many total gallons of water can this tender deliver to the scene in one hour?

Accepted Answer

9,000 gallons

Answer

First, determine how many trips the tender can make in one hour (60 minutes). With a cycle time of 20 minutes, the tender can complete 60 minutes / 20 minutes/cycle = 3 cycles. Then, multiply the number of cycles by the tender's capacity: 3 cycles * 3,000 gallons/cycle = 9,000 gallons.

FCTC Test Practice Test

FCTC Test Practice Test

FCTC Firefighter Math Applications Questions and Answers