Relay Pump Pressure at 200 and 300 GPM
Engine 12 is taking water from a confirmed working hydrant and supplying Engine 30 through 500 feet of 2.5-inch hose. Engine 30 needs 20 psi at its intake to operate safely. From Engine 30, a 100-foot 2.5-inch line feeds a deck gun that requires 80 psi at the nozzle plus 10 psi appliance loss. The department training sheet gives friction loss for 2.5-inch hose as 2 psi per 100 feet at 100 gpm, and states that friction loss rises with the square of the flow. Initial target flow is 200 gpm. Engine 12's pump is rated at 150 psi discharge. Engine 12 carries a 500-gallon booster tank, though the hydrant is the primary source.
1. Compute the required discharge pressure at Engine 12 and at Engine 30 for 200 gpm.
Read the worked answer
Step 1 – friction loss per 100 feet at 200 gpm. Flow doubles from 100 to 200 gpm. Squared, that is 2 squared = 4 times the loss. Base loss is 2 psi per 100 feet at 100 gpm, so at 200 gpm it is 2 x 4 = 8 psi per 100 feet.
Step 2 – Engine 12 (500 feet of supply line).
- 500 feet = 5 sections of 100 feet
- 5 x 8 = 40 psi friction loss
- Add 20 psi required at Engine 30's intake
- Engine 12 discharge = 40 + 20 = 60 psi
Step 3 – Engine 30 (100 feet to the gun).
- 1 section x 8 = 8 psi friction loss
- Add 10 psi appliance loss
- Add 80 psi nozzle pressure
- Engine 30 discharge = 8 + 10 + 80 = 98 psi
Sanity check: both numbers sit well under the 150 psi pump rating, so 200 gpm is comfortably achievable. The Engine 30 figure is higher than the Engine 12 figure even though its hose lay is one-fifth as long, because the nozzle and appliance losses live on that side of the relay.
2. Repeat the calculation for 300 gpm and state whether Engine 12 can supply it.
Read the worked answer
Step 1 – friction loss per 100 feet at 300 gpm. Flow triples from 100 to 300 gpm. Squared, that is 3 squared = 9 times the base loss. 2 x 9 = 18 psi per 100 feet.
Step 2 – Engine 12.
- 5 sections x 18 = 90 psi friction loss
- Add 20 psi intake requirement
- Required discharge = 110 psi
- Pump rating is 150 psi, so margin = 150 - 110 = 40 psi
Answer: yes, Engine 12 can supply 300 gpm.
Step 3 – Engine 30.
- 1 section x 18 = 18 psi
- 18 + 10 + 80 = 108 psi, still below its 150 psi rating
Caution worth stating: a 40 psi margin is real but not generous. Any added appliance, a kink, or a longer lay would erase it, and a pump running near its rating at a relay is where pressure problems show up first. The officer should confirm the actual intake pressure at Engine 30 by gauge rather than by calculation alone.
3. If the hydrant failed at the moment flow was set at 300 gpm, how long would the 500-gallon booster tank last, and what does that number mean for the relay decision?
Read the worked answer
Arithmetic: 500 gallons divided by 300 gpm = 1.67 minutes, or about 1 minute 40 seconds.
What that means:
- At 200 gpm the same tank gives 500 / 200 = 2.5 minutes.
- Either figure is shorter than a typical arrival-to-establish-supply window, so the booster tank is not a supply. It is a buffer that covers the seconds between the pump engaging and the hydrant supply being confirmed.
Decision impact: because the hydrant is confirmed working, the tank is irrelevant to whether the relay can run. But the number matters for the failure case: at 300 gpm the crew has under 2 minutes to recognize a supply loss and either throttle back or switch sources before the pump runs dry. Running a pump dry damages it and can leave the crew without water at the moment the fireground needs it most.
Reasoning to state plainly: the pressure math said 300 gpm is achievable; the water math says the tank is not the reason it is achievable. Keep the two questions separate - can the pump deliver the pressure and is there water behind it are different problems with different numbers.