Fire Hose Friction Loss Calculator: FL = C × Q² × L
Fire hose friction loss with FL = C × Q² × L for ¾ to 6 inch hose (or your own flow-tested coefficient, US or metric): loss per 100 ft and for the whole lay, parallel (siamese) lines, the most flow or length within a target loss, an optional pump discharge pressure, and a comparison across hose sizes.
How it works
FL = C × Q² × L, where FL is friction loss in psi, Q = flow (gpm) ÷ 100 and L = hose length (ft) ÷ 100 · C from the hose table (1¾″ = 15.5, 2½″ = 2, 3″ = 0.8, 5″ = 0.08) · Metric: FL (bar) = C × (L/min ÷ 1,000)² × (m ÷ 100), C metric ≈ 1.58 × C US · Parallel lines: Q per line = total flow ÷ lines · Pump discharge pressure = nozzle pressure + FL + appliance loss + 0.5 psi per foot of elevation
Water rubbing along the hose lining loses pressure in proportion to the square of the flow and to the length of the lay, with a coefficient that falls steeply as the diameter grows. That is the fire-service formula FL = C × Q² × L, with Q in hundreds of gpm and L in hundreds of feet. At the same flow, 1¾″ attack hose loses nearly eight times as much as 2½″, and 5″ supply hose almost nothing, which is why pump operators think in loss per 100 ft and why a long 1¾″ stretch at 185 gpm can use 60–70 psi before the water reaches the nozzle. The coefficients are the standard training values for typical double-jacket fire hose. Couplings matter for 3″ hose (0.8 with 2½″ couplings, 0.677 with 3″ couplings), and modern low-friction hose can be 20–40% better than the table, so the most accurate figure comes from flow-testing your own hose with an inline gauge; enter it as a custom coefficient in US or metric units. Parallel (siamese) lines split the flow, and because loss depends on flow squared, two identical lines lose a quarter as much as one. Add a nozzle pressure to get the pump discharge pressure, including appliance loss and elevation at the field rule of 0.5 psi per foot (the exact hydrostatic value is 0.434).
Worked example
200 ft of 1¾″ hose flowing 150 gpm: Q = 1.5 and L = 2, so the loss is 15.5 × 1.5² = 34.9 psi per 100 ft, or 15.5 × 2.25 × 2 = 69.8 psi for the lay (4.81 bar). To keep the loss within 60 psi you could flow at most 100 × √(60 ÷ 31) = 139 gpm, or shorten the lay to 172 ft. The same 150 gpm in 2½″ hose would lose 2 × 2.25 × 2 = 9 psi. With a 100 psi fog nozzle the pump would need about 170 psi.
Sources: Task Force Tips: Hydraulic calculations every firefighter needs to know (FL = C(Q/100)² × L/100, PDP) · Task Force Tips: Metric hydraulic calculations (FL bar = C(Q/1000)² × L/100, worked examples) · Key Hose: Friction loss calculator by hose product
Frequently asked questions
How do you calculate friction loss in a fire hose?
Use FL = C × Q² × L: divide the flow in gpm by 100 and square it, multiply by the hose coefficient and by the length in hundreds of feet. For 200 ft of 1¾″ at 150 gpm: 15.5 × 1.5² × 2 = 69.8 psi.
What is the friction loss coefficient for 1¾ and 2½ inch hose?
The standard training values are 15.5 for 1¾″ hose, 24 for 1½″, 8 for 2″, 2 for 2½″, 0.8 for 3″ with 2½″ couplings, 0.2 for 4″ and 0.08 for 5″. Low-friction hose can be lower, so flow-test your own.
What happens to friction loss if I double the flow?
It goes up four times, because loss depends on the square of the flow. Going from 150 to 300 gpm in 1¾″ hose raises the loss from about 35 to about 140 psi per 100 ft.
How do I do friction loss in metric?
Use FL (bar) = C × (L/min ÷ 1,000)² × (m ÷ 100) with a metric coefficient. For a 52 mm hose with C = 16 flowing 400 L/min over 100 m: 16 × 0.4² × 1 = 2.56 bar. A US coefficient converts to metric by multiplying by about 1.58.
Does elevation count as friction loss?
No. It is a separate term in pump pressure: about 0.5 psi per foot (5 psi per storey) added when the nozzle is above the pump and subtracted when it is below. The exact hydrostatic value is 0.434 psi per foot.
Why is 3 inch hose listed twice?
Because the couplings restrict flow. 3″ hose with 2½″ couplings uses C = 0.8, and with full 3″ couplings about 0.677. Use the combination you actually carry.
Related calculators
Uses the standard fire-service field formula and training coefficients for planning and training. Department SOPs, the authority having jurisdiction, listed hose and equipment data and flow tests govern real operations.