Friction loss is the pressure that disappears between the pump and the nozzle because water is rubbing against the inside of the hose. The formula every pump operator learns is:
C is a coefficient that depends on hose diameter, Q is flow in hundreds of gallons per minute, and L is hose length in hundreds of feet. For 200 ft of 1¾-inch hose flowing 150 gpm, FL = 15.5 × 1.5² × 2 = 70 psi. This article covers where the formula comes from, gives the coefficient chart in both unit systems, works three examples, and explains why the hose on your apparatus may not match the chart.
What friction loss is
Water moving through a hose is not a solid plug sliding along. The water touching the liner barely moves, the water in the middle moves fastest, and every layer in between drags on its neighbours. That shearing, plus the turbulence it creates, converts pressure into heat. The faster the water moves and the longer the hose, the more pressure is lost.
You can see it directly with two inline gauges. Put one at the pump discharge and one at the nozzle on a 200 ft 1¾-inch line, open the nozzle, and the two readings will differ by about 70 psi at 150 gpm. Close the nozzle and the readings become equal, because friction loss only exists when water is moving. That last point matters: a charged, static line shows pump pressure at the nozzle, which is why a crew can be fooled about how much pressure they will have once they open up.
The four principles of friction loss
IFSTA summarizes the behaviour with four principles. They are worth knowing because exam questions and fireground decisions both lean on them.
- Friction loss varies directly with hose length. Double the length, double the loss. This is the L in the formula.
- Friction loss varies approximately with the square of the flow. Double the flow, quadruple the loss. This is the squared Q, and it is the principle that surprises people.
- For the same flow, friction loss varies inversely with roughly the fifth power of the hose diameter. A small increase in diameter produces a large drop in loss. This is why the coefficient for 2½-inch hose is about one eighth of the coefficient for 1¾-inch hose.
- For a given flow, friction loss is essentially independent of pressure. Pumping at 200 psi instead of 150 psi does not change how much pressure the hose eats at a fixed flow.
Beyond the principles, several factors change the real-world number: the hose liner material and smoothness, the condition and age of the hose, the number and type of couplings, kinks and sharp bends, and whether the hose is lying flat or wrapped around obstacles. The coefficient is meant to absorb the average of these effects for a given hose size.
The friction loss formula in both unit systems
Imperial, as above:
Metric, in the form IFSTA and most Canadian training material use:
The formulas have the same shape. Only the coefficients and the units change. A metric coefficient is roughly 1.58 times its imperial counterpart, which is what you get when you convert psi to kPa, gallons to litres, and feet to metres and multiply the conversion factors through.
Friction loss coefficient chart
These are the coefficients the Fire Pump Simulator engine uses. The imperial values are the standard textbook coefficients. The metric column is converted directly from them, so it can differ by a few percent from the rounded metric tables in some texts.
| Hose diameter | Imperial C | Metric C |
|---|---|---|
| 1½ inch (38 mm) | 24 | 38 |
| 1¾ inch (45 mm) | 15.5 | 24.5 |
| 2½ inch (65 mm) | 2 | 3.16 |
| 3 inch (77 mm) with 3-inch couplings | 0.677 | 1.07 |
| 4 inch (100 mm) | 0.2 | 0.316 |
| 5 inch (125 mm) | 0.08 | 0.126 |
Two notes on the chart. Three-inch hose with 2½-inch couplings is usually listed at 0.8 rather than 0.677, because the smaller couplings add turbulence at every connection. And published tables vary slightly by source and edition, so if your department's standard operating guidelines list a different number, use that one on the fireground and in your department's own training.
Hard suction hose used for drafting has a much higher coefficient than lay-flat hose of the same diameter because of its rigid, corrugated construction. It is a different problem and is covered in the drafting guide.
Friction loss per 100 feet at common flows
Most operators do not calculate from scratch at the panel. They memorize friction loss per 100 ft for their department's standard lines and multiply by the number of sections. This table gives the figures the formula produces at the flows crews actually use.
| Line | Flow | FL per 100 ft (30 m) |
|---|---|---|
| 1¾ inch (45 mm) | 150 gpm (570 L/min) | 35 psi (240 kPa) |
| 1¾ inch (45 mm) | 185 gpm (700 L/min) | 53 psi (365 kPa) |
| 2½ inch (65 mm) | 250 gpm (950 L/min) | 12.5 psi (86 kPa) |
| 2½ inch (65 mm) | 300 gpm (1,135 L/min) | 18 psi (124 kPa) |
| 3 inch (77 mm) | 500 gpm (1,900 L/min) | 17 psi (117 kPa) |
| 4 inch (100 mm) | 1,000 gpm (3,800 L/min) | 20 psi (138 kPa) |
| 5 inch (125 mm) | 1,000 gpm (3,800 L/min) | 8 psi (55 kPa) |
Look at the first two rows. Going from 150 to 185 gpm on 1¾-inch hose is a 23 percent increase in flow and a 50 percent increase in friction loss. Then look at the last two rows. At the same 1,000 gpm, 5-inch hose loses less than half of what 4-inch hose loses. The squared flow and the fifth-power diameter relationship are both visible in a single table.
Worked example 1: a long 1¾-inch stretch
A 1¾-inch (45 mm) line, 250 ft (75 m) long, flowing 185 gpm (700 L/min).
C = 15.5, Q = 1.85, L = 2.5. FL = 15.5 × 1.85² × 2.5 = 15.5 × 3.42 × 2.5 = 132.6 psi. Call it 133 psi.
Metric: C = 24.5, Q = 7, L = 0.75. FL = 24.5 × 49 × 0.75 = 900 kPa. The imperial answer converts to about 914 kPa, so the two agree within rounding of the flow.
With a 100 psi fog nozzle, this line needs a pump discharge pressure of about 233 psi (1,600 kPa). That is a pump pressure most departments never want to run on a handline, and well into the range where the pump is working hard. The practical lesson is that 1¾-inch hose is a 150 to 200 ft attack line, not a long stretch line. For 250 ft and beyond at high flow, step up to 2½-inch hose or accept a lower flow. The pump discharge pressure guide covers how this friction loss figure feeds into the final pump setting.
Worked example 2: a large-diameter supply line
An engine is supplied from a hydrant through 800 ft (240 m) of large diameter hose, flowing 1,000 gpm (3,800 L/min).
With 5-inch (125 mm) hose: C = 0.08, Q = 10, L = 8. FL = 0.08 × 100 × 8 = 64 psi.
With 4-inch (100 mm) hose: C = 0.2, Q = 10, L = 8. FL = 0.2 × 100 × 8 = 160 psi.
Metric, 125 mm: C = 0.126, Q = 38, L = 2.4. FL = 0.126 × 1,444 × 2.4 = 437 kPa, which matches the 64 psi answer (441 kPa).
The 4-inch line would need 160 psi at the hydrant end to deliver 1,000 gpm to the engine, which no hydrant provides. In practice the 4-inch line simply would not move 1,000 gpm over that distance without a relay pumper in the middle. The 5-inch line will, from a strong hydrant, with pressure to spare. This is the entire argument for 5-inch supply hose and for relay pumping on long lays.
Worked example 3: parallel lines to a master stream
A portable monitor needs 500 gpm (1,900 L/min) and sits 400 ft (120 m) from the engine. Compare one 2½-inch line with two 2½-inch lines siamesed into the monitor.
One line carrying 500 gpm: C = 2, Q = 5, L = 4. FL = 2 × 25 × 4 = 200 psi. Impractical.
Two equal lines each carrying 250 gpm: C = 2, Q = 2.5, L = 4. FL = 2 × 6.25 × 4 = 50 psi in each line. Because the lines are identical and the flow splits evenly, the friction loss for the pair is 50 psi, not 100.
Splitting the flow in half cut the friction loss to a quarter. That is the squared term working in your favour. When lines of equal size and length run in parallel, divide the total flow by the number of lines and calculate friction loss for one of them. Add the appliance loss for the siamese and the master stream device on top when you set pump discharge pressure.
Why your hose may not match the chart
Coefficients are averages, and hose has changed. Lightweight double-jacket hose with smooth polyurethane or rubber liners often tests well below the published coefficients. Old hose, hose with liner damage, and hose with several couplings in a short length can test above them. Two departments running the same nominal 1¾-inch line can see friction loss figures that differ by a noticeable margin at the same flow.
The only way to know your own coefficients is to flow test your own hose: lay out a known length, put inline gauges at each end, flow a measured amount of water, and solve the formula for C. Many departments do this once per hose type and build their pump charts from the results. Companies that have done the test often find they can run slightly lower pump pressures than the textbook numbers suggest, which is easier on the pump and on the crew holding the line.
Departments on the Fire Pump Simulator can enter their own coefficients by hose size, so operators train on the numbers from their own flow tests rather than the chart defaults. Individual users can do the same in their settings. Courses always use the standard coefficients above, so the answers match the textbook. Sandbox sessions and JPR drills use your overrides.
Practice this
- Pull up the pump discharge pressure calculator and recreate the three worked examples. Change one variable at a time and watch how the friction loss responds. Doubling the length is boring. Doubling the flow is not.
- In the simulator, charge the stock 1¾-inch attack line and watch the gap between the pump discharge gauge and the pressure at the tip (turn on the inline tip readout in the simulator settings). That gap is friction loss, live. Then charge the stock 2½-inch line and compare how much the hose takes on top of its nozzle pressure.
- Memorize the per-100-ft figures for your department's standard lines. Being able to say "35 a section at 150" without a calculator is what separates a pump operator from someone who can pass a pump operator test.
- If you are studying for certification, friction loss questions are a fixed feature of the written exam. The NFPA 1002 study guide walks through how they are framed, and the practice test has a bank of them.
Friction loss is the term in the pump discharge pressure formula that does the most work and causes the most mistakes. Learn the coefficients for the hose you carry, respect the squared flow term, and the rest of fireground hydraulics gets a lot easier.