Pipe friction loss calculator (Hazen-Williams)

Hazen-Williams: the core of fire sprinkler hydraulic calculations

The step repeated most often in a sprinkler hydraulic calculation is finding the friction loss in each length of pipe. From the most remote sprinkler back to the pump or the town main, every section turns flow, diameter and length into a pressure drop; add the elevation changes and you have the pressure the water supply must deliver. Both NFPA 13 and EN 12845 calculate this loss with the Hazen-Williams formula. It is empirical: the loss rises with flow to the power 1.85, falls with internal diameter to the power 4.87 and depends on a C factor that represents pipe roughness.

NFPA 13 gives two forms

NFPA 13 (2025) 28.2.2.1.1 states the formula in US units and 28.2.2.1.2 gives the SI equivalent:

With NFPA 13 selected, the calculator uses the first form (with the inch column of the diameter tables) when the unit switch is on US, and the second form (with the mm column) when it is on SI. The difference between them is a few parts per thousand, caused by rounding of the constants and of the tabulated bores; the formula panel shows the other form’s result as a cross-check.

EN 12845 Equation (3)

EN 12845:2015+A2:2026 clause 13.2.1 writes the loss directly as a total in bar: p = 6.05·10⁵ · L · Q^1.85 / (C^1.85 · d^4.87), where L is the equivalent length of pipe and fittings in metres and d is the mean internal diameter in millimetres. The standard says the calculated loss must be no less than this formula gives and that velocity pressure may be ignored. Table 24 sets the accuracy: 1 mbar/m for pressure loss and 0.1 m/s for velocity.

Choosing the C factor

A higher C means less loss. The two standards use different tables and the calculator opens the one for the standard you pick:

A footnote to the NFPA 13 table lets the authority having jurisdiction allow other C values, so the calculator flags that option separately. EN 12845 requires the values in Table 22, and the table NOTE says the list is not exhaustive. For a pipe that is not listed, the calculator takes C as a user input and reminds you to document where the value comes from (maker, listing).

Internal diameter: the real bore, not the nominal size

The d in the formula is the actual internal diameter, not the nominal size. Because loss varies with the 4.87th power of diameter, small differences grow: a 4 in Schedule 40 pipe has a 102.3 mm bore and Schedule 10 has 108.2 mm (NFPA 13 Table A.16.3.2), so at the same flow Schedule 10 loses about 24% less. The calculator takes steel bores verbatim from NFPA 13 Table A.16.3.2 (Schedules 5, 10, 30 and 40) and copper tube from Table A.16.3.6 (Types K, L and M). Where the table gives only inches for the large sizes, the mm value is derived as in × 25.4 and the page says so.

EN 12845 has no bore table. For EN 10255 or ISO 65 series pipe choose “I will enter the internal diameter” and use the manufacturer’s actual bore; ASTM table sizes are not a substitute for EN pipe.

Velocity check

EN 12845 clause 13.2.3 limits water velocity to 6 m/s through any valve, flow monitoring device or strainer and to 10 m/s anywhere else. These limits apply to the stabilised flow of both the hydraulically most unfavourable and the most favourable area. In a pumped system the most favourable area draws a larger flow (Q_max) off the pump curve, so a check at the design area flow can look green while the same pipe exceeds the limit at Q_max. EN mode therefore asks for the pipe's most favourable area flow as a separate input and checks the velocity at both flows. The calculator colours its warning green, amber or red against those two thresholds. NFPA 13 clause 28.2.1.4 sets no velocity limit unless another NFPA standard requires one; its annex note reminds designers that the formula was derived empirically and may lose validity at very high velocities.

Worked example

NFPA 13, 4 in (DN100) Schedule 40 black steel wet pipe (C = 120, d = 102.3 mm), 1500 L/min, 30 m of pipe:

The US form with 396.3 gpm and 4.026 in gives 0.0467 psi/ft, or 4.59 psi (≈ 0.317 bar) over 98.4 ft. The comparison table shows how much size matters: at the same flow DN80 loses 39.7 mbar/m at 5.25 m/s and DN65 loses 114.4 mbar/m at 8.10 m/s. DN65 stays inside EN 12845’s 10 m/s limit in plain pipe but breaks the 6 m/s limit through a valve.

The calculator has been checked against the hydraulic calculation example in NFPA 13 Annex A (Figure A.28.4.1.2(c)): 0.124 psi/ft for 19.5 gpm in 1 in pipe, 0.236 psi/ft for 85.2 gpm in 1½ in pipe and 0.061 psi/ft for 259.6 gpm in 3 in Type M copper all match the published values.

Common mistakes

• Using the nominal size as the bore. Entering 100 mm for DN100 overstates the loss by about 12% for Schedule 40 and by about 47% for Schedule 10.
• A wet-pipe C value in a dry system. NFPA 13 uses C = 100 for dry and preaction steel pipe; using 120 understates the loss by about 29%.
• Forgetting fittings. The equivalent length of elbows, tees and valves must be added to the pipe length — use the equivalent pipe length calculator.
• Mixing units. The 4.52 constant only works with gpm, inches and psi/ft; 6.05·10⁵ only with L/min, mm and bar.
• Antifreeze systems. For antifreeze systems larger than 40 gal (150 L) NFPA 13 also requires a Darcy–Weisbach calculation (28.2.4.8.2); this tool does not do that.

Frequently Asked Questions

Which diameter goes into the Hazen-Williams formula?

The actual internal diameter, not the nominal size. NFPA 13 lists steel and copper bores in its annex tables (Tables A.16.3.2 and A.16.3.6). EN 12845 asks for the mean internal diameter but gives no table, so use the manufacturer’s bore for EN pipe.

What C factor applies to dry pipe systems?

NFPA 13 Table 28.2.4.8.1 gives C = 100 for black or galvanised steel in dry and preaction systems, or 120 in new systems using nitrogen, vacuum or a vapour corrosion inhibitor. EN 12845 Table 22 makes no wet/dry distinction and gives 120 for steel.

Why do NFPA 13’s US and SI formulas give slightly different answers?

The 4.52 and 6.05·10⁵ constants are rounded conversions, and the tabulated bores are rounded separately in the inch and mm columns. The difference is usually a few parts per thousand, and the calculator shows the other form’s result too.

Is there a limit on water velocity in the pipe?

EN 12845 clause 13.2.3 limits velocity to 6 m/s through valves, flow monitoring devices and strainers and 10 m/s elsewhere, at the stabilised flow of both the most unfavourable and the most favourable area. NFPA 13 sets no velocity limit for hydraulic calculations unless another NFPA standard requires one.

How are fitting and valve losses added?

Each fitting and valve is converted into an equivalent length of pipe from the tables and added to the pipe length. Use the equivalent pipe length calculator for the total and enter it in this tool’s equivalent length field.

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