EN 12845 Pipe Friction Loss: The Hazen-Williams Formula (Clause 13.2)

In TS EN 12845+A2:2026 the calculation of the pressure loss in sprinkler pipework is regulated in Clause 13.2 (TS p.85-88 / EN p.82-85). This article gives the formula, the definitions of the symbols as they appear in the standard, the C values of Table 22, the equivalent lengths of Table 23, the velocity limits and the calculation accuracy with their sources; at the end there is a numerical example worked using only the formula and the table values of the standard.

The formula

Clause 13.2.1 Pipe friction loss (TS p.85 / EN p.82): "Calculations of pipe friction loss shall be not less than those derived from the Hazen-Williams formula":

6.05 × 10^5 × L × Q^1.85 p = ------------------------------ C^1.85 × d^4.87

The definitions of the symbols as given in the standard (TS p.85-86 / EN p.82-83):

Two points deserve particular attention. First, d is not the nominal diameter but the mean internal diameter. Second, L is not the straight pipe length but the equivalent length, which includes the fittings.

The clause also adds that the pressure loss due to velocity may be neglected (TS p.86 / EN p.83).

Table 22: C values

Clause 13.2.1 is mandatory: "The values of C specified in Table 22 shall be used." (TS p.86 / EN p.83)

The only note below the table is: "The list is not exhaustive." This note says that a pipe material not in the table may exist; it does not permit a different C to be used for a material that is in the table on the basis of a manufacturer's declaration.

Static pressure difference

Clause 13.2.2 (TS p.86 / EN p.83): the static pressure difference between two connection points in a system shall be calculated from the following formula:

p = 0.098 h

where p is the static pressure difference (bar) and h the vertical distance between the points (m).

Velocity limits

Clause 13.2.3 Velocity (TS p.86 / EN p.83): under steady flow conditions for the hydraulically most favourable and most unfavourable areas of operation, the water velocity shall not exceed:

• 6 m/s through any valve, flow monitoring device or strainer;
• 10 m/s at any other point in the system.

Losses in fittings and valves

Clause 13.2.4 (TS p.86 / EN p.83): the friction loss in valves and in fittings where the direction of water flow changes by 45° or more shall be calculated using the formula specified in 13.2.1. The appropriate equivalent length shall be one of the following:

• a) as specified by the equipment supplier;
• b) where a) is not available, the value taken from Table 23.

An additional rule (TS p.87 / EN p.84): where an elbow, tee or cross has both a change in direction of flow and a change in diameter at the same point, the equivalent pipe length and pressure loss shall be determined using the smaller diameter.

Table 23 (selected rows)

Table 23 gives the equivalent length (m) of straight steel pipe for C = 120 (TS p.87 / EN p.84). The DN20 to DN100 range is shown below; the full table continues up to DN250.

Footnote a of the table gives the conversion factors for the equivalent lengths for pipes with other C values:

These factors are consistent with the C^1.85 term of the Hazen-Williams formula: for example the ratio 140/120 raised to the power 1.85 is 1.33. In other words, in a smoother pipe the same fitting is written as a longer equivalent length, because the same physical loss has to be expressed in terms of a pipe that loses less.

Calculation accuracy

Clause 13.2.5.1 (TS p.88 / EN p.85): calculations shall be carried out in the units and to the accuracy given in Table 24.

Clause 13.2.5.2 (TS p.88 / EN p.85): calculations shall be balanced as follows:

• the algebraic sum of the pressure losses around a loop shall equal (0 ± 1) mbar;
• where water flows combine at a junction, the calculation shall be balanced to ± 1 mbar;
• the algebraic sum of the water flows at a junction shall equal (0 ± 0.1) l/min.

Flow from a sprinkler and minimum pressure

The start and end points of the hydraulic calculation are in two clauses.

Clause 14.3 Flow from sprinklers (TS p.107-108 / EN p.104-105): the flow of water from a sprinkler shall be calculated from the formula Q = K√P, where Q is in litres per minute, K is the constant given in Table 37a and P is the pressure in bar.

Clause 13.4.4 Minimum sprinkler discharge pressure (TS p.105 / EN p.102): with all sprinklers in the area of operation discharging, the pressure at the hydraulically most unfavourable sprinkler shall be not less than that required to give the density specified in 13.4.1 or, whichever is the higher, the following:

The value of 0.70 bar is for LH only; the threshold applying in a high bay logistics warehouse is not that value but 0.50 bar for HHS (excluding in-rack) or 1.00 / 2.00 bar depending on the in-rack sprinkler type.

Clause 13.4.5 (TS p.106 / EN p.103) gives the minimum pipe diameters in Table 36: LH 20 mm; OH and HH range and vertical pipes feeding a single sprinkler with a K-factor not exceeding 80, 20 mm; all others 25 mm. The same clause states that pipe diameters downstream of the control valve set may only reduce in the direction of water flow (except in grid and loop arrangements).

Numerical example

The following calculation uses only the formula of Clause 13.2.1 and the values of Table 22 and Table 23. Because the internal diameter of the pipe is not given in the standard, d = 50 mm is taken here as an example input; in a real project the mean internal diameter value of the pipe manufacturer is used.

Inputs: galvanized steel pipe (Table 22: C = 120), d = 50 mm, Q = 200 l/min, straight pipe length 20.00 m.

Step 1, the terms of the formula:

• Q^1.85 = 200^1.85 = 18 068
• C^1.85 = 120^1.85 = 7 022
• d^4.87 = 50^4.87 = 1.879 × 10⁸
• Numerator: 6.05 × 10⁵ × 18 068 = 1.093 × 10¹⁰
• Denominator: 7 022 × 1.879 × 10⁸ = 1.320 × 10¹²

Step 2, loss per metre: 1.093 × 10¹⁰ / 1.320 × 10¹² = 8.28 × 10⁻³ bar/m, that is 8 mbar/m to the accuracy of Table 24.

Step 3, straight pipe: 20.00 m × 8.28 × 10⁻³ = 0.166 bar (166 mbar).

Step 4, fittings (Table 23, DN50, C = 120): 2 no. 90° screwed elbows 2 × 1.5 = 3.00 m; 1 no. standard screwed tee (flow turned through branch) 2.90 m; 1 no. gate valve 0.38 m. Total equivalent length 6.28 m.

Step 5, total equivalent length and loss: L = 20.00 + 6.28 = 26.28 m, so p = 26.28 × 8.28 × 10⁻³ = 0.218 bar (218 mbar). The fittings make up roughly a quarter of the total loss.

Step 6, velocity check (13.2.3): 200 l/min = 0.00333 m³/s; cross sectional area π × 0.050² / 4 = 1.963 × 10⁻³ m²; velocity = 1.7 m/s. This is below both the 6 m/s and the 10 m/s limits.

Step 7, the effect of the C value: had the same line been cast iron (Table 22: C = 100), the loss would increase by a factor of (120/100)^1.85 = 1.40; over 20 m of straight pipe it would be 0.232 bar instead of 0.166 bar. Had it been stainless steel or copper (C = 140), the loss would fall to (120/140)^1.85 = 0.752 times, that is 0.125 bar.

Step 8, the effect of an internal diameter error: because of the d^4.87 term, a small error in the internal diameter is magnified. If a pipe with a mean internal diameter of 54 mm is entered as 50 mm, the ratio is (54/50)^4.87 = 1.45; the calculated friction loss is therefore about 1.45 times the true value.

Step 9, static difference (13.2.2): if the line rises by 6.00 m, the static pressure difference is 0.098 × 6.00 = 0.588 bar. This is calculated separately from the friction loss and added to it.

Field note

The fact that L in the formula is the equivalent length is the fastest check point when reviewing a hydraulic calculation: if only the straight pipe length is entered between each node, the fitting losses have not entered the calculation at all. The mushroom type alarm/check valve row of Table 23 is notable in this respect; at DN50 its equivalent length of 12.0 m is five times that of the swing type (2.4 m). (This paragraph is engineering commentary.)

Frequently Asked Questions

What is the Hazen-Williams formula in EN 12845?

TS EN 12845+A2:2026 Clause 13.2.1 (TS p.85 / EN p.82): calculations of pipe friction loss shall be not less than those derived from the Hazen-Williams formula: p = 6.05 x 10^5 x L x Q^1.85 / (C^1.85 x d^4.87). Here p is the pressure loss in the pipe (bar), Q the flow through the pipe (litres per minute), d the mean internal diameter of the pipe (mm), C a constant for the type and condition of the pipe (see Table 22) and L the equivalent length of pipe and fittings (m).

Where do the C values come from, can manufacturer data be used?

Clause 13.2.1 (TS p.86 / EN p.83) is explicit: 'The values of C specified in Table 22 shall be used.' Table 22: cast iron 100, ductile iron 110, mild steel 120, galvanized steel 120, spun cement 130, cement lined cast iron 130, stainless steel 140, copper 140, reinforced glass fibre 140. The only note below the table is that the list is not exhaustive; there is no provision allowing a different C on the basis of a manufacturer's declaration.

What is the minimum pressure at the most remote sprinkler?

Clause 13.4.4 (TS p.105 / EN p.102): with all sprinklers in the area of operation discharging, the pressure at the hydraulically most unfavourable sprinkler shall be not less than that required to give the density specified in 13.4.1 or, whichever is the higher, the following values: 0.70 bar for LH; 0.35 bar for OH; 0.50 bar for HHP and HHS excluding in-rack sprinklers; 1.00 bar for K115 in-rack sprinklers; 2.00 bar for K80 in-rack sprinklers.

What are the water velocity limits?

Clause 13.2.3 (TS p.86 / EN p.83): under steady flow conditions for the hydraulically most favourable and most unfavourable areas of operation, the water velocity shall not exceed 6 m/s through any valve, flow monitoring device or strainer, and 10 m/s at any other point in the system.

To what accuracy shall the hydraulic calculation be balanced?

Clause 13.2.5.2 (TS p.88 / EN p.85): the algebraic sum of the pressure losses around a loop shall equal (0 ± 1) mbar; where water flows combine at a junction the calculation shall be balanced to ± 1 mbar; the algebraic sum of the water flows at a junction shall equal (0 ± 0.1) l/min. Table 24 gives the unit accuracies: length, height and equivalent length 0.01 m; flow 1.0 l/min; pressure loss 1.0 mbar/m; pressure 1.0 mbar; velocity 0.1 m/s; area 0.01 m2; water application density 0.1 mm/min.

References

• TS EN 12845+A2:2026 Clause 13.2.1 Pipe friction loss and the symbols of the formula (TS p.85 / EN p.82)
• TS EN 12845+A2:2026 Table 22 C values, Clause 13.2.2 Static pressure difference, 13.2.3 Velocity, 13.2.4 Fittings (TS p.86 / EN p.83)
• TS EN 12845+A2:2026 Table 23 Equivalent length of fittings and valves and the footnote conversion factors (TS p.87 / EN p.84)
• TS EN 12845+A2:2026 Clause 13.2.5.1, Table 24, Clause 13.2.5.2 (TS p.88 / EN p.85)
• TS EN 12845+A2:2026 Clause 13.4.4 Minimum sprinkler discharge pressure (TS p.105 / EN p.102)
• TS EN 12845+A2:2026 Clause 13.4.5, Table 36 Minimum pipe diameters (TS p.106 / EN p.103)
• TS EN 12845+A2:2026 Clause 14.3 Flow from sprinklers (TS p.107-108 / EN p.104-105)

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