Sprinkler Flow with Q = K√P: EN 12845 K-Factor and Clause 13.4.4

Source: TS EN 12845+A2:2026 (EN 12845:2015+A2:2026), Clauses 3.39, 13.4.4, 14.2 and 14.3; TS EN 12845-2:2025.

The whole of sprinkler hydraulics rests on a single formula, and when the unit convention of that formula is misremembered the entire calculation shifts. In EN 12845 the pressure is in bar, not in kPa. This article deals one by one with the formula, the K-factors the standard recognises, the minimum pressures per class and how these bind each other.

The formula and its units

Clause 14.3 (TSE p.107-108 / EN p.104-105): the water flow from a sprinkler is calculated from the following formula.

Q = K √P

• Q: flow, litres per minute,
• K: the constant given in Table 37a,
• P: pressure, bar.

Clause 3.39 (TSE p.21 / EN p.18) gives the same thing as a definition: the discharge coefficient "K" is the discharge coefficient in the formula Q = K√p, where Q is the flow in litres per minute and p is the pressure in bar.

This should not be confused with variants that take the pressure in kPa. As long as one stays within EN 12845, P is entered directly in bar and there is no additional factor of 10.

Clause 4.4.3.3 e) 2) (TSE p.30 / EN p.27) requires, for each operating sprinkler in a fully calculated system, that the nominal K-factor in accordance with EN 12259-1 be documented; that is, the K used in the calculation is the documented nominal value of the product.

The K-factors recognised by EN 12845: Table 37a

Table 37a (Clause 14.2.1, TSE p.107 / EN p.104):

Three conclusions follow directly from the table:

1. K57 is for LH only. It does not appear in the OH row.
2. There is no K57 and no K160 in OH; only K80 and K115.
3. K80 cannot be used at HH densities above 10 mm/min; K115 or K160 is required. K115 is not "mandatory", since K160 is equally valid.

Clause 7.2.2.3 Option 1 (TSE p.39-40 / EN p.36-37) sets a K limit in one more place: in HHS, where the clearance between the top of the stack and the ceiling sprinkler deflector exceeds 4 m and the density increase option is used, sprinklers with a K-factor of at least K115 shall be used.

Clause 14.2.2 (TSE p.107 / EN p.104): ceiling, flush, recessed and concealed sprinklers shall not be installed in OH4, HHP or HHS areas. Clause 14.2.3: sidewall sprinklers may be used in HH installations only for the protection of corridors, cable ducts and columns, and shall not be used at all in OH storage areas or above suspended ceilings. Clause 14.2.4: flat spray sprinklers shall be used only in concealed spaces, above suspended open ceilings and in racks.

The minimum pressure floors: Clause 13.4.4

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

These values cannot be reduced to a single figure in the form "EN 12845 never operates a sprinkler below 0.5 bar"; the OH floor is 0.35 bar and the LH floor is 0.70 bar.

Flow per K-factor at the floor pressures

The table below is only the result of the formula Q = K√P calculated with the floor values of Clause 13.4.4:

Comparing the density requirement with the floor requirement

The real design decision is which of the two requirements governs. The comparison is made from the density of Table 3 and the maximum area of coverage of Table 19.

LH. Table 3 (TSE p.39 / EN p.36): 2.25 mm/min. Table 19 (TSE p.73 / EN p.70): a maximum of 21.0 m² per sprinkler. The required flow is 2.25 × 21.0 = 47.25 l/min. The pressure required for K57 is (47.25/57)² = 0.687 bar. The 0.70 bar floor of Clause 13.4.4 is slightly above this; in other words, at maximum spacing in LH the floor governs and the sprinkler delivers 47.7 l/min.

OH. Table 3: 5.0 mm/min. Table 19: a maximum of 12.0 m² per sprinkler. The required flow is 5.0 × 12.0 = 60 l/min.

• The pressure required for K80 is (60/80)² = 0.5625 bar. This is above the 0.35 bar floor; the density governs.
• The pressure required for K115 is (60/115)² = 0.272 bar. This is below the 0.35 bar floor; the floor governs and the sprinkler delivers 68.0 l/min, which over 12.0 m² is 5.67 mm/min.

HHP and HHS. Table 19 gives a maximum of 9.0 m² per sprinkler. At a density of 10.0 mm/min the required flow is 10.0 × 9.0 = 90 l/min; the pressure required for K115 is (90/115)² = 0.613 bar and for K160 (90/160)² = 0.316 bar. In the second case the 0.50 bar floor governs.

The role of the K-factor in pre-calculated systems

In pre-calculated HH design the K-factor determines not only the flow but also which pipe table is to be used. Clauses 13.3.5.2 to 13.3.5.4 (TSE p.92-94 / EN p.89-91):

Table 7 (TSE p.43 / EN p.40) lowers the required pressure at the same density as the block changes. For 10.0 mm/min and 9 m² per sprinkler: block (1) 3.90 bar, block (2) 3.00 bar, block (3) 1.60 bar, block (4) with K115 0.95 bar.

There is a K-dependent provision on the pipe side as well. Table 36 (Clause 13.4.5, TSE p.106 / EN p.103): in OH and HH, horizontal and upright pipes feeding a single sprinkler with a K-factor not exceeding 80 may be 20 mm; in all other cases the minimum diameter is 25 mm.

ESFR and CMSA: the k-factors are in EN 12845-2

EN 12845 Annex P (TSE p.167 / EN p.164): for ESFR sprinkler systems, EN 12845-2 shall be applied together with this document. Because of the different hazard classification systems, the conversion Table A.1 of EN 12845-2:2024 Annex A or the flow chart in Figure A.1 is used.

TS EN 12845-2 Table 2 (TSE p.13 / EN p.10) gives the maximum vertical distance of the sprinkler thermal element below the ceiling according to the k-factor, and thereby also shows which k-factors are defined for which concept:

The design tables are consistent with this list. EN 12845-2 Table 7 (TSE p.39 / EN p.36) carries columns for K200, K240, K320, K360, K400 and K480 in ceiling-only ESFR design. The CMSA design tables (Table 15 onwards, TSE p.52 onwards) contain rows for K160, K240, K280, K360 and K480.

Field note: the k-factor lists of these two concepts are entirely separate from the list in Table 37a of EN 12845. In an ESFR project the choice of K-factor is not made through the density, but through the row of the relevant design table of EN 12845-2 covering the commodity category, the ceiling height, the storage height, the number of sprinklers and the minimum operating pressure.

Frequently Asked Questions

What is the sprinkler flow formula in EN 12845?

Clause 14.3 (TSE p.107-108 / EN p.104-105): Q = K sqrt(P). Q is the flow in litres per minute, K is the constant given in Table 37a and P is the pressure in bar. Clause 3.39 (TSE p.21 / EN p.18) likewise defines the discharge coefficient K as the coefficient in the formula Q = K sqrt(p) and states that p is in bar.

Which K-factors does EN 12845 define?

Table 37a (TSE p.107 / EN p.104) defines four nominal K-factors: 57 for LH; 80 or 115 for OH; for HHP and HHS ceiling sprinklers, 80, 115 or 160 at densities of 10 mm/min and below and 115 or 160 above 10 mm/min; and 80 or 115 for HHS in-rack intermediate sprinklers.

What is the minimum inlet pressure at a sprinkler?

Clause 13.4.4 (TSE p.105 / EN p.102) varies by class: LH 0.70 bar, OH 0.35 bar, HHP and HHS (excluding in-rack) 0.50 bar, in-rack K115 1.00 bar and in-rack K80 2.00 bar. Whichever is the higher of these values and the pressure required to achieve the design density applies.

What does a K57 sprinkler deliver at the minimum pressure in LH?

The floor in LH is 0.70 bar. Q = 57 x sqrt(0.70) = 47.7 l/min. Divided by the maximum area of coverage of 21.0 m2 that Table 19 gives for LH, this is 2.27 mm/min and achieves the 2.25 mm/min design density of Table 3.

Are the ESFR and CMSA k-factors in EN 12845?

No, they are in EN 12845-2. TS EN 12845-2 Table 2 (TSE p.13 / EN p.10) contains rows for 200, 240, 320, 360, 400 and 480 for ESFR and 160, 240, 280 and 360 for CMSA. EN 12845 Annex P (TSE p.167 / EN p.164) states that for ESFR systems EN 12845-2 shall be applied together with this document.

References

• TS EN 12845+A2:2026 Clause 3.39 (TSE p.21 / EN p.18)
• TS EN 12845+A2:2026 Clause 4.4.3.3 (TSE p.30 / EN p.27)
• TS EN 12845+A2:2026 Table 3 (TSE p.39 / EN p.36), Clause 7.2.2.3 (TSE p.39-40 / EN p.36-37)
• TS EN 12845+A2:2026 Table 7 (TSE p.43 / EN p.40)
• TS EN 12845+A2:2026 Clause 12.2, Table 19 (TSE p.73 / EN p.70)
• TS EN 12845+A2:2026 Clauses 13.3.5.2, 13.3.5.3, 13.3.5.4 (TSE p.92-94 / EN p.89-91)
• TS EN 12845+A2:2026 Clause 13.4.4 (TSE p.105 / EN p.102), Clause 13.4.5, Table 36 (TSE p.106 / EN p.103)
• TS EN 12845+A2:2026 Table 37a, Clauses 14.2.1, 14.2.2, 14.2.3, 14.2.4, 14.3 (TSE p.107-108 / EN p.104-105)
• TS EN 12845+A2:2026 Annex P (TSE p.167 / EN p.164)
• TS EN 12845-2:2025 Table 2 (TSE p.13 / EN p.10), Table 7 (TSE p.39 / EN p.36), Table 15 (TSE p.52 / EN p.49)

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