EN 12845 Pre-calculated and Fully Calculated Design: Clauses 13.1, 13.3 and 13.4

Source: TS EN 12845+A2:2026 (EN 12845:2015+A2:2026), Clauses 4.4.4.3, 8.5.1, 13.1, 13.2, 13.3, 13.4 and Annex P.

There are two ways of determining pipe sizes in EN 12845, and both are normative. The difference lies in how far the designer relies on tables and from which point on calculation. This article deals with the two branches of Clause 13, the transition point between them, and the hydraulic rules common to both.

Two methods and two exceptions: Clause 13.1

Clause 13.1 (TSE p.85 / EN p.82) says pipe sizes shall be determined by one of the following methods:

• pre-calculated systems, in which some of the sizes are taken from tables and some are calculated (see 13.3);
• fully calculated systems, in which all sizes are determined by hydraulic calculation (see 13.4).

The designer may choose between the two; but full calculation shall always be used in the following cases:

• layouts with HHS intermediate sprinklers,
• gridded or looped layouts.

The note added by A2 ties the earthquake subject to a separate standard: it is recommended that, in areas subject to seismic risk in accordance with EN 12845-3, the requirements given in EN 12845-3 be applied for the sprinkler system.

Clause 7.2.3.4 (TSE p.40 / EN p.37) states the same limit from the storage side: in-rack sprinklers and their associated ceiling sprinklers shall always be fully calculated.

Common ground: the calculation of pressure losses

In both methods the same formulae apply wherever calculation is carried out.

Pipe friction loss: Clause 13.2.1

Pipe friction loss calculations shall not be less than those obtained from the Hazen-Williams formula. Equation (3) (TSE p.85 / EN p.82):

p = 6.05 × 10^5 × L × Q^1.85 / (C^1.85 × d^4.87)

where:

• p: pressure loss in the pipe, bar,
• Q: flow in the pipe, l/min,
• d: mean internal diameter of the pipe, mm,
• C: a constant for the type and condition of the pipe (Table 22),
• L: equivalent length of pipe and fittings, m.

The exponents are 1.85 and 4.87. The last sentence of the clause: pressure loss due to velocity may be neglected.

Table 22 - values of C for various types of pipe (TSE p.86 / EN p.83):

NOTE to the table: the list is not exhaustive. Because the effect of C is exponential, a small change alters the loss noticeably: assuming C = 100 instead of C = 120 raises the loss by a factor of (120/100)^1.85 = 1.40, that is by about 40 %. This is the arithmetic of the formula itself.

Static pressure difference: Clause 13.2.2

The static pressure difference between two connected points is calculated with Equation (4) (TSE p.86 / EN p.83):

p = 0.098 h

where p is in bar and h is the vertical distance between the points in m.

Velocity limits: Clause 13.2.3

The water velocity shall not exceed (TSE p.86 / EN p.83):

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

This limit shall be satisfied for the steady flow condition of the hydraulically most favourable and most unfavourable area of operation. In other words, the most favourable area binds not only the pump selection but the pipe sizing too.

Fittings: Clause 13.2.4 and Table 23

The pressure loss due to friction in valves and in fittings where the direction of water flow changes by 45° or more shall be calculated using the formula in 13.2.1. The equivalent length shall be either a) the value stated by the equipment supplier or, where a) is not available, b) taken from Table 23. Table 23 gives equivalent lengths of straight steel pipe for C = 120; for example, at 50 mm diameter a 90° screwed elbow is 1.5 m, a standard screwed tee or cross (flow turned through the branch) 2.9 m, a gate valve straight way 0.38 m, a butterfly valve 2.2 m, and an alarm or non-return valve of the swinging type 2.4 m. The footnote to the table states that these equivalent lengths may be converted for pipes with other C values.

The same clause contains a rule of application: in an elbow, tee or cross where the direction of flow changes and a change of diameter also occurs at the same point, the equivalent pipe length and the pressure loss shall be determined using the smaller diameter.

Accuracy of calculations: Clause 13.2.5

Table 24 (TSE p.88 / EN p.85) binds the units and accuracies: length, height and equivalent length 0.01 m; flow 1.0 l/min; pressure loss per metre 1.0 mbar/m; pressure 1.0 mbar; velocity 0.1 m/s; area 0.01 m²; water application density 0.1 mm/min.

Clause 13.2.5.2 gives the balancing tolerances:

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

The pre-calculated branch: the concept of the design point

In a pre-calculated system, some of the sizes come from a table and the rest are calculated. The place where the two separate is the design point.

Clause 13.3.2.1 (TSE p.88 / EN p.85): the design point is at the point where a horizontal distribution pipe connects to one of the following: a range pipe; a riser or drop pipe connecting ranges to distribution pipes; a pipe feeding a single sprinkler.

Tables 25 and 26 (TSE p.89 / EN p.86) give, by class, the sprinkler after which the design point comes:

Clause 13.3.1.2 (TSE p.88 / EN p.85): range pipe sizes and the maximum number of sprinklers each size may feed shall be determined in accordance with Table 30; in Light Hazard, Table 27 covers only the pipes feeding the last three or four sprinklers on each range. Clause 13.3.1.3: all pipes upstream of each design point shall be sized by calculation as specified in 13.3.3.2 for LH and 13.3.4.2 for OH.

Clause 13.3.1.4: risers and drop pipes connecting distribution pipes to ranges, and pipes feeding a single sprinkler (other than arm pipes), shall be considered as distribution pipes and sized accordingly.

The fully calculated branch: Clause 13.4

Design density: Clause 13.4.1

The discharge density shall be taken as the total flow in l/min from the four adjacent sprinklers closest to each other, divided by the area in m² covered by those four sprinklers. Where fewer than four sprinklers are in open communication, it shall be taken as the lowest flow from any one sprinkler divided by the area covered by that sprinkler.

The discharge density from each area of operation (or from the whole protected area where that is smaller) shall not be less than the design density specified in Clause 7, with each available water supply or combination of supplies.

The area covered by each sprinkler is defined by centre lines drawn midway between adjacent sprinklers, perpendicular to the line joining the sprinklers, and by the boundary of the protected area or half the distance to the nearest sprinkler, whichever is the greater (Figure 22).

Position of the area of operation: Clause 13.4.2

Most unfavourable position (13.4.2.1): all possible positions shall be considered, taking into account changes in sprinkler spacing, layout, level, range centres, sprinkler orifice size and pipe diameters. In gridded installations the correct position shall be proven by moving the area of operation one sprinkler pitch at a time in each direction along the range pipes, until the area producing the highest pressure demand is found. In looped installations the same procedure is carried out along the distribution pipe.

Most favourable position (13.4.2.2): all possible positions on distribution pipes and between distribution pipes connected by range pipes shall be considered.

Shape of the area: Clause 13.4.3

In the most unfavourable position, the area of operation shall be as nearly rectangular as possible and symmetrical with respect to the sprinkler layout. In terminal and looped arrangements the remote edge of the area is defined by a range (or, in end-centre arrangements, by a pair of ranges). In gridded arrangements:

• where the ranges run parallel to the ridge of a roof with a slope greater than 6 degrees, or along the compartments formed by beams deeper than 1.0 m, the length L of the remote edge parallel to the ranges shall be at least 2 times the square root of the area of operation;
• in all other gridded arrangements, L shall be at least 1.2 times the square root of the area of operation.

In the most favourable position the area shall be as nearly square as possible.

Minimum pressures and minimum diameters

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:

Table 36 (Clause 13.4.5, TSE p.106 / EN p.103): LH 20 mm; in OH and HH, 20 mm for horizontal and upright pipes feeding a single sprinkler with a K-factor not exceeding 80; 25 mm in all other cases. On the installation side of the control valve set, pipe sizes may only reduce in the direction of flow; grid and loop arrangements are excepted from this.

The documentation burden that full calculation brings

Clause 4.4.3.3 (Fully calculated pipework, TSE p.29-30 / EN p.26-27) requires, in a fully calculated system, for each operating sprinkler: the node number, the nominal K-factor in accordance with EN 12259-1, the flow in l/min and the inlet pressure in bar; and for each hydraulically significant pipe: the node numbers, the nominal diameter in mm, the Hazen-Williams constant, the flow, the velocity, the length, the number/type/equivalent length of fittings, the change in static head, the inlet and outlet pressures, the friction loss and the direction of flow. In addition, the positions of the most unfavourable and most favourable areas of operation and the four sprinklers on which the design density is based shall be shown on the drawing.

Clause 4.4.4.3 f) and g) (TSE p.31 / EN p.28) require two further graphs for the town main where the pipework is fully calculated: a pressure/flow characteristic graph showing the pressure available at each flow up to the maximum demand flow, and a demand pressure/flow graph for the most unfavourable (and where necessary the most favourable) area of operation of each installation.

Clause 8.5.1 d) (TSE p.47 / EN p.44) sizes the test equipment accordingly: where a calculated system is used, the capacity of the flow measuring device shall be selected so as to measure the system demand of both the most unfavourable and the most favourable area, and the device shall in addition have a measuring capacity of at least 140 % of the maximum demand flow.

Where ESFR and CMSA fall

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, EN 12845-2:2024 Annex A applies; the conversion is made using Table A.1 or the flow chart in Figure A.1. Annex P also recommends the use of three 50 % pump sets in accordance with EN 17451 for the ESFR water supply.

Frequently Asked Questions

In which cases does EN 12845 make full calculation mandatory?

Clause 13.1 (TSE p.85 / EN p.82): the designer may choose between the two methods, but full calculation shall always be used in two cases: layouts with HHS intermediate sprinklers and gridded or looped layouts.

What is the pipe friction equation in EN 12845?

Clause 13.2.1, Equation (3) (TSE p.85 / EN p.82): 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 bar, Q the flow in l/min, d the mean internal diameter in mm, C a constant for the type and condition of the pipe, and L the equivalent length of pipe and fittings in m.

How is the design density defined in full calculation?

Clause 13.4.1 (TSE p.101 / EN p.98): the discharge density shall be taken as the total flow in l/min from the four adjacent sprinklers closest to each other divided by the area in m2 covered by those four sprinklers. Where fewer than four sprinklers are in open communication, it is the lowest flow from any one sprinkler divided by the area covered by that sprinkler.

What are the velocity limits?

Clause 13.2.3 (TSE p.86 / EN p.83): the water velocity shall not exceed 6 m/s through any valve, flow monitoring device or strainer, or 10 m/s at any other point in the system. This applies to the steady flow condition of both the hydraulically most favourable and the most unfavourable area of operation.

What is the balancing tolerance of the calculation?

Clause 13.2.5.2 (TSE p.88 / EN p.85): the algebraic sum of the pressure losses around a loop shall be (0 plus or minus 1) mbar, the calculation shall balance to within plus or minus 1 mbar at a node where water flows combine, and the algebraic sum of the water flows at that node shall be (0 plus or minus 0.1) l/min.

References

• TS EN 12845+A2:2026 Clause 4.4.3.3 (TSE p.29-30 / EN p.26-27), Clause 4.4.4.3 (TSE p.31 / EN p.28)
• TS EN 12845+A2:2026 Clause 7.2.3.4 (TSE p.40 / EN p.37)
• TS EN 12845+A2:2026 Clause 8.5.1 (TSE p.47 / EN p.44)
• TS EN 12845+A2:2026 Clauses 13.1, 13.2.1, Equation (3) (TSE p.85 / EN p.82)
• TS EN 12845+A2:2026 Table 22, Clause 13.2.2, Equation (4), Clauses 13.2.3, 13.2.4 (TSE p.86 / EN p.83)
• TS EN 12845+A2:2026 Table 23 (TSE p.87 / EN p.84)
• TS EN 12845+A2:2026 Table 24, Clauses 13.2.5.2, 13.3.1.2, 13.3.1.3, 13.3.1.4, 13.3.2.1 (TSE p.88 / EN p.85)
• TS EN 12845+A2:2026 Table 25, Table 26 (TSE p.89 / EN p.86)
• TS EN 12845+A2:2026 Clause 13.4.1 (TSE p.101 / EN p.98), Clauses 13.4.2, 13.4.3 (TSE p.102-103 / EN p.99-100)
• 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 Annex P (TSE p.167 / EN p.164)

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