FM Global DS 3-0: The Hydraulically Most Demanding Sprinkler Area

A sprinkler hydraulic calculation starts from the hardest point in the system. FM Global DS 3-0 (Hydraulics of Fire Protection Systems, March 2010) calls it the most hydraulically remote sprinkler and carries the calculation from there back to the base of the riser (BOR) (Sections 2.1.2.1–2.1.2.3, pp. 17–34). The design itself (density and demand area, or number of sprinklers and pressure) comes from the occupancy-specific data sheet: DS 3-26 for nonstorage occupancies and DS 8-9 for storage.

Flow and Pressure at the Most Remote Sprinkler (2.1.2.2.1)

• Density/demand area format: q = D × S × L (Equation 3), with D the density, S the spacing along the branch line and L the spacing between branch lines; round L/min to the nearest multiple of 5. Pressure p = (q/K)² (Equation 4), rounded to 0.01 bar.
• Number of sprinklers/pressure format: the minimum pressure at the most remote sprinkler is given, and the flow follows from q = K × √p (Equation 7).
• For DS 3-26 density/area designs, a minimum of 0.5 bar applies at the most remote sprinkler in all cases (DS 3-26 2.3.1.11).

Size, Shape and Position of the Design Area (2.1.2.2.2–2.1.2.2.5)

• Total sprinklers in the calculation: TNOS = DA / (S × L) (Equation 10).
• Sprinklers per branch line: NORSBL = SF × √DA / S (Equation 11). Unless the occupancy data sheet says otherwise, the shape factor SF is 1.2 under ceilings sloped 5° or less and 1.4 above 5°; the result is rounded normally.
• Tree systems: the most remote sprinkler is usually obvious; with mixed pipe sizes, convert the piping to one diameter and C value with the equivalent length method (Equation 13).
• Gridded systems: the location is not obvious; for a regular grid the skew formula (Equation 14) gives an approximation, otherwise computer trial and error is needed.
• The design area is laid out from the most remote sprinkler; where TNOS/NORSBL is not a whole number, the extra sprinklers are grouped on one branch line as close as possible to the cross main (tree) or near main (grid).

Calculating Back to the Base of the Riser (2.1.2.3)

1. From the most remote sprinkler, calculate friction to the next sprinkler with the Hazen-Williams formula (Equation 15), add it to the pressure and find that sprinkler’s flow from q = K × √p.
2. Continue to the last sprinkler in the design area and on to the cross main (or riser nipple), where the branch line K value is K_LINE = Q / √P (Equation 18).
3. Where two flows meet at different pressures, balance the lower one up: Q_ADJ = Q_L × [(P_H − P_E) / (P_L − P_E)]^0.5 (Equation 19; exponent 0.54 for large flows such as balancing two systems).
4. Along the cross main, add each branch line flow Q = K_LINE × √P (Equation 20) and continue to the BOR, adding friction and elevation (0.098 bar/m, Equation 2).
5. FM’s calculation method does not include velocity pressure (2.1.2.3.1). Fittings are included as equivalent lengths where they change the direction or velocity of flow (p. 27).

Worked Example: HC-2 Manufacturing Area

A machine shop (HC-2), ceiling under 9 m, wet system, flat ceiling. DS 3-26 Table 2.3.1.10 design: 8 mm/min over 230 m². K115 (K8.0) standard sprinklers at S = 3.5 m and L = 3.4 m (11.9 m², within the HC-2 limits of 12.1 m² and 4.6 m in DS 2-0 Table 2.5.2.3.1.1(b)).

• Most remote sprinkler flow: q = 8 × 3.5 × 3.4 = 95.2, rounded to 95 L/min
• Most remote sprinkler pressure: p = (95/115)² = 0.68 bar, above the DS 3-26 minimum of 0.5 bar
• Sprinklers in the design area: 230 / 11.9 = 19.3, so 20 sprinklers
• Sprinklers per branch line: 1.2 × √230 / 3.5 = 5.2, so 5; the design area is 4 branch lines of 5 sprinklers
• Minimum sprinkler flow: 20 × 95 = 1,900 L/min; the actual BOR flow is higher because pressure rises along the lines
• Hose stream allowance: 950 L/min (DS 3-26 2.3.1.12), deducted from the water supply curve (DS 3-0 2.1.2.4.4)
• Duration: 60 minutes (DS 3-26 2.3.1.13); minimum water volume (1,900 + 950) × 60 = 171 m³, more with the actual sprinkler flow

Comparing Against the Water Supply (2.1.1.6 and 2.1.2.4)

• A public supply test is plotted on N^1.85 paper as static pressure plus residual pressure at the measured flow; a fire pump needs at least three points: churn, 100% and 150% of rated flow (2.1.1.6.1).
• The test result is moved from the Effective Point to the BOR by allowing for friction and elevation (2.1.1.6.2).
• The sprinkler demand curve runs through the BOR demand point and the elevation pressure of the highest sprinkler: P₂ = (Q₂/Q₁)^1.85 × (P₁ − P_E) + P_E (Equation 25).
• If the supply after deductions meets the demand for the full duration, the system is rated Adequate; otherwise Inadequate (2.1.2.4.5). DS 3-0 does not define a separate safety margin.
• Fire pumps are selected to deliver at least 65% of rated pressure at 150% of rated flow (DS 3-7 Section 2.4, p. 13).
• For an existing supply, use flow test data no more than 12 months old (DS 2-0 2.6.4.6).

Quick Checklist

• Design format (density/area or number of sprinklers/pressure) taken from the occupancy data sheet
• Most remote sprinkler flow and pressure from Equations 3–4 or 7
• Sprinklers per branch line from the 1.2 (≤5°) or 1.4 (>5°) shape factor
• Most remote point on gridded systems found by computer analysis
• Flows balanced at junctions; no velocity pressure used
• Hose allowance deducted from the supply curve and duration checked
• Flow test data less than 12 months old

Frequently Asked Questions

What makes an area hydraulically most demanding?

Distance from the supply, which drives friction loss, elevation, which drives static head, and how well the branch is fed. Under FM DS 3-0 2.1.2.2.4 the most remote sprinkler is usually obvious on tree systems, but with mixed pipe sizes it is found with the equivalent length method (Equation 13); on gridded systems it generally needs computer analysis.

How many sprinklers are in the design area?

DS 3-0 Equation 10 gives TNOS = demand area / (S × L). For the DS 3-26 HC-2 design of 230 m² at 11.9 m² per sprinkler that is 19.3, so 20 sprinklers. The number per branch line comes from Equation 11 with a shape factor of 1.2 under flat ceilings: 1.2 × √230 / 3.5 = 5 sprinklers.

Does FM require a safety margin between demand and supply?

FM DS 3-0 does not define a separate margin. Under 2.1.2.4.5 a system is rated Adequate if the water supply, after deductions such as hose demand, can provide the full flow and pressure for the required duration, and Inadequate otherwise. Current data matter: DS 2-0 2.6.4.6 calls for flow test data no more than 12 months old for an existing supply.

What is included in the demand besides sprinkler flow?

Friction loss in branch lines, cross mains and the riser, elevation pressure, fitting losses as equivalent lengths, and the hose stream allowance, which DS 3-0 2.1.2.4.4 deducts from the water supply curve. FM does not include velocity pressure in its method (2.1.2.3.1).

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