Fire sprinkler hydraulic calculation summary.

How to read a fire sprinkler hydraulic calculation packet

A hydraulic calculation shows that the water supply can push enough water through the pipes to the sprinklers the design assumes are flowing. Every program lays its packet out a little differently, but each prints the same three things: a summary of the design, an analysis of the water supply with its graph, and the pipe tables that carry the pressure from the sprinklers back to the supply one pipe at a time. The figures below are the example packet's, so each one can be found in the summary above.

The summary page: what the design assumes

The first page states the design the rest of the packet proves. For a density design it prints the occupancy or hazard, the density in gpm per square foot, the design area (the remote area), the coverage per sprinkler, how many sprinklers were calculated, and the hose allowance. The example prints Residential occupancy, 0.05 gpm per square foot over 900 square feet, and 2 sprinklers calculated at up to 196 square feet each. A residential design flows the few sprinklers in the room that is hardest to supply, each at the flow its listing gives, so on a residential packet the sprinkler count and the listing matter more than the density.

These are the figures to hold against the plans: the hazard against the use of the space, the design area outlined on the sprinkler drawings, and the sprinklers counted inside it.

The water supply analysis and the N^1.85 graph

The supply analysis prints the flow test the calculation rests on: the static pressure with no water flowing, the residual pressure, and the flow that was running when the residual was read. The example's test is 76.000 psi static and 64.000 psi residual at 1,020.00 gpm. Beside it the packet prints the system's demand, the flow and the pressure the system needs where it connects to the supply: 27.97 gpm at 35.668 psi here.

The graph is drawn on hydraulic graph paper, whose flow scale is stretched to the 1.85 power (N^1.85), so the supply's curve from the static pressure through the test point is a straight line. The demand is plotted as a point, and the pressure the supply gives at that flow is read off the line: 75.985 psi in the example. Available minus required is the safety margin, 40.317 psi here. A demand point above the supply line means the supply cannot deliver the design. Many departments ask for a minimum margin; that figure is a local rule, not the program's.

The pipe table, one line at a time

The pipe tables are where the arithmetic is. Each line is one run of pipe between two nodes, the named points of the calculation: a sprinkler, a tee, the base of a riser. The columns vary by program, but every packet prints the same quantities:

• Node 1 and node 2 and their elevations: where the line starts and ends.
• K-factor and flow added (q): at a sprinkler, the water it discharges.
• Total flow (Q): everything the pipe carries.
• Nominal and actual inside diameter: the pipe size on the drawings, and the inside diameter the friction is worked out from.
• Fittings and devices: each fitting as a code with its equivalent length, and each device with a fixed loss.
• Length: the pipe, the fittings' equivalent length, and the two added together.
• C-factor: how smooth the inside of the pipe is taken to be.
• Friction loss per foot, and the three pressures: Pt, the total pressure at the start of the line; Pe, the pressure gained or lost to elevation; and Pf, the pressure lost to friction.

The table starts at the sprinkler farthest from the supply, and each line hands its pressure to the next: the pressure at node 2 is Pt + Pe + Pf. In the example the line from node 1 to node 2 starts at 8.664 psi and loses 6.833 psi to friction on the level, so node 2 needs 15.497 psi.

A sprinkler's flow: q = K√P

A sprinkler discharges its K-factor times the square root of the pressure at it. The example's first sprinkler, node 201, is K-4.9 at 8.000 psi: 4.9 × √8.000 = 13.86 gpm. The pressure a calculation starts at is the designer's choice, usually the least that the density over the sprinkler's coverage, or the sprinkler's listing, needs. Check the K-factor against the sprinkler the drawings' legend names.

Friction loss: the Hazen-Williams formula

The friction loss in each foot of pipe is p = 4.52 × Q^1.85 ÷ (C^1.85 × d^4.87), with Q the flow in gpm, C the C-factor and d the actual inside diameter in inches. The example's line from node 1 carries 27.97 gpm through 1 inch pipe, 1.1010 inches inside, at C 150: 0.126536 psi a foot. Its fittings (6Tr(1'-0), T(5'-0), E(7'-0)) add 18'-0 to 36'-0 of pipe, and 54'-0 at 0.126536 psi a foot is the line's 6.833 psi. Friction is where a small change matters most: a smaller pipe, a lower C-factor or a longer run each raise the demand, so check the sizes and the route on the drawings.

Fittings and equivalent length

A fitting counts as the length of straight pipe that would lose the same pressure: its equivalent length, which depends on the fitting and on the pipe size. The packet's legend spells out its codes, and the table prints each fitting with its equivalent length on its line. A fitting on the drawings that is missing from the line, or the other way round, changes the friction on that run.

Elevation: 0.433 psi a foot

A column of water one foot high presses 0.433 psi. Working back toward the supply, a node lower than the one before needs that much more pressure for every foot of drop, and a higher one that much less. In the example node 3 sits 9'-6 below node 2 (19'-8 to 10'-2), so the line's Pe is 4.114 psi. Check the elevations against the building sections and the riser details.

Where two routes meet: balancing

Where pipes join, water arriving at a node from two directions must arrive at one pressure. The second route is worked out so that it reaches the joining node at the pressure the first route has there, and its sprinkler runs at whatever pressure that leaves. In the example the second sprinkler, node 202, runs at 8.292 psi and flows 14.11 gpm, and route 2 reaches node 1 at 8.664 psi, the pressure route 1 printed there. From that node on, the table carries both sprinklers' flow.

Fixed losses: backflow preventers, meters and other devices

Some devices are not worked out with the formula: a backflow preventer, a water meter or a valve assembly is taken as a fixed pressure loss from its manufacturer's data at the flow. The example's line from node 5 to node 6 takes 3.000 psi for the device coded f and 4.500 psi for the device coded BFP, so most of that line's 7.633 psi of Pf is theirs. Check that the device on the drawings is the one the calculation took the loss for.

The hose allowance

A design may set water aside for fire department hose lines. It raises the flow the supply must give, so it moves the demand point on the graph, and it is usually added at the source rather than carried through the sprinkler pipes. The example sets none aside.

From the table to the supply

The first route's last line ends at the source, node 7 in the example, at 35.668 psi and 27.97 gpm: the demand the supply analysis plots. If the table's last pressure and the supply analysis's required pressure differ, ask the designer which the graph used.

Summarize a calculation packet