Hydraulic Calculations and Pipe Sizing
The calculation path
Start at the most remote sprinkler, determine its minimum flow and pressure, add downstream sprinkler flows, apply friction loss and elevation to each pipe segment, and continue to the supply. NFPA 13 uses the Hazen-Williams formula: FL = 4.52 Q^1.85 / (C^1.85 d^4.87) psi per foot, with Q in gpm and d as internal diameter in inches. Add hose allowance at the base of the riser, and compare the total demand with the supply curve.
Pipe sizing
Velocity is a check, not the design basis; high velocity increases friction and noise. Use the actual internal diameter, not nominal pipe size. C factors depend on pipe material and lining. Elevation adds 0.433 psi per foot of rise; a basement supply subtracts pressure.
Worked example
A 4-in. Schedule 40 steel main carries 500 gpm with C = 120. d = 4.026 in. Q^1.85 = 98,600; 4.52Q^1.85 = 445,700. C^1.85 = 7,020; d^4.87 = 880; denominator = 6.18 million. FL = 0.072 psi/ft. Over 100 ft, friction = 7.2 psi. If the pipe rises 20 ft, add 20 × 0.433 = 8.7 psi, for about 15.9 psi total.
Traps
Using nominal diameter; forgetting elevation; omitting hose allowance; mixing C factors; and calculating only to the riser instead of the supply source.