Water Supply, Hydraulics, and Fire Protection Analysis
Fundamental relationships
Pressure and elevation: 1 psi = 2.31 ft of water, and 0.433 psi per foot of rise. Bernoulli's equation (with friction losses) explains why residual pressures fall as flow increases. Discharge from an orifice or sprinkler follows q = K√P, so the K-factor is the hydraulic fingerprint of a head.
Friction loss
Hazen-Williams is the workhorse: p = 4.52 Q^1.85 / (C^1.85 d^4.87) psi per foot, with Q in gpm and d in inches. Loss rises steeply with flow and falls sharply with diameter - doubling flow roughly quadruples friction loss, and a modest diameter increase yields large gains. Equivalent lengths handle fittings, and C-factors express internal roughness (cement-lined and plastic high, unlined steel lower, older pipe lower still).
Supply and pumps
A flow test establishes static, residual, and pitot-derived flow. A large drop between static and residual signals a weak main. Pump curves express shutoff (churn) head at zero flow, rated head at rated flow, and overload at 150% of rated flow (limited to 65% of rated head for centrifugal fire pumps). NPSH margin prevents cavitation. Fire department connections, gravity tanks, suction and discharge piping, and backflow prevention all influence the delivered curve.
Analysis approach
Build the demand (sprinkler + hose) at the base of the riser, add elevation, device, and pipe friction losses back to the supply, then compare with the supply curve at that point - never against static pressure alone.
Worked example
A K = 5.6 sprinkler at 25 psi discharges q = 5.6 × √25 = 5.6 × 5 = 28 gpm. A 10 ft elevation rise costs 0.433 × 10 = 4.33 psi.
Traps
Confusing static, normal operating, and residual pressure; forgetting elevation; applying flow-test extrapolation outside its valid range; and misreading pump churn versus rated point.