Sprinkler Pressure Demand at the Base of Riser (NFPA 13)
The pressure the water supply must deliver at the base of the riser to drive the hydraulically most remote sprinkler: the K-factor start pressure at the end head (P1 = (Q/K)^2), plus the NFPA 13 Hazen-Williams friction loss p = 4.52 Q^1.85 / (C^1.85 d^4.87) carried over the governing run, plus the 0.433 psi/ft elevation head to lift the water. A 26 gpm K-5.6 head needs 21.6 psi, and 260 gpm through 150 ft of 3 in steel adds 12.1 psi of friction and 6.5 psi of lift for a 40.1 psi demand - the point that must fall under the supply curve and the fire pump's rated point. Smoother CPVC (C = 150) trims about 4 psi. One representative flowing path; a full design balances every node and grid loop. A design aid, not a stamped hydraulic submittal; a qualified fire-protection engineer and the AHJ govern.
Formula and source
P1 = (q_head_gpm / k_factor)^2; pf = 4.52 x q_total_gpm^1.85 / (c_factor^1.85 x pipe_id_in^4.87); friction = pf x equiv_length_ft; elevation = 0.433 x elevation_ft; demand = P1 + friction + elevation.
NFPA 13 (Standard for the Installation of Sprinkler Systems), 2022, by name; the Hazen-Williams friction coefficient 4.52 and exponents 1.85 / 4.87, the pipe-type C values, the 0.433 psi/ft water column, and the K-factor discharge relation Q = K sqrt(P) are the NFPA 13 hydraulic-calculation method.
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