The relationship between flow rate (Q), pressure (P), and the sprinkler discharge coefficient (K-factor) is defined by the hydraulic formula Q = K√P. To find the K-factor, the formula is rearranged to K = Q / √P.

Given:

Flow (Q) = 65 gpm

Pressure (P) = 14.9 psi

Calculation:

1. Find the square root of the pressure: √14.9 ≈ 3.86

2. Divide the flow by this value: K = 65 / 3.86 ≈ 16.84

The calculated value of 16.84 corresponds to the nominal K-factor of 16.8.

A. 8.0 (115): A K-factor of 8.0 at 14.9 psi would only discharge approximately 31 gpm (8.0 × √14.9), not the required 65 gpm.

B. 11.2 (160): A K-factor of 11.2 at 14.9 psi would discharge approximately 43 gpm (11.2 × √14.9), which is significantly less than 65 gpm.

D. 25.2 (360): A K-factor of 25.2 at 14.9 psi would discharge a much higher flow of approximately 97 gpm (25.2 × √14.9).

1. NFPA 13, Standard for the Installation of Sprinkler Systems (2022 Edition). Section 27.2.2.1.1 explicitly states the formula for calculating the discharge from a sprinkler orifice as q = k√p, where q is the flow in gpm, k is the nominal K-factor, and p is the pressure in psi. The calculation performed directly applies this fundamental formula.

2. SFPE, Handbook of Fire Protection Engineering (5th Edition). Chapter 19, "Automatic Sprinklers," Section 19.4.1, "Sprinkler K-Factor," presents the orifice equation Q = K√P and defines the terms. This peer-reviewed source validates the formula used to determine the correct K-factor from the given flow and pressure.

3. Oklahoma State University, School of Fire Protection and Safety. Course FSE 3233, Fire Protection Hydraulics and Water Supply. Course materials on hydraulic calculations for sprinkler systems use the formula K = Q / √P as the basis for determining sprinkler performance characteristics. This is a standard application taught in accredited fire protection engineering programs.