Restriction orifices, test orifices, and orifice-plate sketches in fire protection often start from the ideal orifice relation Q = Cd · A · √(2gh), where Q is volumetric flow, Cd is a discharge coefficient, A is the orifice area, g is gravity, and h is the head across the orifice. This page explains that sketch and gives a free browser calculator that accepts orifice diameter, head (ft) or differential pressure (psi via 2.31 ft/psi freshwater), and Cd. It is for learning and quick checks—not a substitute for manufacturer data, the criteria adopted by your authority having jurisdiction, or review by a licensed design professional.
How the orifice equation is used
- Measure or select the orifice diameter and convert it to area A = πd²/4 (consistent units).
- Estimate the head h across the orifice (feet of water). If you have differential pressure in psi for freshwater, convert with h ≈ psi × 2.31.
- Choose a discharge coefficient Cd appropriate to the orifice geometry (sharp-edge teaching values often sit near 0.60–0.65; do not invent Cd for a listed device—use the manufacturer value).
- Compute Q = Cd · A · √(2gh). Convert to gpm when needed (1 ft³/s ≈ 448.8 gpm).
- Treat the result as a sketch only. Listed sprinklers use K-factor relationships (Q = K√P), not a free-hand Cd·A·√(2gh) substitute for listing data.
Free calculator
Educational approximation only. Freshwater head factor 2.31 ft/psi when converting from psi. Nothing you enter leaves your browser. For listed sprinkler flow vs pressure see the sprinkler K-factor calculator or the Sprinkler Pipe Friction Loss workbook. For elevation pressure sketches see PSI to feet of head.
Worked example
A 1 in sharp-edge teaching orifice with Cd = 0.62 and 50 ft of head: A = π(1/12)²/4 ≈ 0.00545 ft², √(2gh) = √(2×32.174×50) ≈ 56.7 ft/s, Q ≈ 0.62×0.00545×56.7 ≈ 0.192 ft³/s ≈ 86 gpm. Change Cd, diameter, or head and the sketch moves with them. A listed sprinkler is sized with its published K-factor (Q = K√P), not this free-hand orifice model—always check against the adopted edition, manufacturer data, and AHJ.
Next steps: convert pressure and head with the free PSI to feet of head calculator, check listed sprinkler flow with the sprinkler K-factor calculator, estimate pipe velocity with the sprinkler pipe velocity calculator, and run full segment friction tables in the Sprinkler Pipe Friction Loss workbook.