Sprinkler Nozzle Flow
Compute sprinkler nozzle flow Q given pressure and discharge coefficient Cd. Q = Cd × A × √(2gh).
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Irrigation nozzle discharge: Q = Cd · A · √(2gH)
The orifice-flow equation Q = Cd · A · √(2 · g · H) tells you the volumetric discharge through a nozzle. Here Cd is the discharge coefficient, running about 0.6 for sharp-edged round orifices, around 0.8 for conical or streamlined nozzles, and as high as 0.97 for rounded bellmouths. A is the cross-section area in m², g ≈ 9.81 m/s², and H is the pressure head in meters of water column (m.w.c.). Most irrigation systems work between 1 and 3 bar, or 10–30 m.w.c. Example: a 4 mm nozzle (A ≈ 1.257 × 10⁻⁵ m²) at H = 20 m.w.c. with Cd = 0.95 yields Q ≈ 0.95 · 1.257e-5 · √(2 · 9.81 · 20) ≈ 2.37 × 10⁻⁴ m³/s ≈ 0.85 m³/h.
Applications: pivots, drip lines and sprinklers
Engineers reach for it to size center-pivot sprinklers, microsprinklers and drip emitters — usually 1–4 L/h per emitter on Netafim, Rain Bird or NaanDanJain lines — to even out pressure along the laterals and to pick the right booster pump. The same equation sizes spillways, weir gates and garden sprinklers, and it lets a grower match crop water demand (ETc) without runoff or washing fertilizer past the root zone.
FAQ
What Cd should I use? Roughly 0.6 for thin-plate round orifices, 0.8 for short conical nozzles, and 0.90–0.97 for well-rounded converging nozzles. When the manufacturer publishes a catalog value, trust it over the textbook number.
Bar or m.w.c.? 1 bar ≈ 10.2 m of water column. Convert first, then plug into the formula. Mixing the two units is the mistake people make most often.
Does the formula work for drip emitters? Up to a point. Most drippers are pressure-compensating (PC) and keep flow nearly constant from 0.5 to 4 bar. For non-PC emitters, the Q = k · Hx equation with x ≈ 0.5 belongs to the same family.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.