Sprinkler Nozzle Flow

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 · H^x equation with x ≈ 0.5 belongs to the same family.