What is a nozzle flow rate calculator?
A nozzle or emitter's flow rate depends on its orifice size and how much pressure is pushing water through it. This calculator works out orifice flow in gpm at a given psi from diameter and pressure using the standard orifice discharge equation, and separately works out nozzle flow at a different pressure once you already know its flow at one pressure.
This covers a single nozzle or orifice. For a zone's total flow, add up each head's flow, or see the sprinkler GPM calculator for working out zone totals directly.
How this nozzle flow rate calculator works
Flow from diameter and pressure
Orifice discharge equation
Q = 29.84 × Cd × d² × √P
Q in gallons per minute, d in inches, P in psi. This is the standard orifice discharge equation for water, derived from Torricelli's equation for flow through an opening and converted into these practical US units.
General hydraulics engineering references give roughly 0.60-0.62 as a typical discharge coefficient (Cd) for a sharp-edged orifice, rising toward 0.95 or higher for a smoothly rounded or nozzle-shaped opening. This calculator defaults to 0.61; use a manufacturer's or measured value for your actual nozzle where you have one.
Flow at a different pressure
Pressure-flow relationship
Q2 = Q1 × √(P2 ÷ P1)
Follows directly from the orifice equation above: since diameter and Cd don't change with pressure, flow scales with the square root of the pressure ratio.
In metric mode, diameter, pressure and flow are converted to inches, psi and gpm first, so the same underlying formulas and constant are used; the result is then converted back to L/min for display.
When this calculator isn't the right tool
Use a different approach for:
- A zone's total flow rather than one nozzle. See the sprinkler GPM calculator.
- Sizing pipe or checking your supply once you know your zone's total flow. See the sprinkler zone calculator.
Nozzle flow rate calculation example
A 0.1 in diameter orifice at 30 psi, Cd 0.61:
- Q: 29.84 × 0.61 × 0.1² × √30 = 29.84 × 0.61 × 0.01 × 5.477 ≈ 1.00 gpm.
The same idea in metric
A 3 mm (0.118 in) diameter orifice at 2.5 bar (about 36.26 psi), Cd 0.61:
- Q: 29.84 × 0.61 × 0.118² × √36.26 ≈ 1.53 gpm ≈ about 5.79 L/min.
Flow at a different pressure
A nozzle flowing 3 gpm at 40 psi; find its flow at 25 psi:
- Q2: 3 × √(25 ÷ 40) = 3 × √0.625 ≈ 2.37 gpm.
As a check, applying the first formula directly at 45 psi for the same 0.1 in, Cd 0.61 orifice from the first example gives about 1.221 gpm, matching what the pressure-ratio formula gives for that same jump from 30 to 45 psi — confirming both formulas agree, as they should since one is derived from the other. All examples use the exact formulas the calculator runs; enter your own nozzle's numbers above for your result.
Practical guidance
Measure or look up the actual orifice diameter, the smallest opening water passes through, rather than an outer dimension of the nozzle body. Because the formula squares the diameter, a small measurement error has an outsized effect on the calculated flow; a manufacturer's published orifice size is more reliable than a field measurement with calipers on a tiny opening.
Where you have it, a manufacturer's own tested performance chart for that specific nozzle will be more accurate than this general equation, since it reflects the nozzle's actual discharge coefficient and internal flow path rather than an assumed Cd. Use this calculator for a general estimate, a nozzle without published data, or to see how flow shifts with pressure changes on an existing system.
Check local watering rules. Many water utilities set watering days, hours or restrictions, especially during drought. Where those apply, they take priority over any design based on this calculation.
What changes the flow
| Factor | Effect | What to check |
|---|---|---|
| Orifice diameter | Flow scales with the square of diameter, so a small change has a large effect. | Use the actual orifice size, ideally from the manufacturer's specification. |
| Pressure | Flow scales with the square root of pressure, so large pressure changes are needed to meaningfully change flow. | Use the pressure actually at the nozzle, not a supply-side reading, if the two differ. |
| Discharge coefficient (Cd) | A higher Cd (smoother, more rounded entry) increases flow at the same diameter and pressure. | Use a manufacturer or measured value where available rather than the default. |
| Nozzle design | Pressure-compensating and flow-path emitters don't follow this simple orifice relationship. | Use the manufacturer's flow-versus-pressure data for those designs. |
Frequently asked questions
What is the nozzle or orifice flow rate formula?
Q = 29.84 × Cd × d² × √P, where Q is flow in gallons per minute, Cd is the discharge coefficient, d is orifice diameter in inches, and P is pressure in psi. It's the standard orifice discharge equation, derived from Torricelli's equation for flow through an opening, converted into these practical US units.
What discharge coefficient (Cd) should I use?
General hydraulics engineering references give roughly 0.60 to 0.62 as typical for a sharp-edged orifice, rising toward 0.95 or higher for a smoothly rounded or nozzle-profile opening. This calculator defaults to 0.61, in the middle of the sharp-edged range, but you should adjust it if you have a manufacturer-specified or measured value for your actual nozzle.
How do I find nozzle flow at a different pressure?
Use Q2 = Q1 × √(P2 ÷ P1), where Q1 is the known flow at the known pressure P1, and Q2 is the flow at the new pressure P2. This follows directly from the orifice equation, since diameter and discharge coefficient stay the same and only pressure changes.
Why does flow only increase with the square root of pressure, not proportionally?
The orifice equation relates flow to the square root of pressure because pressure relates to the square of jet velocity through an opening. Doubling pressure raises flow by a factor of √2 (about 1.41×), not 2×, which is why a large pressure change is needed to meaningfully change a nozzle's output.
How accurate is this compared to the manufacturer's chart?
A manufacturer's own performance chart, tested for that specific nozzle, is more accurate than this general equation, since it reflects that nozzle's actual discharge coefficient and internal geometry rather than an assumed Cd. Use this calculator for a general estimate or for a nozzle without published data, and a manufacturer's chart whenever one is available.
What if I need a zone's total GPM, not one nozzle?
This calculator covers a single nozzle or orifice. For a zone's total flow, add up each head's flow, or see the sprinkler GPM calculator.
See the sprinkler GPM calculator.
What orifice diameter should I measure?
Use the actual diameter of the smallest opening water passes through, typically the nozzle orifice itself rather than the outer nozzle body. Manufacturers often publish this as part of a nozzle's specifications; measuring a tiny orifice accurately by hand is difficult, and a small measurement error has an outsized effect since the formula squares the diameter.
Does this work for drip emitters?
Many drip emitters are pressure-compensating or use a flow path rather than a simple round orifice, so this general orifice equation may not match a specific emitter's published flow curve. Use the emitter manufacturer's own flow-versus-pressure data where available.
Who built and checked this calculator
Licensed Professional Engineer and Irrigation Association Certified Irrigation Designer with more than 20 years in irrigation design, system auditing and landscape water management. Full profile
How this page was checked
- The 29.84 orifice constant was independently re-derived from Torricelli's equation and standard US unit conversions (gallons, inches, psi), confirming it matches the value the brief specifies.
- All three worked examples were hand-calculated and traced against the code, including a cross-check confirming the diameter-based and pressure-ratio formulas agree with each other on the same nozzle.
- Typical Cd ranges for sharp-edged orifices are checked against general hydraulics engineering references.
Sources
- Standard orifice discharge equation (Torricelli's equation converted to US practical units of gpm, inches and psi), consistent with the general form Q = Cd × A × √(2gh) used across hydraulics engineering references.
- AJ Design Software. Orifice Flow Design Calculator (typical discharge coefficient ranges by orifice geometry).
- FIRGELLI Engineering. Orifice Discharge Interactive Calculator (typical Cd for sharp-edged vs. rounded orifices).