In short: a 1-inch sharp-edged orifice under 3 ft of head passes about 20.7 GPM (78.5 L/min). Flow scales with the orifice area and with the square root of the head, so doubling the diameter roughly quadruples the flow, while doubling the head only increases it by about 41%.
These figures are planning aids based on the standard orifice equation. For metering, code-required drainage sizing or safety-critical work, confirm with a licensed engineer.
How to calculate flow through an orifice
When water discharges through a hole below a free surface, its exit velocity depends only on how far it has effectively "fallen" — the head, h. That is Torricelli's theorem: the ideal velocity is √(2gh), the same speed an object would reach falling that same height. Real openings lose some of that ideal velocity to friction and to the jet contracting just past the edge, which is why the equation includes a discharge coefficient, Cd:
This calculator converts your diameter and head to meters, computes the area A = πd²/4, applies your chosen Cd, and returns the flow rate in GPM, liters per minute, liters per second, cubic meters per hour, cfs and cubic meters per second.
Worked example. Take the calculator's default: a 1-inch orifice (0.0254 m diameter, area 0.0005067 m²) under 3 ft of head (0.9144 m), sharp-edged so Cd = 0.61. First, √(2 × 9.807 × 0.9144) = 4.235 m/s. Then Q = 0.61 × 0.0005067 × 4.235 = 0.001309 m³/s, which converts to 20.7 GPM (78.5 L/min). That is exactly what the tool shows above.
Why area matters more than you'd expect. Area grows with the square of diameter, but flow only grows with the square root of head. A hole twice as wide passes roughly four times the water at the same head — which is why drilling one large hole drains a container far faster than doubling the head above a small one.
Why head and discharge coefficient change the answer
Head is the vertical distance from the free water surface down to the center of the orifice. It behaves like stored pressure: a taller column pushes harder, so the jet leaves faster. Because velocity depends on the square root of head, the relationship flattens out — quadrupling the head only doubles the exit velocity, not quadruples it.
The discharge coefficient accounts for what an ideal, frictionless model misses. As the jet squeezes through a sharp-edged hole, it necks down just past the opening — the vena contracta — so the effective flow area is smaller than the drilled hole itself, and friction trims a bit more. A smoothly rounded entrance avoids most of that contraction, which is why its Cd (≈0.98) sits so much closer to the ideal value of 1.0 than a plain drilled hole (≈0.61). A tube that projects into the tank (Borda mouthpiece) makes the contraction worse still, dropping Cd to about 0.51. For pipe and channel flow driven by friction rather than a sharp discharge, see the pipe flow rate calculator instead.
Discharge coefficients by orifice type
Typical published values for common opening geometries. These are the presets built into the calculator above.
| Orifice type | Typical Cd | Notes |
|---|---|---|
| Sharp-edged (thin plate) | 0.61 | Most drilled holes and tank fittings |
| Well-rounded (bell-mouth) | 0.98 | Smooth entrance, little contraction |
| Short flush tube | 0.80 | Length ≈ 2–3 × diameter |
| Borda (re-entrant) tube | 0.51 | Tube projects into the tank |
Flow rate by orifice size
Sharp-edged orifice (Cd 0.61) under a fixed 5 ft (1.52 m) head, across common sizes. Every value below matches the calculator for these inputs.
| Diameter | GPM | L/min |
|---|---|---|
| ⅛ in (3.2 mm) | 0.42 | 1.58 |
| ¼ in (6.4 mm) | 1.67 | 6.34 |
| ⅜ in (9.5 mm) | 3.77 | 14.26 |
| ½ in (12.7 mm) | 6.70 | 25.35 |
| ¾ in (19.1 mm) | 15.07 | 57.03 |
| 1 in (25.4 mm) (common) | 26.78 | 101.4 |
| 2 in (50.8 mm) | 107.1 | 405.6 |
Worked examples
Drilled overflow hole
20.7 GPM
A 1-inch hole drilled through a tank wall, 3 ft below the water surface, sharp-edged (Cd 0.61), passes about 20.7 GPM (78.5 L/min) — the calculator's default scenario.
Rounded floor drain
≈109 GPM
A 2-inch rounded drain opening (Cd 0.98) under 2 ft of standing water passes roughly 109 GPM (412 L/min) — over five times the flow of a sharp-edged hole at the same size, thanks to the smoother entrance.
Small pinhole leak
≈0.59 GPM
A ⅛-inch pinhole leak in a pipe or tank wall under 10 ft of head, sharp-edged, leaks about 0.59 GPM (2.24 L/min) — roughly 850 gallons per day, useful for estimating an unexplained water bill.
What else affects the result
A draining, not steady, reservoir. If the tank has no inflow, its head — and therefore its flow rate — drops continuously as it empties. The number above is the instantaneous rate at the head you entered, not an average over the full drain-down.
Submerged discharge. If the orifice empties into standing water rather than air, use the difference in surface elevations between the two sides as your head, not the orifice's absolute depth.
Non-circular openings. The formula works the same way for a square or slotted opening — just compute A directly from its actual shape instead of πd²/4, and use a discharge coefficient appropriate to that geometry.
Open-channel discharge. For water flowing over a weir or edge rather than through a submerged hole, the depth-flow relationship is different — see the weir flow calculator.
Frequently asked questions
What is the orifice flow equation?
Q = Cd · A · √(2gh), where Q is flow rate, Cd is the discharge coefficient, A is the orifice area, g is gravity (9.807 m/s²) and h is the head of water above the orifice. It comes from Torricelli's theorem, which treats the jet velocity as if the water fell freely through height h, then corrects for real-world losses with Cd.
What discharge coefficient should I use?
For a plain hole drilled through a thin wall, use 0.61 (sharp-edged). Use 0.98 for a smoothly rounded, bell-mouth entrance, 0.80 for a short flush tube, and 0.51 for a re-entrant (Borda) tube that projects into the tank. If you have a manufacturer-tested value for a specific fitting, use that instead — it will be more accurate than a textbook default.
Does the size of the tank or reservoir matter?
Only through the head, not the volume. The equation assumes a steady head — the water surface staying at a fixed height above the orifice. If you are draining a tank with no inflow, the head drops as it empties, so the flow rate calculated here is the instantaneous rate at that moment, not an average over the whole drain-down.
Does water temperature or density affect orifice flow?
Essentially no, for ordinary water. Density appears on both sides of the underlying pressure-to-velocity relationship and cancels out, which is why the equation uses head (a length) rather than pressure or density directly. Viscosity has a small effect on very small orifices at low head, but for typical drilled holes and drain openings it is negligible.
What if the orifice is submerged on both sides?
Use the difference in water-surface elevation between the two sides as your head, not the depth of the orifice itself. A submerged orifice connecting two tanks discharges based on that differential head, using the same Q = Cd · A · √(2gh) form.
How accurate is the orifice equation?
With a well-chosen discharge coefficient, it is accurate to within a few percent for typical sharp-edged and rounded openings — good enough for drainage, tank sizing and leak estimates. For custody-transfer flow metering, use a calibrated orifice plate and the coefficients in ISO 5167 rather than the textbook defaults here.
Sources & references
- Torricelli, E. (1643). Torricelli's theorem — velocity of efflux of a liquid under a hydraulic head.
- International Organization for Standardization. ISO 5167 — Measurement of fluid flow by means of pressure differential devices.
- Crane Co. Flow of Fluids Through Valves, Fittings, and Pipe. Technical Paper No. 410.
John Mac, PE
Water Systems Specialist · Austin, Texas
Texas-licensed Professional Engineer with 13+ years in residential water systems and 180+ completed projects. Writes and reviews the calculators on watercalculator.us. Read full bio
Texas PE (2016) · BS Civil Engineering, Hydraulics (2013)