Orifice Flow Calculator
Estimate volumetric discharge through a circular tank orifice from its diameter, discharge coefficient, centerline head, and gravitational acceleration.
Inputs
Required. Use a positive diameter and a dot for decimals.
Required, dimensionless. Enter a value greater than 0 and no greater than 1.
Required. Vertical distance from the liquid surface to the orifice center; zero head is allowed.
Gravitational acceleration
Required. The demonstration uses 9.81 m/s²; edit it only when a different local or modeled gravity is intended.
Live results
Changes display and workbook presentation only; the underlying SI area is unchanged.
Select the reporting unit that fits your application; all conversions come from the same SI flow value.
Q = Cd × A × √(2gH), with A = πd² / 4
How to use this orifice flow calculator
What this calculator does. This tool estimates the volumetric discharge through a circular orifice in a tank or reservoir using the standard free-orifice relationship Q = Cd × A × √(2gH). It combines the circular opening area with the ideal velocity produced by the liquid head and then applies the empirical discharge coefficient. The result is an engineering estimate for steady, incompressible liquid flow under the assumptions represented by that equation; it is not a substitute for a calibrated meter, a full piping-network model, or a compressible-flow calculation. The U.S. Bureau of Reclamation describes the same area-times-velocity basis in its Water Measurement Manual section on orifice relationships.
When to use it. Use this calculator when sizing or checking a simple gravity-fed tank outlet, estimating drain or drawdown discharge at a known liquid level, comparing two candidate orifice diameters under the same head, or translating a known head-and-coefficient condition into a convenient flow unit for a hydraulic calculation. For precise custody transfer, highly viscous fluids, submerged outlet conditions with downstream backpressure, strong transient effects, or flow in a pressurized pipe with an orifice plate, use the governing method and calibration data for that specific system.
How to calculate. The calculator opens with a complete demonstration set, so the result and the Excel workbook are immediately available. (1) Replace Diameter of orifice (d) with the circular opening diameter and choose its unit. (2) Enter the empirical Coefficient of discharge (Cd). (3) Enter the Centerline head (H), measured vertically from the free liquid surface to the center of the opening, and choose its unit. (4) Leave Gravitational acceleration (g) at the demonstration value unless your model needs a different value. (5) Choose the Area display unit and Discharge display unit you want to read. The calculation updates live. Use Download Excel to export the current validated model. Reset deliberately clears the demonstration data rather than restoring it; after Reset, Excel export is disabled until a complete valid input set is entered again.
Input guide. Diameter of orifice (d) is a required positive decimal length. Accepted units are mm, cm, m, in, and ft; a realistic example is 50 mm. Increasing diameter raises area with the square of diameter, so it can increase discharge strongly. Do not enter an area in this field, and use a decimal point rather than an ambiguous decimal comma. Coefficient of discharge (Cd) is required, dimensionless, and must be greater than zero and no greater than one; 0.8 is the demonstration value. A lower coefficient reduces the predicted flow in direct proportion. It should represent the actual orifice geometry and flow regime rather than being treated as a universal constant. Centerline head (H) is a required nonnegative length in mm, cm, m, in, or ft; the example uses 200 mm. More head raises the ideal jet speed according to the square root of head. A common mistake is measuring to the bottom or top of the opening instead of its centerline. Gravitational acceleration (g) is required and positive; the demonstration uses 9.81 m/s², with ft/s² also available. Changing its unit converts the current value so the physical acceleration stays the same.
Output guide. Area of orifice (A) is the exact circular area derived from diameter before display rounding; its display can be switched among mm², cm², m², in², and ft². The startup diameter gives 1,963.50 mm². Discharge (Q) is the estimated volumetric flow rate and can be displayed in m³/s, L/s, L/min, m³/h, ft³/s, or US gal/min. It is driven by all four physical inputs: diameter, coefficient, head, and gravity. A zero head produces zero discharge; larger diameter, coefficient, gravity, or head increase the estimate. The Area and Discharge summary pills repeat these same canonical outputs, not separate calculations. The Area display unit and Discharge display unit controls only change presentation and exported display values; they do not alter the underlying SI model.
Worked example. With d = 50 mm = 0.05 m, the circular area is A = π(0.05²)/4 = 0.0019634954 m². Using Cd = 0.8, H = 200 mm = 0.2 m, and g = 9.81 m/s², the ideal velocity term is √(2 × 9.81 × 0.2) ≈ 1.9809 m/s. Multiplying 0.8 × 0.0019634954 × 1.9809 gives a first-open discharge of approximately 0.003112 m³/s, equivalent to about 3.1116 L/s. Those are the same values used by the initial controls, live result, and workbook checkpoints.
Learn more. For the experimental meaning of the discharge coefficient and free-jet behavior, see the Applied Fluid Mechanics orifice and free-jet experiment. For unit conversion checks, NIST publishes SI conversion factors including volumetric flow units.
How the model should be interpreted
The equation separates geometry, available hydraulic head, and non-ideal losses. The area term converts diameter into opening size. The square-root term comes from the energy relationship for a liquid accelerating under head. The discharge coefficient then corrects ideal flow for contraction and loss effects near the opening. Because diameter is squared while head sits under a square root, a percentage change in diameter usually has a much larger effect on predicted discharge than the same percentage change in head.
Discharge is a volume-per-time quantity. The U.S. Geological Survey explains the broader meaning of discharge as volume moving past a point per unit time and describes the familiar area-times-velocity relationship in its guide to measuring streamflow. This calculator applies that idea to the effective jet velocity at a circular orifice rather than to a river cross section.
Common modeling mistakes
- Using the pipe diameter instead of the actual orifice diameter. The area in this model belongs to the opening through which the jet exits.
- Entering a discharge coefficient without checking whether it matches the orifice geometry, Reynolds-number range, or calibration basis.
- Mixing head and diameter units manually. Use the built-in selectors so the model converts everything to SI before calculating.
- Treating a steady-head result as a full tank-emptying prediction. If the liquid level falls significantly, head changes with time and the discharge changes with it.
- Applying the free-orifice form when downstream pressure or submergence materially changes the effective head across the opening.