Orifice Flow Calculator - Q, Velocity, and Mass Flow

An orifice flow calculator turns a measured upstream head and a known orifice geometry into the volumetric discharge Q passing through the orifice, using the standard fluid-mechanics result Q = C_d * A * sqrt(2 g H) where C_d is the coefficient of discharge, A is the orifice area, g is gravitational acceleration, and H is the centerline head measured from the upstream free surface to the orifice centerline.

• • Tank drain sizing: Estimate the flow rate leaving a tank through a side or bottom orifice to size pump-down or fill-time requirements.
• • Small-scale flow metering: Calibrate a circular orifice plate as a simple flow meter where differential pressure transducers are not available.
• • Hydraulic bench and lab work: Convert a measured head on a tank-mounted circular orifice into a discharge value for undergraduate fluid-mechanics labs.
• • Orifice plate comparison: Sanity-check a published flow coefficient for a sharp-edged or rounded orifice against the theoretical Torricelli velocity.

An orifice is a hole or cutout, usually circular, installed in a tank wall or pipe so that flow is restricted and a measurable pressure drop forms. The equation applies whenever the flow is incompressible, the upstream velocity is small compared with the jet velocity, and the orifice is sharp-edged with a well-defined diameter.

Use this orifice flow calculator when you know the orifice diameter, the head of liquid above the orifice centerline, and a reasonable estimate of the coefficient of discharge, and you want Q in a useful engineering unit without running CFD or experimental calibration.

The orifice equation is the simplest application of Bernoulli along a streamline between a free surface and a contracted jet, so when you want to handle more general two-point energy problems Bernoulli equation calculator works through the same conservation law with elevation and pressure terms included.

The calculator combines the circular area formula A = pi d^2 / 4 with the ideal Torricelli velocity sqrt(2 g H) and the empirical discharge coefficient C_d, then converts the resulting discharge into several engineering units and reports the optional mass flow rate when a fluid density is supplied.

• Q: Volumetric discharge through the orifice, in cubic meters per second (m^3/s).
• C_d: Dimensionless coefficient of discharge; 0.62 is the standard first approximation for a sharp-edged orifice.
• A: Cross-sectional area of the orifice, computed from the diameter as A = pi d^2 / 4 in square meters.
• d: Internal diameter of the circular orifice, in meters.
• g: Local gravitational acceleration, in m/s^2 (ISO 80000-3 standard is 9.80665 m/s^2).
• H: Centerline head, the vertical distance from the upstream free water surface to the orifice centerline, in meters.

The orifice equation is a conservation-of-energy statement between the free surface (atmospheric pressure, small velocity) and the contracted jet downstream of the orifice (atmospheric pressure again, accelerated flow). Real orifices deviate from the ideal because of viscous losses at the edge and the contraction of the jet just past the opening; both effects are folded into C_d.

For sharp-edged circular orifices with fully developed approach flow, C_d is typically 0.60 to 0.65. Rounded entrances push C_d toward 1.0; thick plates or viscous fluids can drop C_d below 0.60. The default of 0.62 in this calculator is the standard first approximation in most fluid-mechanics textbooks.

According to Wikipedia, Orifice plate, the coefficient of discharge for a sharp-edged orifice plate is typically between 0.6 and 0.85, with a first approximation of about 0.62 for fully developed flow.

The exact value of C_d drifts with Reynolds number because viscous losses at the orifice edge change with the flow regime, so when you want to quantify that regime explicitly Reynolds number calculator is the next step after this one.

Four ideas show up every time you apply the orifice equation. Keeping them straight stops a single C_d number from being used outside the conditions it was measured in.

Orifice discharge is essentially free-surface flow collapsing into a contracted jet, and the same gravity-driven head-discharge relationship shows up in channel control sections, so Open channel flow calculator is a useful companion when the geometry stops being a simple tank and hole.

Five quick steps take you from a tank drawing to a discharge number. The defaults match a standard sharp-edged circular orifice at sea-level gravity, so most users only need to enter d and H.

1. 1 Look up the orifice diameter: Use the nominal diameter from the spec, or measure across the opening with calipers. Convert to meters before entering d.
2. 2 Read the centerline head: From the upstream free water surface, drop a vertical line to the orifice centerline. That distance in meters is H.
3. 3 Pick the coefficient of discharge: Leave C_d at 0.62 for a sharp-edged orifice. Raise toward 0.95 for a rounded entrance, or drop below 0.60 for thick plates or viscous fluids.
4. 4 Confirm gravity and fluid density: Leave g at 9.80665 m/s^2 for sea-level work. Leave density at 1000 kg/m^3 for water, or change for oils and brines.
5. 5 Read the discharge and velocity: Use Q in the unit that matches your pump, pipe, or schedule. The actual velocity output is a useful cross-check against any published velocity rating for the orifice.

For a 50 mm circular orifice in the side of a tank with 30 cm of water above the centerline and a sharp edge, the calculator returns Q = 3.06 L/s (about 48.5 gpm) with the default C_d = 0.62. With 5 cm of head above the orifice, the same orifice discharges only about 0.246 L/s.

When the tank cross-section is rectangular and the opening stretches across the full channel instead of being a localized hole, the same kind of head-discharge math turns into a weir problem, which is exactly what Broad crested weir calculator is set up to handle.

The calculator is built for the kind of quick Q estimates that come up in fluid-mechanics homework, lab work, and small-engineering decision-making.

• • Five discharge units in one place: Q is reported in m^3/s, L/s, L/min, cfs, and U.S. gpm so the value drops directly into a pump curve, an irrigation schedule, or a lab notebook.
• • Cd override for any orifice shape: The Cd field accepts the full 0.30 to 1.00 range so sharp-edged, rounded, thick-plate, and conical-entrance orifices are all covered with a single formula.
• • Built-in Torricelli sanity check: Ideal and actual mean velocity are both shown, so it is obvious when a chosen Cd is pushing the discharge outside what the head can physically deliver.
• • Optional mass flow rate: Entering a fluid density turns the calculator into a mass-flow tool as well as a volumetric one, which is useful for oil, brine, or chemical-service fluids.
• • Standard gravity pre-filled: g is pre-loaded with the ISO 80000-3 standard value of 9.80665 m/s^2 but can be edited for planetary, high-altitude, or historical unit work.

For tank-outlet calculations where the line downstream of the orifice also has real length, the friction-loss correction layered on top of the orifice result uses the same Darcy-Weisbach form handled by friction factor calculator.

Q = C_d A sqrt(2 g H) is short, but several physical effects move the real discharge away from the calculator value. Check these before publishing a number.

• • The calculator assumes steady, incompressible flow with a fully developed upstream velocity profile. Pulsating flows, two-phase mixtures, and choked compressible flows need a different formulation.
• • Submerged outlet conditions (orifice below the downstream water level) are not auto-corrected; subtract the downstream submergence from H before entering the head.
• • Non-circular orifices (rectangular, triangular, segmental) need a different area formula and Cd. Use this calculator only for circular orifices.

According to NIST Special Publication 811, the standard acceleration of free fall used in fluid-flow calculations is g = 9.80665 m/s^2.

When the upstream velocity is not negligible compared with the jet velocity, the simple Q = C_d A sqrt(2 g H) form over-predicts and a full Bernoulli energy balance between the two sections is required, which is exactly what Bernoulli equation calculator is set up to compute.