Orifice Flow Calculator

About the Orifice Flow Calculator

When fluid flows through an orifice under a head of liquid, the theoretical jet velocity follows Torricelli's theorem: V = √(2gh). The actual discharge is lower because the jet contracts and loses energy, which is why the formula uses a discharge coefficient Cd.

This calculator applies Q = Cd × A × √(2gh) for a chosen orifice size, head, and fluid. It includes common entrance geometries such as sharp-edged, beveled, and rounded openings, and it lets you compare how changes in diameter or coefficient affect both velocity and flow rate.

That makes it useful for tank drain estimates, outlet sizing, simple irrigation checks, and other first-pass hydraulic problems where the geometry is known but a full pipe-network model would be excessive. It also keeps the theoretical velocity and the corrected discharge side by side so you can see how much the coefficient changes the final flow estimate before using it for design or troubleshooting.

When This Page Helps

Use this calculator when you need a first-pass flow estimate for a tank outlet, free discharge opening, or simple metering orifice.

It is useful for drain sizing, irrigation hardware, nozzle comparison, and quick hydraulic checks where head and opening diameter are known but a full CFD or piping model is unnecessary. It also helps you compare how much a change in diameter or entrance shape matters before you spend time on a more detailed analysis.

How to Use the Inputs

1. Select the orifice type to set the discharge coefficient (or enter a custom Cd).
2. Choose the fluid or enter a custom density.
3. Enter the orifice diameter in mm, or click a preset size.
4. Enter the upstream head or pressure driving flow through the orifice.
5. Select the head unit (m, ft, kPa, or psi).
6. Read the theoretical and actual velocity, volume flow, and mass flow from the outputs.
7. Compare flow rates for different orifice diameters in the table.

Example Calculation

Tips & Best Practices

• For submerged orifices, use the net head (upstream head minus downstream head).
• In time-to-drain calculations, combine this formula with the continuity equation dh/dt = −Q/A_tank.
• Beveled and rounded orifices have much higher Cd — a small machining change can nearly double the flow.
• For pulsating flow (e.g., engine intake), use time-averaged head or integrate over the cycle.
• Temperature affects density and viscosity — correct for high-temperature applications.

Practical Guidance

Orifice flow is a good first-order model when the discharge is driven mainly by a liquid head and the opening geometry is known. It is especially helpful for comparing candidate diameters or checking whether a target drain time or emitter rate is realistic before moving to a more detailed design.

Common Pitfalls

The largest errors usually come from using the wrong head, ignoring downstream submergence, or assuming Cd stays fixed under every condition. Free-discharge tank outlets, submerged openings, and compressible gas flow are different cases, so make sure the physical setup matches the formula before you rely on the number.

Frequently Asked Questions

• What is the vena contracta?

  After passing through a sharp-edged orifice, the jet contracts to a cross-section smaller than the orifice. This contracted section (vena contracta) occurs about half a diameter downstream and is the point of minimum pressure and area.

• Why is Cd only 0.61 for sharp-edged orifices?

  The jet contraction ratio (Cc ≈ 0.64) and velocity coefficient (Cv ≈ 0.97) multiply to give Cd = Cc × Cv ≈ 0.61. Rounded entrances eliminate contraction, raising Cd close to unity.

• Can I use this for gas flow?

  For low-pressure drops (< 10% of absolute pressure) in gases, the incompressible formula is a reasonable approximation. For higher ratios, use compressible-flow orifice equations.

• How does head relate to pressure?

  h = ΔP / (ρg). For water, 1 meter of head = 9.81 kPa. The calculator converts automatically when you select kPa or psi as the unit.

• Does orifice diameter affect Cd?

  For very small orifices (< 3 mm), surface-tension and viscous effects increase, slightly lowering Cd. For standard industrial sizes (10–100 mm), Cd is essentially constant for a given geometry.

• How is this different from an orifice plate in a pipe?

  This calculator models free discharge from a tank or reservoir. In-pipe orifice plates additionally involve the approach velocity and beta ratio — see the Differential Pressure calculator for that case.