What is the discharge coefficient (Cd)?

Cd accounts for real-world losses such as viscous effects and flow contraction at the orifice. For a sharp-edged circular orifice in a thin plate, Cd ≈ 0.61 is the most widely used value. Rounded-entry or well-formed nozzles may have Cd as high as 0.98.

What does "head" mean in this context?

Head (h) is the vertical height of the fluid surface above the center of the orifice, measured in meters or feet. It represents the potential energy per unit weight driving the flow.

What is the orifice flow equation?

Q = Cd × A × √(2 × g × h), where Q is volumetric flow rate, Cd is the discharge coefficient, A is the orifice cross-sectional area, g is gravitational acceleration (9.81 m/s² or 32.174 ft/s²), and h is the upstream head.

When is this formula valid?

The formula assumes steady, incompressible flow with a free jet (atmospheric pressure downstream). It is valid for liquids at moderate velocities. Compressible gas flow or submerged orifices require different equations.

How do I find Cd for my orifice?

Cd depends on orifice geometry and Reynolds number. Sharp-edged orifice: 0.60–0.63. Re-entrant (Borda) orifice: ~0.51. Well-rounded nozzle: 0.95–0.99. When in doubt, 0.61 is a conservative default for sharp-edged holes.

Can I use this for gas flow?

This calculator uses the incompressible liquid formula. For gas or compressible flow through an orifice plate, an expansion factor (Y) must be applied. Use a dedicated compressible flow tool for gases.

Orifice Flow Calculator

Calculate volumetric flow rate through an orifice using the discharge coefficient method — enter orifice area, head, and Cd to get Q instantly.

Orifice Parameters

Unit System

Orifice Diameter (mm)

Upstream Head (m)

Discharge Coefficient (Cd) (dimensionless)

Typical values: sharp-edged 0.61 • rounded nozzle 0.97

Common Cd Presets

Flow Rate Results

Enter values and click Calculate to see results.

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Summary

The Orifice Flow Calculator computes the volumetric flow rate (Q) of a fluid discharging through a circular orifice using the standard discharge coefficient formula: Q = Cd × A × √(2g×h). It supports both SI and US customary unit systems and instantly converts results to m³/s, L/s, and GPM. This tool is useful for hydraulic engineering, process design, and fluid mechanics coursework.

How it works

Enter the orifice diameter in millimeters or inches.
Enter the upstream head (fluid depth above the orifice center) in meters or feet.
Enter the discharge coefficient (Cd) — typically 0.61 for a sharp-edged circular orifice.
Select your preferred unit system (SI or US customary).
Click Calculate to see the volumetric flow rate in multiple units simultaneously.

Use cases

Sizing drainage orifices in stormwater management systems.
Designing flow-control devices in chemical process piping.
Estimating tank drain time for storage vessel design.
Verifying orifice plate sizing in HVAC and hydraulic systems.
Fluid mechanics homework and coursework problems.
Quick cross-checks during engineering feasibility studies.

Frequently Asked Questions

Last updated: 2026-05-29 · Reviewed by Nham Vu