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

Name: Orifice Flow Calculator
Availability: InStock
Author: Nham Vu

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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