Coefficient of Discharge Calculator

What Is the Coefficient of Discharge?

The coefficient of discharge $C_d$ compares actual flow through an orifice, nozzle, or valve to the ideal flow predicted by Bernoulli's equation. Values below 1 account for friction, contraction, and turbulence.

Coefficient of Discharge Formula

$$C_d = \frac{Q}{A \sqrt{2\Delta P / \rho}}$$

Where:

$Q$ is volumetric flow rate (m³/s)
$A$ is orifice area (m²)
$\Delta P$ is pressure drop across the opening (Pa)
$\rho$ is fluid density (kg/m³)

Example: water ($\rho \approx 998$ kg/m³) through a 1 cm² orifice with 5 kPa drop and measured flow 0.01 m³/s gives $C_d$ near 0.71 if ideal velocity is about 0.099 m/s.

Related tools: Darcy's Law Calculator and Pump Calculator.

Frequently Asked Questions

What is a typical coefficient of discharge?

Sharp-edged orifices often fall between 0.60 and 0.65. Smooth nozzles and well-formed venturis can reach 0.95–0.98.

Why is actual flow less than ideal?

The jet contracts after leaving the orifice (vena contracta), viscosity dissipates energy, and upstream flow may not be uniform. $C_d$ bundles these effects into one factor.

Can $C_d$ exceed 1?

It should not for a simple orifice under standard definitions. Values above 1 suggest measurement error, wrong area, or non-standard geometry.

Which units should I use?

This calculator uses SI: m³/s, m², Pa, and kg/m³. Convert liters, cm², bar, or g/cm³ to SI before entering values.

Is this the same as flow coefficient $C_v$?

No. $C_d$ is dimensionless from Bernoulli. Valve $C_v$ uses US customary units and different definitions; convert carefully between standards.

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What Is the Coefficient of Discharge?

Coefficient of Discharge Formula

Frequently Asked Questions

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