Real flow through an orifice is less than ideal because the jet contracts (vena contracta) and loses energy to friction. The discharge coefficient – about 0.61 for a sharp-edged orifice and 0.95–0.99 for a smooth nozzle – captures this.
How to use the Coefficient of Discharge Calculator
- Method
- Orifice diameter d
- Measured volumetric flow
- Head H
- Measured mass flow
- Pressure difference ΔP
- Fluid density ρ
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose the method and enter the measured flow, orifice size and head or pressure drop.
Inputs explained
| Field | What to enter |
|---|---|
| Method | Choose one: Head (gravity flow), Pressure difference |
| Orifice diameter d | Units: mm, cm, m, in, µm |
| Measured volumetric flow | Units: L/s, m³/s, m³/h, L/min, US gpm, ft³/s |
| Head H | Units: m, cm, mm, km, in, ft … |
| Measured mass flow | Units: kg/s, kg/h, g/s, lb/s, lb/min |
| Pressure difference ΔP | Units: kPa, Pa, bar, psi, atm, MPa |
| Fluid density ρ | Units: kg/m³, g/cm³, g/mL, lb/ft³, lb/in³ |
Example values
How the main result changes when Orifice diameter d changes and everything else stays at the example values above:
| Orifice diameter d (mm) | Coefficient of discharge C_d |
|---|---|
| 12.5 | 3.1226 |
| 18.75 | 1.3878 |
| 25 | 0.7806 |
| 31.25 | 0.4996 |
| 37.5 | 0.347 |
| 50 | 0.1952 |
Formula
Head: C_d = Q / (A·√(2gH)) · Pressure: C_d = ṁ / (A·√(2ρΔP))
Worked example
Inputs — Method: Head (gravity flow); Orifice diameter d: 25 mm; Measured volumetric flow: 1.2 L/s; Head H: 0.5 m.
Results — Orifice area = 0.000491 m²; Coefficient of discharge C_d = 0.7806.
Key terms
- Vena contracta
- Narrowest cross-section of a jet.
Frequently asked questions
What is a typical C_d?
About 0.61 for a sharp-edged orifice, 0.95–0.99 for a well-rounded nozzle.
Why is C_d less than 1?
Jet contraction and friction.
What is the vena contracta?
The narrowest point of the jet just after the orifice.
How is it measured?
By timing flow into a tank and comparing with theory.