Hong Life CalculatorsUnderstanding the coefficient of discharge calculator — concept and principle
The coefficient of discharge Cd tells you how much water actually flows through an orifice, nozzle or flow meter compared with the ideal, frictionless flow. This calculator finds Cd from a measured flow and either a tank head (Torricelli) or a pressure difference across a meter.
How it is calculated
- Cd = Qactual ÷ Qtheoretical; Qactual = collected volume ÷ time.
- Orifice under head h: Qth = A × √(2gh).
- Flow meter with pressure difference Δp: Qth = A × √(2Δp ÷ (ρ(1 − β⁴))), with β = d ÷ D.
- Cd = Cc × Cv: contraction coefficient Cc = (djet ÷ d)², velocity coefficient Cv.
The principle
Bernoulli's equation gives the ideal speed of fluid leaving an opening. Real flow falls short for two reasons. The jet keeps contracting just after a sharp-edged opening, so its narrowest section (the vena contracta) is smaller than the hole; for a sharp edge Cc is about 0.62. Friction also slows the fluid a little (Cv about 0.97–0.99). Typical Cd values: sharp-edged orifice about 0.61, well-rounded nozzle 0.95–0.99, venturi about 0.98.
Worked example
Default inputs: Torricelli method, 29 L collected in 60 s, orifice 15 mm, head 1.0 m.
- Actual flow = 29 ÷ 60 ≈ 0.483 L/s.
- Area = π ÷ 4 × 0.015² ≈ 1.767 × 10⁻⁴ m²; ideal jet velocity = √(2 × 9.80665 × 1.0) ≈ 4.429 m/s.
- Theoretical flow = 1.767 × 10⁻⁴ × 4.429 ≈ 7.83 × 10⁻⁴ m³/s = 0.783 L/s.
- Cd = 0.483 ÷ 0.783 ≈ 0.618.
- Mean velocity in the opening = 0.483 × 10⁻³ ÷ 1.767 × 10⁻⁴ ≈ 2.735 m/s. No jet diameter was entered, so Cc and Cv show —.
| Orifice or throat diameter (mm) | Coefficient of discharge Cd |
|---|---|
| 3.75 | 9.881 |
| 7.5 | 2.47 |
| 11.2 | 1.098 |
| 15 | 0.618 |
| 18.8 | 0.395 |
| 22.5 | 0.274 |
| 30 | 0.154 |
How to read the result
A Cd near 0.61 confirms a sharp-edged orifice behaving as expected. Much higher values suggest a rounded entrance; much lower values suggest measurement errors, a blocked opening or a head that dropped during collection. For flow meters, use the Cd from the relevant standard or calibration.
Common mistakes
- Letting the tank level fall during collection without averaging the head.
- Measuring head from the tank bottom instead of the orifice centre.
- Using the pipe diameter instead of the orifice diameter for A.
- Mixing litres and cubic metres.
Frequently asked questions
What is a typical coefficient of discharge for an orifice?
About 0.61 for a sharp-edged orifice.
Why is Cd less than 1?
The jet contracts after the opening and friction reduces velocity.
What is the vena contracta?
The narrowest section of the jet just downstream of the opening.
Sources: ISO 5167-1:2022, Measurement of fluid flow by means of pressure differential devices · White, F. M., Fluid Mechanics, 8th ed. McGraw-Hill