Torricelli showed in 1643 that liquid leaves a hole as fast as if it had fallen freely from the surface. Real orifices pass less because the jet contracts – a sharp-edged hole has a discharge coefficient of about 0.61.
How to use the Orifice Flow Calculator
- Orifice diameter d
- Discharge coefficient C_d
- Head above the orifice H
- Gravitational acceleration g
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the orifice diameter, the discharge coefficient and the head above the orifice centre.
Inputs explained
| Field | What to enter |
|---|---|
| Orifice diameter d | Units: mm, cm, m, in, µm |
| Discharge coefficient C_d | A number |
| Head above the orifice H | Units: m, cm, mm, km, in, ft … |
| Gravitational acceleration g | Units: m/s², ft/s², g, cm/s² |
What each result means
- Theoretical jet velocity = sqrt(2×[Gravitational acceleration g]×[Head above the orifice H])
- Discharge Q = [Discharge coefficient C_d]×pi×[Orifice diameter d]^2÷4×sqrt(2×[Gravitational acceleration g]×[Head above the orifice H])
- Orifice area = pi×[Orifice diameter d]^2÷4×1e4
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) | Discharge Q (L/s) |
|---|---|
| 12.5 | 0.4688 |
| 18.75 | 1.0549 |
| 25 | 1.8754 |
| 31.25 | 2.9303 |
| 37.5 | 4.2196 |
| 50 | 7.5015 |
Formula
v = √(2gH) (Torricelli), Q = C_d·A·√(2gH)
Worked example
Inputs — Orifice diameter d: 25 mm; Discharge coefficient C_d: 0.61; Head above the orifice H: 2 m; Gravitational acceleration g: 9.80665 m/s².
Results — Theoretical jet velocity = 6.26311 m/s; Discharge Q = 1.87538 L/s; Orifice area = 4.90874 cm².
Key terms
- Torricelli's law
- Outflow velocity from an orifice.
Frequently asked questions
What is Torricelli's law?
Outflow speed equals √(2gH), like free fall from the surface.
Why is C_d about 0.61?
The jet contracts to about 61% of the hole area.
Does the tank empty at a constant rate?
No – the flow falls as the head drops.
How can C_d be increased?
Round the orifice edge or add a short nozzle.