# Orifice Flow Calculator

URL: https://speedycalculator.com/calculators/physics/orifice-flow/
Last updated: 2026-10-30

> The orifice flow calculator finds the discharge and jet velocity through an orifice or opening in a tank from its diameter, the head of liquid above it and the discharge coefficient.

## Inputs

- Orifice diameter d (mm, cm, m, in, µm)
- Discharge coefficient C_d
- Head above the orifice H (m, cm, mm, km, in, ft, yd, mi)
- Gravitational acceleration g (m/s², ft/s², g, cm/s²)

## Results

- Theoretical jet velocity
- Discharge Q
- Orifice area

## Formula

```
v = √(2gH) (Torricelli),  Q = C_d·A·√(2gH)
```

## Explanation

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

FieldWhat to enterOrifice diameter dUnits: mm, cm, m, in, µmDischarge coefficient C_dA numberHead above the orifice HUnits: m, cm, mm, km, in, ft …Gravitational acceleration gUnits: 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)12.50.468818.751.0549251.875431.252.930337.54.2196507.5015

## 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.

## FAQ

**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.


## Sources

- [Fluid Mechanics (F. M. White) – reference text](https://www.mheducation.com/highered/product/fluid-mechanics-white-chul/M9781260258318.html)
- [The Engineering ToolBox](https://www.engineeringtoolbox.com/)