When to use this calculator
Find flow speed after a cross-sectional area change under continuity. Steady incompressible flow without branch flow or leakage.
Explore the fluids & flow calculators for other questions in this topic. For a related calculation, use the Darcy Weisbach Head Loss Calculator: Estimate straight-pipe friction head loss from an entered Darcy factor.
PUTTING IT INTO PRACTICE
Continuity Equation: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Upstream area (m²) | 0.02 |
| Upstream mean velocity (m/s) | 2 |
| Downstream area (m²) | 0.01 |
| Result | 4 m/s |
- Check the input labels and enter the example values above.
- Apply the relationship: Downstream velocity = upstream area × upstream velocity/downstream area.
- The result is 4 m/s, rounded for display.
How to interpret your result
Steady incompressible flow without branch flow or leakage.
Use the fluid properties at the relevant conditions. Gauge pressure is measured relative to a reference and differs from absolute pressure. Average flow velocity and characteristic length must match the geometry being modelled.
Frequently asked questions
Should hydrostatic pressure be added to atmospheric pressure?
Add the surface absolute pressure when an absolute result is needed. The basic liquid-column calculation alone gives the pressure increase with depth.
When is the continuity equation calculator useful?
Find flow speed after a cross-sectional area change under continuity. Steady incompressible flow without branch flow or leakage.
How do I use the continuity equation calculator?
Enter upstream area (m²), upstream mean velocity (m/s), downstream area (m²). The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Downstream velocity = upstream area × upstream velocity/downstream area.
What should I check before using the result?
Steady incompressible flow without branch flow or leakage.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
Further reading
For background on this topic, see OpenStax: fluids, density and pressure ↗. This is a topic reference, not an external review or endorsement of this tool.
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