Calculator Inputs
Use circular, rectangular, or custom sections. Leave one field blank in auto mode, or choose exactly what to solve.
Formula Used
Continuity equation for incompressible flow:
Q = A × V
A₁ × V₁ = A₂ × V₂
Where Q is volumetric flow rate, A is cross-sectional area, and V is average fluid velocity.
Circular area: A = πd² / 4
Rectangular area: A = width × height
Velocity relationship: V₂ / V₁ = A₁ / A₂
When area decreases, velocity increases to keep the same volumetric flow. This is why reducers accelerate flow and expanders slow it down.
How to Use This Calculator
- Select the unit system that matches your project.
- Choose the inlet and outlet section shapes.
- Enter dimensions or direct custom areas.
- Pick auto mode or choose the exact variable to solve.
- Provide the known velocity or flow values.
- Press calculate to show the result above the form.
- Review the continuity check, ratios, and graph.
- Use the CSV or PDF buttons to export your results.
Example Data Table
| Case | Inlet Area | Outlet Area | Inlet Velocity | Outlet Velocity | Flow Rate |
|---|---|---|---|---|---|
| Pipe reducer | 0.0707 m² | 0.0177 m² | 2.20 m/s | 8.80 m/s | 0.1555 m³/s |
| Rectangular duct contraction | 0.1200 m² | 0.0600 m² | 3.00 m/s | 6.00 m/s | 0.3600 m³/s |
| Custom channel sizing | 0.0850 m² | 0.1100 m² | 4.00 m/s | 3.09 m/s | 0.3400 m³/s |
Frequently Asked Questions
1. What does the continuity equation calculate?
It links cross-sectional area and average velocity for steady incompressible flow. The calculator uses that relationship to solve flow rate or missing section speed between two locations.
2. When should I use this calculator?
Use it for pipes, ducts, nozzles, channels, reducers, and expanders when you know section size changes and need a missing velocity or volumetric flow value.
3. Does this tool work for compressible flow?
This version is intended for incompressible or nearly incompressible conditions. For gases with strong density change, use the full mass conservation form with density variation included.
4. Why does velocity increase in a smaller outlet?
If the same volume passes each section every second, a smaller area must carry that volume faster. The reduced cross-section forces the fluid speed upward.
5. What if inlet and outlet values do not match perfectly?
The calculator shows a continuity mismatch percentage and warning. Small differences often come from rounded inputs, estimated dimensions, or measured data uncertainty.
6. Can I enter custom areas directly?
Yes. Choose the custom area option for either section when your cross-section is irregular or already known from drawings, simulation output, or previous calculations.
7. Which units does the calculator support?
It supports metric and imperial input sets. Length, area, velocity, and flow labels change automatically so your entries and outputs remain consistent.
8. Is the flow rate always the same at both sections?
For steady incompressible flow with no leaks or storage, yes. The same volumetric flow must pass each section even though velocity and area may change.