Calculator Inputs
Enter any consistent combination of values. Diameter automatically converts to area. Leave unknown fields blank and solve using continuity relations.
Example Data Table
| Case | Area 1 (m²) | Velocity 1 (m/s) | Area 2 (m²) | Velocity 2 (m/s) | Flow Rate (m³/s) |
|---|---|---|---|---|---|
| Pipe contraction | 0.080 | 2.50 | 0.040 | 5.00 | 0.200 |
| Pipe expansion | 0.030 | 6.00 | 0.090 | 2.00 | 0.180 |
| Air duct check | 0.120 | 4.00 | 0.060 | 8.00 | 0.480 |
Formula Used
The continuity equation expresses conservation of mass in fluid motion. For steady incompressible flow, the volumetric flow rate remains constant between sections:
Q = A × V
A₁V₁ = A₂V₂
When density matters, use mass flow conservation:
ṁ = ρ × A × V
ρ₁A₁V₁ = ρ₂A₂V₂
Where A is cross-sectional area, V is velocity, Q is volumetric flow rate, ρ is density, and ṁ is mass flow rate.
How to Use This Calculator
- Enter known values for section 1 and section 2.
- Use area directly, or enter diameter to calculate area automatically.
- Leave the unknown field blank if you want the calculator to solve it.
- Add density when you want mass flow results.
- Click Calculate to show results above the form.
- Use Download CSV or Download PDF for reporting.
Frequently Asked Questions
1. What does the continuity equation describe?
It describes conservation of mass in fluid flow. What enters one section must leave another section, assuming steady conditions and no fluid storage.
2. When can I use A₁V₁ = A₂V₂?
Use it for steady incompressible flow, where density stays effectively constant. Water systems and low-speed liquid transport problems commonly use this form.
3. Why does velocity increase in smaller pipes?
If the same flow passes through a smaller area, velocity must rise to maintain continuity. This is why contractions speed up fluid motion.
4. Should I enter area or diameter?
You can enter either one. Diameter is converted into area automatically, which helps when pipe geometry is known but area is not.
5. What if I know flow rate but not velocity?
Enter the flow rate and area for that section. The calculator will rearrange Q = A × V to solve the missing velocity.
6. Why are densities optional?
Density is only needed for mass flow calculations or compressible cases. For basic incompressible flow comparisons, area and velocity often suffice.
7. Can I export the calculated results?
Yes. Use the CSV button for spreadsheet data and the PDF button for a print-ready report generated directly from the results section.