Stream Velocity (Continuity) Calculator

For steady, incompressible flow along a streamline, volumetric flow rate is conserved: Q = A·V, so for two cross-sections: A₁V₁ = A₂V₂. This calculator uses that relationship to solve for the selected unknown.

• V₂ = (A₁V₁)/A₂, or V₁ = (A₂V₂)/A₁
• A₂ = (A₁V₁)/V₂, or A₁ = (A₂V₂)/V₁
• Q = A₁V₁ = A₂V₂

1. Select what you want to solve for (V₁, V₂, A₁, A₂, or Q).
2. Enter velocities and choose your velocity unit.
3. Define A₁ and A₂ using area, diameter, or rectangle dimensions.
4. Optionally enter Q to compare with calculated flow rate.
5. Press Calculate. The result appears above the form.
6. Use CSV or PDF buttons to save the result.

1) Why continuity matters in steady flow

The continuity principle states that, for steady incompressible flow, the volumetric flow rate remains constant along a streamtube. When a channel or pipe changes size, velocity must adjust so the same volume passes each section every second. This calculator automates those relationships and keeps units consistent.

2) Core variables: area, velocity, and flow rate

Cross‑sectional area (A) describes how much open space the fluid can occupy. Stream velocity (V) is the average speed through that section. Their product gives flow rate: Q = A·V. In SI, A is in m², V in m/s, and Q in m³/s, but many engineering inputs use cm², ft², or L/min.

3) Working with two sections

With section 1 and section 2, continuity becomes A₁V₁ = A₂V₂. If A₂ is smaller than A₁, velocity rises proportionally (nozzle behavior). If A₂ is larger, velocity drops (diffuser behavior). The tool can solve for V₁, V₂, A₁, A₂, or Q depending on your selection.

4) Area options used by this calculator

You can enter area directly or compute it from geometry. For circular flow passages, the calculator uses A = π(d/2)² from the diameter. For rectangular ducts, it uses A = W×H. Geometry inputs accept m, cm, mm, ft, and in, then the calculator converts internally to m².

5) Data checks and interpretation

If you provide both sections completely, the calculator also estimates a flow mismatch percentage between A₁V₁ and A₂V₂. A small mismatch can come from rounding, measurement uncertainty, or nonuniform velocity profiles. A large mismatch suggests an incorrect unit, an area definition error, or unsteady conditions during sampling.

6) Typical ranges and quick sanity checks

In many water systems, velocities are often in the 0.5–3 m/s range for piping, while nozzles can be higher. Very large velocities with modest flow rates usually indicate a very small computed area. If results look extreme, verify whether you entered diameter versus radius, and confirm area units like cm² versus m².

7) Assumptions and limitations

Continuity in this form assumes incompressible flow and steady conditions. For gases at high Mach numbers or large pressure changes, density variation matters and a mass‑flow form is preferred. Also, the calculator uses average velocities; real profiles in pipes can be nonuniform, so a measured point velocity may need correction.

8) Where this calculator is useful

Use it to size nozzles, compare duct sections, verify test‑bench measurements, and estimate flow from a known area and velocity. It is also a fast classroom tool for exploring how constrictions accelerate flow. Export the computed values to CSV for reports, or print to PDF for documentation.

1) What is the continuity equation used here?

For steady incompressible flow, the calculator uses Q = A·V and A₁V₁ = A₂V₂ to relate two cross‑sections and solve the selected unknown.

2) Can I use diameter instead of area?

Yes. Choose the circular diameter option for A₁ or A₂. The calculator computes area using A = π(d/2)² after converting your length unit to meters.

3) What does “flow mismatch” mean?

If both sections are entered, mismatch compares A₁V₁ and A₂V₂. A high value indicates inconsistent inputs, unit mistakes, or measurements taken under changing flow conditions.

4) Does this work for gases?

It can be approximate when density changes are small. For large pressure or temperature changes, compressible effects matter and mass flow (ρAV) should be used instead.

5) Why can velocities look too high?

High velocity often comes from a very small area, such as using mm² when you intended cm². Recheck the selected units and whether the entered value is diameter, not radius.

6) What if the channel is rectangular?

Select the rectangular option and enter width and height. The calculator multiplies W×H after converting dimensions to meters, then applies the continuity equation normally.

7) How do I save results for a report?

After calculation, use “Download CSV” for spreadsheet use. For a PDF record, click “Download PDF” and choose “Save as PDF” in your browser’s print dialog.