Solve flow variables using conservation laws with clear units. Check incompressible or compressible cases for steady systems. Export results instantly for faster engineering reporting.
The continuity equation expresses conservation of flow through a streamtube. For steady, one‑dimensional flow, the conserved quantity depends on density variation.
These relations assume steady conditions, uniform average velocity over each section, and negligible accumulation between sections.
If you fill every field, the calculator reports a mismatch percent to help validate measurements.
| Case | A1 (m²) | v1 (m/s) | A2 (m²) | v2 (m/s) | Q (m³/s) |
|---|---|---|---|---|---|
| Nozzle | 0.020 | 3.50 | 0.010 | 7.00 | 0.070 |
| Diffuser | 0.015 | 4.00 | 0.030 | 2.00 | 0.060 |
| Pipe step | 0.008 | 6.25 | 0.012 | 4.17 | 0.050 |
Values shown are illustrative and assume incompressible conditions.
The continuity equation is the first “sanity check” in fluid systems. In a steady stream, whatever enters a section must leave another section, otherwise mass accumulates. This calculator applies that conservation idea to quickly validate field data and size transitions in piping, ducts, and nozzles.
For most liquids, density change is small, so volumetric flow rate stays nearly constant: Q = A·v. For gases, density can vary with pressure and temperature, so mass flow is the stable quantity: ṁ = ρ·A·v. Selecting the correct mode prevents misleading velocity predictions.
Small process lines may have areas from 1×10⁻⁴ to 1×10⁻² m², while larger ducts can exceed 0.1 m². Average velocities often fall between 0.5 and 5 m/s for water services, and 5 to 25 m/s for air handling, depending on noise, losses, and erosion constraints.
A nozzle reduces area, so continuity predicts a rise in velocity. A diffuser increases area, so velocity drops. When you enter A1 and A2 plus one velocity, the calculator solves the missing velocity and reports the resulting flow rate. This helps estimate residence time, mixing quality, and downstream component loading.
Engineering data arrives in mixed units. The tool converts area to m² and velocity to m/s internally, then converts results back to your selected units. This reduces manual conversion errors, especially when switching between ft², in², and metric areas.
If you provide all inputs, the calculator compares both sides of continuity and reports a mismatch percent. Small mismatches are usually instrumentation noise or rounding. Large mismatches can indicate incorrect units, a wrong diameter, flow separation, leaks, or unsteady operation. For high-accuracy work, average multiple readings and document instrument calibration dates.
Continuity gives velocity, but pressure behavior requires additional relations. After finding velocities, you can pair results with Bernoulli, pump curves, or loss coefficients to estimate pressure drops. This workflow is common when auditing a line upgrade or troubleshooting a restriction.
A practical approach is: measure diameters or areas, record average velocities, choose the correct mode, solve the unknown, and export a CSV or PDF summary. Keeping a consistent calculation trail improves QA reviews and speeds up design iterations across multiple operating points.
Yes. Choose the compressible mode and enter densities for both sections. The calculator conserves mass flow (ṁ) and also reports the resulting volumetric flow rates for each section.
Enter all known values and leave exactly one variable blank. The tool solves that missing variable using the continuity relation for the selected mode.
Real measurements include uncertainty. Small deviations can come from rounding, sensor drift, or non-uniform velocity profiles. Larger deviations may indicate leaks, unsteady flow, or incorrect units.
No. Continuity conserves flow only and ignores losses. Use computed velocities with an energy equation and suitable loss coefficients to estimate pressure drop.
This version accepts area directly. If you have diameter, compute area as A = πD²/4, then enter A in your preferred unit.
Use average bulk velocity, not centerline velocity. For many practical checks, average velocity from a flowmeter and cross-sectional area provides the best consistency.
If density change is negligible across the section, incompressible mode is simpler and typically accurate. For significant pressure or temperature variation, switch to compressible mode.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.