Fluid Flow Continuity Equation Calculator

Enter any three values for two pipe cross-sections and the calculator solves the missing fourth using A1v1 = A2v2.

Continuity Equation: A1v1 = A2v2

Select the unknown, fill the other three fields, then click Calculate.

Input as

Section 1 (inlet)

Section 2 (outlet)

Conservation of Mass

A1 × v1 = A2 × v2 = Q

Q = volumetric flow rate (m³/s)

Fill in the fields and click Calculate

Common Scenarios

Condition Result
A2 = A1/2v2 = 2v1
A2 = 2A1v2 = v1/2
A2 = A1v2 = v1
d2 = d1/2 (circles)v2 = 4v1

Summary

Enter any three values for two pipe cross-sections and the calculator solves the missing fourth using A1v1 = A2v2.

How it works

  1. Select which variable you want to solve for (area or velocity at either section).
  2. Enter the known values for the three remaining fields.
  3. Choose appropriate units for each measurement.
  4. Click Calculate to apply A1 × v1 = A2 × v2 and get the result.
  5. The flow rate Q = A × v is also displayed for both sections as a consistency check.

Use cases

  • Find the exit velocity of fluid through a nozzle given the inlet area and speed.
  • Determine the pipe diameter needed to achieve a target flow speed.
  • Verify that a pipe design maintains volumetric flow rate through diameter changes.
  • Analyze venturi tubes, carburetors, and other variable-area flow devices.
  • Solve fluid mechanics homework problems and exam questions.
  • Estimate water speed in a river as the channel narrows or widens.

Frequently Asked Questions

Last updated: 2026-07-01 · Reviewed by Nham Vu