Equação da Continuidade

A₁v₁ = A₂v₂.
Created by
Renato Passos, Eng. de Software
Reviewed by
Renato Passos, Eng. de Software

Last updated: Apr 18, 2026

v₂
4,000 m/s

Formula

A₁v₁ = A₂v₂

About this calculator

The continuity equation calculator solves for the product of cross-sectional area and flow velocity of an incompressible fluid. Based on mass conservation, the formula A₁v₁ = A₂v₂ ensures constant volumetric flow rate along a pipe. Enter three known values to automatically compute the fourth.

Use this tool for hydraulic problems like pipe sizing, irrigation system analysis, or duct velocity calculations. It helps engineers, technicians, and students verify flow conservation across different sections of a conduit.

Caution: the equation applies only to incompressible fluids (liquids) under steady flow. For gases, density changes require modifications. It also ignores friction losses, turbulence, or abrupt direction changes. In real applications, use empirical correction factors.

Frequently asked questions

Can I use this calculator for gases?

Not directly. Gases are compressible, so density varies. For gases, use the continuity equation with constant mass flow rate (ρ₁A₁v₁ = ρ₂A₂v₂).

What does constant volumetric flow rate mean?

It means the volume of fluid passing any pipe section per unit time is the same, provided no leaks or accumulations.

Does the equation account for head loss?

No. The continuity equation only relates area and velocity. Friction losses are handled by Bernoulli's equation or empirical formulas like Darcy-Weisbach.

What units should I use?

Use consistent units: area in m², velocity in m/s, yielding flow rate in m³/s. You can convert, but the calculator assumes coherence.

What if the pipe has branches?

For branches, the sum of outlet flow rates equals the inlet flow rate. The equation applies to each branch individually, but total flow is conserved.

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