EngineeringFluid MechanicsA-Level
CISCEAQAEdexcelOCRAPSATBritish ColumbiaVictoria

Continuity Equation Calculator

Conservation of mass in fluid flow.

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Velocity 2

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Overview

The continuity equation represents the principle of conservation of mass for a moving fluid. For an incompressible fluid flowing through a conduit, the product of the cross-sectional area and the velocity of the fluid remains constant at any point along the flow path.

Symbols

Variables

v_2 = Velocity 2, A_1 = Area 1, v_1 = Velocity 1, A_2 = Area 2

Velocity 2
Area 1
Velocity 1
Area 2

Apply it well

When To Use

When to use: Apply this equation when dealing with steady-state flow of incompressible fluids, such as liquids, moving through pipes or ducts. It is applicable when the fluid's density does not change significantly between two points of interest.

Why it matters: This principle is critical in engineering for designing nozzles, venturi meters, and piping systems where speed and pressure control are necessary. It explains why water speeds up when a hose is partially covered, which is a fundamental concept in fluid dynamics and aerodynamics.

Avoid these traps

Common Mistakes

  • Mixing diameter and area.
  • Using compressible flow cases.

One free problem

Practice Problem

A water pipe with a cross-sectional area of 0.5 m² carries water at a velocity of 4 m/s. If the pipe narrows to an area of 0.2 m², what is the new velocity of the water?

Area 10.5 m^2
Velocity 14 m/s
Area 20.2 m^2

Solve for:

Hint: Divide the initial flow rate (A1 × v1) by the final area to find the new velocity.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Bird, Stewart, Lightfoot, Transport Phenomena
  2. Wikipedia: Continuity equation
  3. Bird, R. Byron, Stewart, Warren E., Lightfoot, Edwin N. Transport Phenomena. John Wiley & Sons.
  4. Incropera, Frank P., DeWitt, David P., Bergman, Theodore L., Lavine, Adrienne S. Fundamentals of Heat and Mass Transfer. John Wiley & Sons.
  5. Britannica, The Editors of Encyclopaedia. 'Continuity equation'. Encyclopedia Britannica, 22 Sep. 2023.
  6. Wikipedia, 'Continuity equation'.
  7. Bird, Stewart, Lightfoot Transport Phenomena
  8. Incropera, DeWitt, Bergman, Lavine Fundamentals of Heat and Mass Transfer