Equation of Continuity

The Equation of Continuity is a statement of mass conservation

The Law of Conservation of Mass states that mass can be neither created or destroyed. Using the Mass Conservation Law on a steady flow process - flow where the flow rate do not change over time - through a control volume where the stored mass in the control volume do not change - implements that

  • inflow equals outflow

This statement is called the Equation of Continuity. Common application where the Equation of Continuity are used are pipes, tubes and ducts with flowing fluids or gases, rivers, overall processes as power plants, diaries, logistics in general, roads, computer networks and semiconductor technology and more.

Equation of continuity

The Equation of Continuity and can be expressed as:

m = ρi1 vi1 Ai1 + ρi2 vi2 Ai2 + .... + ρin vin Aim

    = ρo1 vo1 Ao1 + ρo2 vo2 Ao2 + .... + ρom vom Aom                            (1)


m = mass flow rate (kg/s)

ρ = density (kg/m3)

v = speed (m/s)

A = area (m2)

With uniform density equation (1) can be modified to

q = vi1 Ai1 + vi2 Ai2 + .... + vin Aim

    = vo1 Ao1 + vo2 Ao2 + .... + vom Aom                         (2)


q = flow rate (m3/s)

ρi1 = ρi2 = . . = ρin = ρo1 = ρo2 = .... = ρom

Example - Equation of Continuity

10 m3/h of water flows through a pipe with 100 mm inside diameter. The pipe is reduced to an inside dimension of 80 mm.

Using equation (2) the velocity in the 100 mm pipe can be calculated

(10 m3/h) (1 / 3600 h/s) = v100 (3.14 (0.1 m)2 / 4)


v100 = (10 m3/h) (1 / 3600 h/s) / (3.14 (0.1 m)2 / 4)

    = 0.35 m/s

Using equation (2) the velocity in the 80 mm pipe can be calculated

(10 m3/h) (1 / 3600 h/s) = v80 (3.14 (0.08 m)2 / 4)


v80 = (10 m3/h) (1 / 3600 h/s) / (3.14 (0.08 m)2 / 4)

= 0.55 m/s

Related Topics

  • Dimensions - Sizes and dimensions of pipes and tubes, and their fittings - inside and outside diameter, weight and more
  • Fluid Mechanics - The study of fluids - liquids and gases. Involves velocity, pressure, density and temperature as functions of space and time
  • Fluid Flow and Pressure Drop - Pipe lines - fluid flow and pressure loss - water, sewer, steel pipes, pvc pipes, copper tubes and more

Related Documents

  • Conservation of Mass - The Law of Conservation of Mass states that mass can neither be created or destroyed
  • Equations in Fluid Mechanics - Commonly used equations in fluid mechanics - Bernoulli, conservation of energy, conservation of mass, pressure, Navier-Stokes, ideal gas law, Euler equations, Laplace equations, Darcy-Weisbach Equation and more
  • Orifice, Nozzle and Venturi Flow Rate Meters - The orifice, nozzle and venturi flow rate meters use the Bernoulli Equation to calculate fluid flow rate using pressure difference through obstructions in the flow
  • Bernoulli Equation - Conservation of energy - non-viscous, incompressible fluid in steady flow
  • Sluice Gate Flow Measurements - Sluice gates are used for controlling and measuring flow rates in open channels and rivers, mainly in connection to hydro power plants
  • Technical Terms in Fluid Mechanics - Some of the most commonly used technical terms in fluid mechanics
  • Air Ducts Sizing - The ductwork of ventilation systems are often sized with either the Velocity, the Constant Pressure Loss (or Equal Friction Loss) - or the Static Pressure Recovery Methods
  • Mechanical Energy and Bernoulli Equation - The mechanical energy equation related to energy per unit mass, energy per unit volume and energy per unit weight involving head

Matched Content

Tag Search

  • en: equation continuity mass conservation
  • es: conservación de la masa continuidad ecuación
  • de: Gleichung Kontinuität Massenerhaltung

Search the Engineering ToolBox

- "Search is the most efficient way to navigate the Engineering ToolBox!"

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your SketchUp model with the Engineering ToolBox - SketchUp Extension/Plugin - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!

Translate the Engineering ToolBox!
About the Engineering ToolBox!