Glossary term
Continuity Equation
A conservation relation stating that mass is neither created nor destroyed within a defined flow system, except through specified sources or sinks.
Definition
modelA conservation relation stating that mass is neither created nor destroyed within a defined flow system, except through specified sources or sinks.
The continuity equation is the mass-conservation statement used in fluid mechanics, process engineering, hydraulics, aerodynamics, and computational simulation. It connects density, velocity, area, accumulation, and source terms.
The continuity equation is the mathematical expression of mass conservation in a flow. In a simple steady incompressible streamtube, it reduces to:
where Q is volumetric flow rate, A is cross-sectional area, and v is average velocity. If the area decreases, velocity increases for the same incompressible flow rate.
General meaning
The full continuity equation accounts for density changes and accumulation. In differential form it is commonly written as:
where \rho is density and \mathbf{v} is velocity. Source or sink terms can be added when mass is generated, consumed, injected, or removed in the chosen control volume.
Engineering role
Continuity is the first consistency check for fluid systems. It is used in pipe sizing, nozzles, pumps, ventilation, hydraulic networks, turbomachinery, process equipment, environmental flows, and CFD. It is often combined with the Bernoulli equation, momentum balances, and energy balances.
Compressible and incompressible flow
For liquids and low-speed gases, density may be treated as approximately constant. For high-speed gas flow, large pressure changes, combustion, or acoustic phenomena, density variation is important and mass flow rate must be tracked directly. Confusing volumetric flow rate with mass flow rate can produce major errors when pressure, temperature, or composition changes.
Common mistakes
Common mistakes include using inlet volumetric flow at one pressure and outlet volumetric flow at another pressure as if they were directly equal for a compressible gas. Another error is ignoring leakage, bypass flow, accumulation, or phase change. In simulations, a mass imbalance usually points to a boundary-condition, mesh, solver, or convergence problem that should be resolved before trusting detailed results.