Equations · equation

Continuity Equation

Fluid Dynamics · 1757

Equation: ∂ρ/∂t + ∇·(ρv) = 0
Field: Fluid Dynamics
Named After: Leonhard Euler
Symbols: ρ density · v velocity field · t time · ∇· divergence · for incompressible flow it reduces to ∇·v = 0
Year: 1757

Significance

Mass is neither created nor destroyed as fluid flows — what goes in must come out. Why a river races through its narrows and a thumb over a hose makes the jet fly farther.

Machines

Kaplan Turbine Francis Turbine

Related

MHD Induction Equation Navier–Stokes Equations Kirchhoff's Circuit Laws Noether's Theorem Linear Perturbation Growth Cosmological Fluid Equation

Requires

Divergence Theorem

Required By

Betz Limit Hydraulic Power Navier–Stokes Equations

Referenced by

equation

Betz Limit Cosmological Fluid Equation Divergence Theorem Hydraulic Power Kirchhoff's Circuit Laws Linear Perturbation Growth MHD Induction Equation Navier–Stokes Equations Noether's Theorem

machine

Francis Turbine Kaplan Turbine

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From the Equations database in Notion, last edited 2026-08-18. This page is the row, rendered by the build; nothing on it is written by hand.