Vector Calculus
Math · Advanced · Lesson 6 of 8

Divergence

Sources and sinks

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

  • Divergence ∇ · F = ∂P/∂x + ∂Q/∂y: outflow per unit area.
  • Positive divergence: a source; negative: a sink.
  • Incompressible flow has zero divergence.

Steps

  1. A tiny box
  2. Compute a divergence
  3. Neither source nor sink
  4. Water in a pipe
  5. An outflowing square
  6. Electric charges