Fluid mechanics, from first principles

20 min readFoundationUpdated October 8, 2026

Build physical intuition before reaching for a solver. This short introductory course connects the no-slip condition, conservation of mass, and the velocity profile of fully developed pipe flow.

What you will learn

  • Explain what no-slip means at a stationary wall.
  • Use conservation of mass to relate mean velocity and flow rate.
  • Explore a laminar pipe-flow solution and recognize its limits.

Prerequisites

Basic algebra, SI units, and an interest in how fluids move. No simulation software is required.

A small course, with a clear purpose

Work through the three lessons in sequence. Use each checkpoint to test your understanding, then explore the interactive analytical example.

Course syllabus

0 of 3 lessons completed

  1. 01 · What happens at the wall?
  2. 02 · Follow the mass
  3. 03 · Why a parabola appears