Dimensional Analysis & Similitude

Units as a problem-solving tool. Dimensional homogeneity, the Buckingham Pi theorem, famous dimensionless groups, and the model laws (Froude, Reynolds) that let engineers test ships, dams and aircraft at small scale.

• Dimensional Analysis & Buckingham Pi — Dimensional analysis uses the fact that valid physics equations must be dimensionally consistent. Learn base dimensions (M, L, T, Θ, I), dimensional homogeneity, checking and deriving formulas, the Buckingham Pi theorem step by step, the famous dimensionless groups (Re, Fr, Ma, Nu, Pr) and how experiments are planned with far fewer tests.
• Similitude, Scaling & Model Testing — Model tests of ships, aircraft, dams and buildings work only if the model is geometrically, kinematically and dynamically similar to the prototype. Learn scale ratios, Reynolds and Froude model laws, how to scale velocities, forces and power, what happens when similarity is incomplete, and practical tricks like changing the test fluid.