Exercises

One exercise set per domain, each built on that domain’s gallery. Every problem links the example it builds on. Try a problem before opening its solution: the solutions are hidden in drop-downs, run when the documentation is built, and are checked by the test suite, so the numbers they print are the numbers the code produces.

Structures and Machines

• Structural engineering exercises – sizing a beam for stiffness, a column under four end conditions, a truss by hand and by stiffness.

• Mechanical engineering exercises – damping from a free decay, isolating a machine, a gearbox and its bearing.

Energy and Flow

• Thermodynamics exercises – Otto against Diesel, the best pressure ratio of a gas turbine, a heat pump against the second law.

• Fluid engineering exercises – Colebrook against Swamee-Jain, a venturi meter, water hammer.

• Heat transfer exercises – an insulated wall, a pin fin, quenching a steel ball.

• Aerodynamics exercises – stall speed at altitude, the best glide, a normal shock in an intake.

Circuits, Signals and Control

• Electrical engineering exercises – charging a capacitor, a series resonant circuit, power-factor correction.

• Control systems exercises – the largest stable gain, a servomechanism to specification, an LQR for a double integrator.

• Signal processing exercises – aliasing, bits and SNR, FIR against IIR.

• Communications exercises – where to put the cable, the Shannon limit, Carson’s rule.

Materials and Reliability

• Materials exercises – Tresca against von Mises, fatigue crack growth, the specific stiffness of a composite.

• Reliability exercises – three Weibull shapes, redundant pumps, availability and a safety integrity level.