Mechanics
- Bending stress σ = Mc/I; torsion τ = Tc/J
- Natural frequency ωn = √(k/m)
- Work-energy: ΣW = ΔKE
Thermodynamics
- Steady-flow energy: Q̇ − Ẇ = ṁ(Δh + ΔV²/2 + gΔz)
- Carnot efficiency η = 1 − TL/TH (absolute temperatures)
- Ideal gas: Pv = RT
Fluids and heat transfer
- Reynolds number Re = ρVD/μ
- Conduction q = kAΔT/L; convection q = hAΔT
- Radiation q = εσA(T₁⁴ − T₂⁴)
Design
- Factor of safety = strength ÷ applied stress
- Von Mises: σ′ = √(σ₁² − σ₁σ₂ + σ₂²)
- Gear ratio = N_driven ÷ N_driver
Test yourself on FE
Reading a summary is the easy part. Take the free 10-question diagnostic to see which of these domains you actually have, then drill the rest.