Mechanical Engineering Core Subjects
What is tested
Mechanical core spans Thermodynamics, Fluid Mechanics, Strength of Materials, Theory of Machines, Manufacturing/Production and Industrial Engineering. Numerical questions cluster around efficiency, stress, gear geometry, EOQ and PERT.
Rules worth memorising
- First law: Q − W = ΔU; the second law forbids 100% conversion; Carnot η = 1 − T₂/T₁ using absolute temperatures.
- Otto η = 1 − 1/r^(γ−1); Diesel η = 1 − [1/r^(γ−1)] × [(ρ^γ − 1)/(γ(ρ − 1))], where ρ is the cut-off ratio.
- Viscosity: τ = μ du/dy; Reynolds number Re = ρVD/μ; Darcy–Weisbach hf = fLV²/(2gD).
- Bending σ = My/I; torsion τ = Tr/J; Euler buckling Pcr = π²EI/L² for pinned ends.
- Gears: module m = d/T; circular pitch p = πm; velocity ratio = T₂/T₁.
- Casting: cope on top, drag below, riser feeds shrinkage. Welding: SMAW general purpose, TIG for thin sections.
- Industrial: EOQ = √(2DS/H); PERT te = (to + 4tm + tp)/6; the critical path has zero float; break-even quantity Q = F/(S − V).
Worked example
A Carnot engine works between 600 K and 300 K. η = 1 − 300/600 = 0.5, i.e. 50%. If a real engine between the same limits delivers 30%, its second-law efficiency is 30/50 = 60%. Using 27 °C and 327 °C gives the same result only because they convert to 300 K and 600 K - never assume that coincidence.
Traps
Putting Celsius into efficiency formulas; confusing module (mm) with diametral pitch (in⁻¹); writing τ = T/J instead of Tr/J; treating gauge pressure as absolute in gas-law problems; mixing break-even output with break-even sales revenue.