Mechanical Engineering - The 100-Mark Branch Paper
What the section tests
The branch paper is worth 100 of the 200 marks - half the exam - and covers the diploma mechanical core: engineering materials, mechanics of solids, fluid mechanics and machinery, thermal engineering, production and workshop technology, machine design fundamentals and industrial engineering. Breadth matters more than depth, because each question is one mark.
Core rules
- Stress σ = P/A (N/mm² = MPa); strain ε = δ/L; Hooke's law σ = Eε; elongation δ = PL/AE.
- A fully constrained bar heated by ΔT develops σ = αΔT·E, compressive on heating.
- Continuity A₁v₁ = A₂v₂; Bernoulli's equation P/ρg + v²/2g + z stays constant along a streamline.
- Air-standard efficiencies: Otto = 1 − 1/r^(γ−1); Diesel = 1 − (1/r^(γ−1))·(ρ^γ − 1)/(γ(ρ − 1)).
- Production: risers compensate casting shrinkage; welding defects include slag inclusion and lack of penetration; cutting speed, feed and depth of cut define a turning operation.
Worked example
A mild steel rod of 20 mm diameter and 1 m length carries an axial load of 20 kN; E = 200 GPa. Area = (π/4) × 20² = 314.16 mm². σ = 20 000/314.16 = 63.7 N/mm². ε = 63.7/200 000 = 3.18 × 10⁻⁴. Elongation δ = εL = 3.18 × 10⁻⁴ × 1000 mm = 0.32 mm. Note the unit switch: 200 GPa is 2 × 10⁵ N/mm², which is what makes the division work.
Traps that cost marks
- Using the diameter as a radius, or leaving E in N/m² while the area is in mm².
- Mixing absolute and gauge pressure in pump and turbine problems.
- Confusing the Otto exponent (γ − 1 = 0.4 for air) with γ itself.
- Applying casting terminology to welding defects, or vice versa.
- Ignoring that principal stresses on mutually perpendicular planes are not simply added.