Mathematics, Physics and Basic Engineering Sciences
What the exam tests
Mathematics, Physics and Basic Engineering Sciences tests algebraic manipulation, geometry and trigonometry, SI units, mechanics, hydrostatics, thermodynamics and basic electricity applied to shipboard problems.
Core rules
- Use SI units: length m, mass kg, time s, force N, pressure Pa, power W. Weight is mg; mass is not weight.
- Motion: v = u + at, s = ut + ½at², F = ma. Work = force × distance; power = work/time. Efficiency = useful output / input.
- Hydrostatics: pressure p = ρgh; force on a horizontal area F = pA; flow continuity Q = Av. Pump hydraulic power = ρgQH.
- Electricity: Ohm’s law V = IR; power P = VI = I²R. Thermodynamics: heat energy depends on mass, specific heat and temperature change; absolute pressure = gauge pressure + atmospheric pressure.
- Trigonometry resolves vectors: opposite = hypotenuse × sin θ; adjacent = hypotenuse × cos θ. Check significant figures and unit conversions.
Worked example
A pump raises 10 m³ of water per minute through 20 m. Flow Q = 10/60 = 0.1667 m³/s. Hydraulic power = ρgQH = 1000 × 9.81 × 0.1667 × 20 = 32,700 W, or 32.7 kW. If the pump efficiency is 80%, shaft input = 32.7 / 0.80 = 40.9 kW. The reasoning shows why efficiency divides the hydraulic output when calculating required input.
Traps
Do not use diameter instead of radius in area calculations. Do not mix litres and cubic metres. Do not add gauge and absolute pressures. Do not multiply by efficiency when you need input power; divide. Check whether the question asks for power, energy or head.