BTEB Diploma in Marine Engineering Examination cheat sheet

Indicated power of a multi-cylinder engine: IP = (n × pm × L × A × N) / 60k, where pm is indicated mean effective pressure, L stroke, A bore area, N rpm, n cylinders, k = 1 for two-stroke and 2 for four-stroke.

Brake mean effective pressure: bmep = (brake power × 60 × k) / (n × L × A × N); mechanical efficiency = bp / ip and typically 0.80–0.90 for marine diesels.

Specific fuel consumption: sfoc = fuel mass flow / brake power, expressed in g/kWh; large slow-speed two-strokes commonly run 160–180 g/kWh.

Two-stroke uniflow scavenging uses exhaust valves and ports; scavenge air must exceed exhaust pressure, and air excess ratio is about 2.5–3.5 at full load.

Turbocharger matching: exhaust gas energy drives the turbine; a fouled air cooler or nozzle ring raises exhaust temperature and reduces scavenge pressure.

Diesel engine ignition delay is shortened by higher compression ratio and cetane number; knocking in CI engines follows prolonged ignition delay.

Propeller law: power varies approximately as shaft speed cubed (P ∝ N³) and thrust as N² for a fixed-pitch propeller in calm water.

Crankshaft deflection readings detect bedplate/engine misalignment; a change in sag or hog beyond maker limits indicates bearing wear or hull deformation.

Four-stroke medium-speed engines use trunk pistons and separate cylinder heads; two-stroke crosshead engines separate crankcase from scavenge space with a diaphragm.

Centrifugal pump affinity laws: Q ∝ N, H ∝ N², P ∝ N³; for impeller diameter change at constant speed, Q ∝ D, H ∝ D², P ∝ D³.

Pump net positive suction head available: NPSHa = (p_atm − p_vap)/(ρg) + static head − friction losses; cavitation occurs when NPSHa falls below NPSHr.

Positive displacement pumps deliver near-constant flow independent of discharge pressure; a relief valve must be fitted on the discharge side.

Fuel oil viscosity is controlled to about 10–15 cSt at injection by steam or thermal fluid heaters; viscosity above range causes poor atomisation and pump wear.

Purifier separation depends on density difference and centrifugal force; bowl speed and back-pressure disc size set the separation zone.

Fresh water generator uses jacket water heat; evaporation occurs under vacuum of roughly 90–95% vacuum so boiling is near 40–60 °C.

Air compressor intercooling reduces compression work and condensate is drained from intercoolers and air bottles; safety valves and fusible plugs protect receivers.

Steering gear is tested before departure: full port to starboard within 28 s at rated speed with one power unit, and emergency steering drill within 12 hours.

Archimedes principle: displacement (tonnes) = underwater volume (m³) × water density (t/m³); block coefficient CB = ∇ / (L × B × T).

TPC = (waterplane area × water density) / 100; FWA (mm) = displacement / (4 × TPC) for seawater-to-freshwater correction.

Longitudinal strength is analysed by simple beam theory: still-water bending moment plus wave-induced moment; hogging puts deck in tension, sagging puts bottom in tension.

Transverse framing uses floors, frames and beams; longitudinal framing uses girders, longitudinals and transverses, giving better buckling resistance in long ships.

Freeboard is assigned under the Load Line Convention; minimum bow height and hatch coaming heights depend on ship type and assigned freeboard.

Double bottom height is at least B/20 or 760 mm, whichever is greater, and tank capacity must satisfy MARPOL oil outflow rules.

GM (metacentric height) = KB + BM − KG; positive GM gives stable equilibrium; BM = I / ∇ for small angles of heel.

Watertight subdivision is governed by damage stability; collision bulkhead is located between 0.05L and 0.08L from the forward perpendicular.

Bilge and ballast systems use non-return valves and segregated lines; sounding pipes with self-closing cocks are fitted to all double-bottom tanks.

Three-phase power: P = √3 × V_L × I_L × cos φ; apparent power S = √3 × V_L × I_L in VA.

Synchronous generator frequency: f = (p × N)/120, where p is pole count and N rpm; a 4-pole machine at 1800 rpm gives 60 Hz.

Generator paralleling requires matching voltage, frequency and phase sequence; load sharing is set by governor droop (kW) and excitation (kVAr).

Insulation resistance is measured with a 500 V DC megger; minimum acceptable value is generally 1 MΩ, and readings are corrected to 40 °C.

Circuit breakers must be selected for breaking capacity above prospective short-circuit current; discrimination ensures the downstream breaker trips first.

Earthing systems: an insulated neutral distribution requires an earth fault detection relay; a hull-earthed system uses the ship's steel as return.

PID controller: proportional action responds to error, integral removes offset, derivative damps rate of change; integral windup is limited by anti-windup logic.

4–20 mA current loop is standard for marine transmitters because a broken wire reads below 4 mA and is detected as a fault.

Alternator voltage is controlled by the automatic voltage regulator acting on the exciter field; reactive load sharing depends on excitation balance.

First law for a closed system: Q − W = ΔU; for steady-flow open systems: Q − W = Δh + ΔKE + ΔPE.

Ideal gas law: pV = mRT; R = 287 J/(kg·K) for air and 8314 J/(kmol·K) universal.

Carnot efficiency: η = 1 − T_cold/T_hot, with absolute temperatures; no real engine between the same reservoirs can exceed it.

Diesel cycle efficiency depends on compression ratio r, cut-off ratio rc and k: η = 1 − (1/r^(k−1)) × (rc^k − 1)/(k(rc − 1)).

Entropy change for an ideal gas: Δs = cp ln(T2/T1) − R ln(p2/p1); reversible adiabatic processes are isentropic.

Specific heat relation: cp − cv = R and γ = cp/cv; for air γ ≈ 1.4, cp ≈ 1.005 kJ/(kg·K).

Boiler efficiency by indirect method = 100 − (sum of percentage losses: dry flue gas, moisture, radiation, unburnt carbon).

Steam quality x = (h − hf)/hfg; throttling calorimeter uses constant-enthalpy expansion to find dryness fraction of wet steam.

Continuity: A1V1 = A2V2 for incompressible flow; Bernoulli: p/(ρg) + V²/(2g) + z = constant along a streamline.

Reynolds number Re = ρVD/μ = VD/ν; flow is laminar below about 2000 and turbulent above about 4000 in pipes.

Darcy–Weisbach head loss: hf = f (L/D)(V²/2g); friction factor f from Moody chart depends on Re and relative roughness.

Fourier conduction law: Q = kA ΔT/L; thermal resistance of a plane wall R = L/(kA).

Newton's law of cooling: Q = hA(Ts − T∞); overall heat transfer coefficient 1/U = 1/hi + t/k + 1/ho plus fouling resistances.

Log mean temperature difference for heat exchangers: LMTD = (ΔT1 − ΔT2)/ln(ΔT1/ΔT2) for counterflow and parallel flow.

Pump/system curve intersection gives operating point; throttling moves the system curve, while speed change follows the affinity laws.

Heat exchanger effectiveness ε = actual heat transfer / maximum possible heat transfer; NTU = UA/Cmin.

Carbon content in steel: mild steel up to about 0.25% C, medium carbon 0.25–0.6%, high carbon 0.6–1.4%; higher carbon raises hardness and lowers weldability.

Fe–C diagram: eutectoid at 0.8% C and 723 °C forms pearlite; austenite transforms to martensite on rapid quenching.

Tempering after hardening reduces brittleness and relieves internal stress; annealing softens and improves machinability.

Stainless steel 316 contains molybdenum for chloride resistance; 304 is the general-purpose austenitic grade.

Galvanic corrosion occurs where dissimilar metals contact in an electrolyte; the less noble metal becomes anodic and corrodes.

Sacrificial anodes of zinc or aluminium protect hull steel; impressed current cathodic protection uses inert anodes and a DC supply.

Bronze and gunmetal are copper alloys used for sea-water pump impellers and valve bodies because of corrosion resistance.

Tensile test gives yield strength, ultimate tensile strength and elongation; hardness tests include Brinell, Vickers and Rockwell.

Cutting speed V = πDN/1000 m/min; feed and depth of cut determine material removal rate MRR ≈ V × f × d.

Drilling feed and speed depend on material; centre punching before drilling prevents wander, and coolant controls heat and swarf clearance.

TIG welding suits thin sections and stainless steel with a non-consumable tungsten electrode and separate filler; MIG uses a consumable wire electrode.

Oxy-acetylene flame types: neutral (1:1), oxidising (excess oxygen) and carburising (excess acetylene); neutral flame suits general steel welding.

Welding defects include porosity, slag inclusion, lack of fusion and undercut; non-destructive tests are dye penetrant, magnetic particle, ultrasonic and radiography.

Lathe operations include turning, facing, taper turning and thread cutting; thread depth for a metric thread ≈ 0.6135 × pitch.

Tolerance and fits: clearance fit, interference fit and transition fit; H7/g6 is a common clearance fit, H7/p6 an interference fit.

Surface roughness Ra is the arithmetic mean deviation; surface finish improves with higher speed, smaller feed and sharp tooling.

MARPOL Annex I limits oily water discharge to 15 ppm from machinery space bilge; the oil filtering equipment and 15 ppm alarm must be operational.

MARPOL Annex VI sulphur limit is 0.50% m/m outside ECAs and 0.10% m/m inside ECAs; exhaust gas cleaning systems may be used as an equivalent.

Annex VI NOx Tier III applies to new ships in NOx ECAs; Tier II applies elsewhere, with Tier I for older engines.

Annex IV sewage discharge requires a comminuted and disinfected system or an approved treatment plant; untreated discharge is prohibited within 3 nm of land.

Annex V prohibits disposal of plastics anywhere; garbage record book entries are required for discharges and incineration.

Ballast water management requires an approved treatment system and a ballast water record book; exchange is acceptable only as a temporary measure.

Life-saving appliances: lifebuoys, lifejackets and immersion suits are inspected weekly; lifeboats and davits are launched and manoeuvred monthly.

Fire triangle: fuel, oxygen and heat; fixed CO2 systems must not be released until all personnel are accounted for and the space is sealed.

Emergency generator must start and supply emergency loads within 45 s; emergency fire pump must deliver at least two jets of water.

First-angle projection: the object is between observer and plane; third-angle projection places the plane between observer and object.

Scale drawing: representative fraction = drawing length / actual length; common scales are 1:50, 1:100 and 1:200.

Orthographic views are front, top and side; hidden edges are shown as dashed lines and centrelines as chain lines.

CAD layers control line type, colour and visibility; blocks group repeated symbols and reduce file size and editing effort.

Geometric tolerance symbols: straightness, flatness, circularity, cylindricity, parallelism and perpendicularity; datum features are identified by letters.

Equilibrium of a rigid body requires ΣF = 0 and ΣM = 0; a simply supported beam has two vertical reactions and a cantilever has fixed reactions.

Bending moment diagram: maximum moment in a simply supported beam under a central point load is WL/4; under UDL it is wL²/8.

Stress and strain: σ = F/A, ε = ΔL/L, Young's modulus E = σ/ε; shear stress τ = F/A and strain energy = ½FΔL.

Quadratic formula: x = [−b ± √(b² − 4ac)]/(2a); discriminant b² − 4ac determines real, repeated or complex roots.

Sine and cosine rules: a/sin A = b/sin B = c/sin C and c² = a² + b² − 2ab cos C for any triangle.

Derivative rules: d/dx(x^n) = nx^(n−1), d/dx(e^x) = e^x, d/dx(ln x) = 1/x; product and quotient rules apply to combined functions.

Definite integral gives area under a curve: ∫ from a to b of f(x) dx; integration by parts uses ∫u dv = uv − ∫v du.

Logarithm laws: log(ab) = log a + log b, log(a/b) = log a − log b, log(a^n) = n log a; ln x = 2.303 log10 x.

Determinant of a 2×2 matrix [[a,b],[c,d]] is ad − bc; a singular matrix has zero determinant and no unique inverse.

Arithmetic progression: nth term a + (n−1)d, sum n/2[2a + (n−1)d]; geometric progression: sum = a(1 − r^n)/(1 − r).

Mean = Σx/n; variance = Σ(x − x̄)²/n; standard deviation is the square root of variance.

Newton's second law: F = ma; weight W = mg with g ≈ 9.81 m/s²; momentum p = mv and impulse = change in momentum.

Work = force × distance in the direction of force; power = work/time; kinetic energy = ½mv² and potential energy = mgh.

Ohm's law V = IR; power P = VI = I²R = V²/R; resistors in series add, in parallel 1/R = 1/R1 + 1/R2.

Boyle's law pV = constant at constant temperature; Charles's law V/T = constant at constant pressure; combined gas law pV/T = constant.

Heat quantity Q = mcΔT; latent heat Q = mL; specific heat of water is 4.186 kJ/(kg·K).

Wave speed v = fλ; sound travels about 340 m/s in air and about 1500 m/s in seawater, faster in denser medium.

Archimedes principle: buoyant force equals weight of displaced fluid; a floating body displaces its own weight of fluid.

Pascal's law: pressure applied to a confined fluid is transmitted equally in all directions; hydraulic press force ratio = area ratio.

Break-even quantity = fixed cost / (selling price − variable cost per unit); contribution margin = price − variable cost.

Depreciation by straight line = (cost − salvage value)/useful life; reducing balance applies a fixed percentage to book value each year.

Gross profit = sales − cost of goods sold; net profit = gross profit − operating expenses; current ratio = current assets/current liabilities.

Inventory turnover = cost of goods sold / average inventory; a low turnover indicates excess stock or slow-moving spares.

Planned maintenance system records jobs by running hours and calendar intervals; condition monitoring includes vibration, thermography and oil analysis.

ISM Code requires a safety management system, designated person ashore, master's overriding authority and documented procedures with records.

STCW requires rest hours of at least 10 hours in any 24-hour period and 77 hours in any 7-day period; watchkeepers must hold valid certificates.

Code of conduct: report unsafe practices, refuse to falsify records, and maintain confidentiality of commercial information.

Before any workshop task, isolate the machine, apply lockout/tagout, and confirm zero energy state by test.

Personal protective equipment for grinding: face shield, safety goggles, hearing protection and dust mask; the tool rest gap is kept below 3 mm.

Machine guards must be in place before starting a lathe or drill; never leave a chuck key in the chuck.

Hot work permit requires gas-free certificate, fire watch, removal of combustible material and standby firefighting equipment.

Engine room simulator: before starting the main engine, confirm turning gear disengaged, jacket water and LO pumps running, and starting air pressure adequate.

Blackout drill sequence: emergency generator auto-start, restore essential services, then restart main generator and re-establish power.

Oil analysis reports wear metals in ppm; rising iron with rising chromium suggests cylinder liner and ring wear.

Attachment logbook records tasks, dates, supervisor sign-off and machinery type; entries must be factual and verifiable.

Pressure test of a system uses 1.5 times design pressure for strength and 1.1 times for tightness, unless the code specifies otherwise.

Section views use hatching at 45°; adjacent parts are hatched in opposite directions to distinguish them.

Dimensioning rules: place dimensions outside the outline, avoid duplicate dimensions, and use the same unit throughout the drawing.

A tolerance stack-up is the sum of individual tolerances; worst-case method adds all tolerances, statistical method uses root-sum-square.

Moment of inertia of a rectangle about its centroidal axis: I = bd³/12; for a circle I = πd⁴/64.

Parallel axis theorem: I = I_centroid + Ad²; used to find section modulus Z = I/y.

Truss analysis by method of joints: ΣF = 0 at each joint; a member in tension pulls on the joint, compression pushes.

Friction force F = μN; on an inclined plane the angle of repose satisfies tan θ = μ.

Factor of safety = ultimate stress / allowable stress; fatigue failure occurs below ultimate strength after repeated cyclic loading.