Power Eng 4th Class 4B cheat sheet

A boiler is a closed pressure vessel in which water is heated to produce steam or hot water at pressures above atmospheric; ASME BPVC Section I governs power boilers, Section IV governs heating boilers.

Safety valve capacity must equal or exceed the maximum evaporating capacity of the boiler; the valve is set at or below the maximum allowable working pressure (MAWP) and is the final overpressure protection.

A try-cock or gauge glass gives the operator a direct water-level indication; the lowest visible level in the gauge glass must be at least 75 mm above the highest point of the heating surface for firetube boilers.

Three-element feedwater control uses steam flow, feedwater flow, and drum level signals to correct level without fighting swell or shrinkage during load changes.

Water column and gauge glass connections must be blown down daily; an obstructed water column can show a false level and lead to low-water trip or carryover.

A low-water fuel cutoff must be tested by evaporating or draining water while firing; the burner must shut off before the water drops below the safe limit.

Boiler efficiency (indirect method) = 100% minus stack losses, unburned carbon, moisture, and radiation losses; each 20 °C reduction in flue gas temperature raises efficiency roughly 1%.

Steam drum internals: cyclone separators remove bulk moisture, scrubbers remove fine droplets, and the dry pipe delivers steam with less than about 0.5% moisture.

Theoretical (stoichiometric) air for natural gas is about 9.5 m³ air per m³ gas; for fuel oil about 14 kg air per kg oil. Excess air is measured as O₂ in flue gas - typically 3% O₂ for gas, 4–5% for oil.

Flue gas O₂ and CO₂ are inversely related: as excess air rises, O₂ rises and CO₂ falls; a sudden CO rise signals incomplete combustion and possible flame impingement.

Draft is the pressure difference between the furnace and atmosphere; natural draft depends on stack height and temperature difference (Δp ≈ h × (ρ_air − ρ_gas) × g).

Forced draft fans pressurize the furnace; induced draft fans pull flue gas to the stack; balanced draft keeps the furnace slightly negative (about −0.05 to −0.1 kPa).

A flame scanner (UV or IR) detects flame presence; loss of flame signal must trip the fuel valve within the safety timing (typically 1 second for the main flame).

Purge before light-off: at least 5 air changes of the furnace and flue at 25–50% airflow to clear combustible gases before introducing fuel.

Fuel/air ratio control: a cross-limited control system prevents air from leading fuel on load increase and fuel from leading air on load decrease.

Combustion efficiency from flue gas: efficiency ≈ 100 − (stack loss) − (radiation); stack loss rises with flue gas temperature and excess air.

External treatment removes impurities before the boiler: softeners exchange Ca²⁺/Mg²⁺ for Na⁺; demineralizers use cation and anion resins; reverse osmosis removes 95–99% of dissolved solids.

Internal treatment: phosphate or polymer programs precipitate or condition hardness; oxygen scavengers (sulfite or hydrazine) remove dissolved O₂; amines raise condensate pH.

Blowdown controls dissolved solids: continuous surface blowdown removes TDS, bottom blowdown removes sludge. Blowdown rate (%) ≈ (feedwater TDS / (boiler water TDS limit − feedwater TDS)) × 100.

Scale is the largest efficiency penalty: 1 mm of scale can raise fuel use by 5–10% because scale conductivity is about 1/40 that of steel.

Carryover causes superheater fouling and turbine deposits; causes include high TDS, high alkalinity, foaming, and sudden load swings.

pH control: boiler water pH 10.5–11.5 for steel protection; condensate pH 8.5–9.5 to limit CO₂ corrosion; below pH 8.5 indicates carbonic acid attack.

Silica limits depend on pressure: below 4 MPa about 150 mg/L; above 10 MPa below 0.5 mg/L to prevent silica carryover into steam.

A deaerator heats feedwater to saturation (about 105 °C at 0.12 MPa) and strips O₂ to below 0.005 mg/L; it also serves as the feedwater storage tank.

Centrifugal pump head H = (p_discharge − p_suction)/(ρg) + (v_d² − v_s²)/(2g) + Δz; flow varies with impeller speed per the affinity laws: Q ∝ N, H ∝ N², P ∝ N³.

NPSH available = (p_suction/(ρg) + v²/(2g)) − vapour pressure head; cavitation occurs when NPSH available falls below NPSH required.

Best efficiency point (BEP) is where a centrifugal pump should operate; running far left or right of BEP causes recirculation, vibration, and seal failure.

Positive displacement pumps deliver nearly constant flow against varying pressure; a relief valve on the discharge is mandatory because the pump can overpressure the line.

Reciprocating compressors use clearance volume; volumetric efficiency falls as clearance or pressure ratio rises. Multistage compression with intercooling reduces work.

Centrifugal compressors surge when flow falls below the surge line; anti-surge control recycles flow to protect the machine.

Fan laws mirror pump affinity laws: for a fan, Q ∝ N, static pressure ∝ N², power ∝ N³.

Air receiver sizing and aftercoolers: cooling compressed air to 40 °C condenses water; drains must be trapped to remove condensate without losing air.

Gate valves are for isolation (low pressure drop, not for throttling); globe valves are for throttling; check valves permit one-direction flow; ball and butterfly valves give quick quarter-turn isolation.

Safety relief valve set pressure is the MAWP; accumulation is normally limited to 10% above set pressure, and blowdown (reseating) is typically 4–7% below set.

Steam traps: thermodynamic (disc) traps for high-pressure drip legs; float-and-thermostatic traps for continuous condensate; inverted bucket traps for modulating loads; thermostatic traps for sensible heat removal.

A steam trap fails open = live steam loss; fails closed = waterlogging and water hammer. Test by ultrasonic, temperature, or sight-glass observation.

Pipe expansion: ΔL = L × α × ΔT; carbon steel α ≈ 0.012 mm/m·°C, so a 30 m line at 200 °C grows about 70 mm and needs expansion loops or slip joints.

Water hammer in steam lines comes from slug flow or rapid valve closure; prevention uses proper trapping, drainage at low points, and slow valve operation.

Steam pipe sizing: velocity limits are about 25–40 m/s for saturated steam mains and 40–60 m/s for superheated steam to limit erosion and pressure drop.

Pressure-reducing valves reduce steam pressure; a safety valve must be installed downstream of the PRV to protect the low-pressure side.

Sensible heat Q = 1.2 × L/s × ΔT (W) for air at standard conditions; latent heat is from moisture, and total heat = sensible + latent.

Psychrometrics: dry-bulb, wet-bulb, dew point, relative humidity, and enthalpy. Relative humidity = (actual vapour pressure / saturation vapour pressure) × 100%.

Cooling coil apparatus dew point (ADP): air leaves near saturation; bypass factor = (leaving DB − ADP)/(entering DB − ADP).

Air changes per hour (ACH) = (airflow in m³/h) / (room volume in m³); typical comfort ventilation is 2–6 ACH, and kitchens need 10–15 ACH.

Duct friction loss is proportional to velocity squared; equal-friction and static-regain methods are used to size ducts, and velocity limits are about 5–8 m/s for supply mains.

Chilled water ΔT design is typically 5–7 °C; a low ΔT syndrome indicates poor coil heat transfer or bypass, and it raises pump energy.

Vapour-compression cooling cycle: evaporator → compressor → condenser → expansion valve; COP = refrigeration effect / compressor work.

Heating load includes transmission (U × A × ΔT) and infiltration (1.2 × L/s × ΔT); ventilation air adds both sensible and latent load.

Refrigeration capacity: 1 tonne of refrigeration = 3.517 kW = 12,000 Btu/h = heat to melt 1 tonne of ice in 24 h.

COP = refrigerating effect / work input; for a Carnot cycle COP = T_evap / (T_cond − T_evap), with temperatures in kelvin.

Subcooling liquid before the expansion valve increases refrigerating effect; superheating suction gas protects the compressor but reduces capacity if excessive.

Refrigerants: R-134a (GWP 1430), R-410A (GWP 2088), R-717 ammonia (GWP 0, toxic), R-744 CO₂ (GWP 1, high pressure); phase-out under the Montreal Protocol and Kigali Amendment.

An expansion valve controls superheat at the evaporator outlet; a flooded evaporator uses a float or level control instead.

Low suction pressure causes: restricted expansion valve, frosted coil, low charge, or blocked filter-drier. High discharge pressure causes: dirty condenser, non-condensables, or high ambient.

Refrigerant leaks: never use open flame to detect; use electronic detectors, soap bubbles, or UV dye. Ammonia is detected by its odour at 5 ppm.

Purging non-condensables from a condenser lowers discharge pressure and improves COP; air in the system raises head pressure and power draw.

Ohm's law V = I × R; power P = V × I × PF for AC single phase, and P = √3 × V × I × PF for three phase.

Three-phase motor current I = P / (√3 × V × PF × efficiency); a 15 kW, 400 V, 0.85 PF, 90% efficient motor draws about 28 A.

Motor protection: overload relays protect against sustained overcurrent; fuses and breakers protect against short circuit; the two functions must be coordinated.

Star-delta starting reduces starting current to one third of direct-on-line; soft starters and VFDs give smoother acceleration and energy savings on variable loads.

Motor insulation classes: B (130 °C), F (155 °C), H (180 °C); a Class F motor run at Class B rise has longer life.

Locked-rotor current is typically 6–8 times full-load current; voltage dip during starting can trip other equipment on the same bus.

Ground fault protection detects current returning outside the intended path; a 30 mA residual current device protects personnel, and 300 mA protects equipment.

VFD cable must be shielded and grounded at both ends to control high-frequency noise; long motor leads need dv/dt filters to protect winding insulation.

A control loop has a sensor/transmitter, controller, and final control element; the error is setpoint minus measured variable.

PID control: proportional output = Kp × error; integral removes steady-state offset; derivative anticipates change and dampens overshoot.

Proportional band (%) = 100 / gain; a narrow band gives aggressive response and possible cycling; a wide band gives slow, stable response.

A 4–20 mA signal represents the process range; 4 mA is the live zero (zero percent) and 20 mA is 100%; a signal below 3.6 mA indicates a fault.

A thermocouple generates voltage from dissimilar metals; a resistance temperature detector (RTD) changes resistance with temperature and is more accurate and stable.

A transmitter calibrated 0–1000 kPa outputting 12 mA reads 500 kPa: value = (mA − 4)/16 × span + LRV.

Control valve fail-safe: air-to-open (fail-closed) or air-to-close (fail-open); the choice depends on whether the process is safer with the valve shut or open on air failure.

Loop tuning: Ziegler-Nichols ultimate gain method uses the proportional gain at which the loop cycles continuously (Ku) and the period (Pu) to set PID values.

Four-stroke diesel cycle: intake, compression, power, exhaust; the camshaft turns at half crankshaft speed. Two-stroke engines fire every revolution and use scavenging ports.

Compression ratio = (swept volume + clearance volume) / clearance volume; diesel ratios are 12:1 to 22:1, and higher ratios raise thermal efficiency.

Indicated power (single cylinder) = (mean effective pressure × stroke × area × revolutions per second × number of power strokes per revolution).

Brake thermal efficiency = brake power output / fuel energy input; typical diesel values are 35–45%, and combined-cycle gas turbines reach 60%.

Detonation (knock) in spark-ignition engines is uncontrolled ignition; it is limited by octane rating, ignition timing, and compression ratio.

Diesel engines are rated by continuous brake power; a generator set must be sized with a margin for starting loads and altitude/temperature derating.

Gas turbines: compressor, combustor, turbine, and generator; the compressor absorbs 50–60% of turbine work, so efficiency depends on firing temperature and pressure ratio.

Engine cooling and lubrication: jacket water at 80–90 °C; lube oil pressure typically 200–400 kPa; low oil pressure must trip the engine.

ASME Boiler and Pressure Vessel Code Section I (power boilers), Section IV (heating boilers), Section VIII (pressure vessels); CSA B51 covers boiler, pressure vessel, and piping code in Canada.

Boiler and Pressure Vessel Act requires periodic inspection and a valid certificate of inspection before operation; operating without one is an offence.

Confined space entry requires a permit, atmospheric testing (O₂ 19.5–23%, LEL below 10%, H₂S below 10 ppm), ventilation, attendant, and rescue plan.

Lockout/tagout: isolate all energy sources, verify zero energy, apply locks and tags by each worker; try the start button to confirm isolation.

WHMIS/GHS labels and safety data sheets (SDS) communicate chemical hazards; 16-section SDS format is standard.

Environmental limits: NOx from boilers is controlled by low-NOx burners, flue gas recirculation, and selective catalytic reduction; SO₂ is controlled by low-sulphur fuel or scrubbers.

Stack emissions monitoring: O₂, CO, NOx, and opacity; opacity is a visible measure of particulate, and continuous emission monitoring (CEM) may be required by permit.

Emergency response: a boiler low-water condition requires immediate fuel cutoff, no feedwater addition to a hot empty boiler, and controlled cooldown to avoid a brittle fracture.

Heat energy Q = m × c × ΔT; water c = 4.18 kJ/kg·°C; steam latent heat at atmospheric pressure is about 2257 kJ/kg.

Sensible and latent heat: total heat of steam h_g = h_f + h_fg; at 1 MPa, h_f ≈ 763 kJ/kg and h_fg ≈ 2015 kJ/kg.

Pressure conversions: 1 bar = 100 kPa = 14.5 psi; 1 atm = 101.325 kPa; gauge pressure = absolute pressure − atmospheric pressure.

Temperature conversion: °F = (°C × 9/5) + 32; K = °C + 273.15; always use absolute temperature in gas law calculations.

Ideal gas law PV = nRT; combined gas law P₁V₁/T₁ = P₂V₂/T₂ for a fixed mass; Boyle's law at constant T, Charles's law at constant P.

Boiler evaporation: 1 kg/h steam output requires about 1 kW of heat input at 100 °C feedwater and saturated steam; fuel input = output / efficiency.

Area and volume: pipe cross-section A = πd²/4; flow Q = A × v; tank volume = πr²h; 1 m³ = 1000 L.

Efficiency and cost: annual fuel cost = heat load / (efficiency × fuel heating value) × hours × fuel price; a 1% efficiency gain on a large boiler saves significant fuel.