ROC-M Exam cheat sheet

Torque T = F × r; power P = T × ω, with ω in rad/s (ω = 2πN/60 for N in rpm).

Shaft power (kW) = 2πNT/60 000 when torque is in N·m and speed in rpm.

Shaft horsepower = T(lb·in) × N(rpm) / 63 025.

Mechanical advantage = load / effort; velocity ratio = effort distance / load distance; efficiency = MA / VR.

Belt drive ratio = driver pulley diameter / driven pulley diameter; belt speed v = πDN.

Gear ratio = teeth on driven gear / teeth on driver gear; torque multiplies by the ratio, speed divides by it.

Bearing life: L10 = (C/P)^p million revolutions, p = 3 for ball bearings and 10/3 for roller bearings.

Shaft stress: torsional shear τ = 16T/(πd³); combined bending and torsion uses equivalent moment Me = 0.5[M + √(M² + T²)].

Boiler horsepower = 33 475 Btu/h ≈ 9.81 kW; one boiler hp evaporates about 34.5 lb of water per hour at 212 °F.

ASME Section I governs power boilers; Section IV governs heating boilers; Section VIII governs unfired pressure vessels.

Thin-cylinder hoop stress = Pr/t; longitudinal stress = Pr/2t, so hoop stress governs wall thickness.

ASME Section VIII Division 1 shell thickness t = PR/(SE − 0.6P) plus corrosion allowance.

Safety valve capacity must equal or exceed the maximum rated steam-generating capacity of the boiler.

A low-water cutoff is a required protective device; it must be tested and the burner locked out on low water.

Try-cocks and a gauge glass confirm water level; the gauge glass is the primary day-to-day level indicator.

Boiler efficiency = heat absorbed / heat input; stack loss rises with excess air and high flue-gas temperature.

Hydrostatic test pressure for new Section VIII vessels is typically 1.3 × MAWP, adjusted for temperature.

Pump power P(kW) = Q(m³/s) × H(m) × ρ(kg/m³) × 9.81 / efficiency.

Pump head in metres H = (pressure difference in Pa) / (ρ × 9.81).

Affinity laws: flow ∝ N, head ∝ N², power ∝ N³; flow ∝ D, head ∝ D², power ∝ D³ for impeller diameter D.

NPSH available must exceed NPSH required by a margin to avoid cavitation; NPSHa = (ps − pv)/(ρg) + z − hf.

Specific speed Ns = N√Q / H^0.75; low Ns favors radial flow, high Ns favors mixed and axial flow.

Centrifugal pumps are constant-head machines; positive-displacement pumps are essentially constant-flow machines.

Compressor polytropic power depends on n/(n−1) and pressure ratio; intercooling reduces work and discharge temperature.

Vibration severity is judged against ISO 10816/20816 zone limits; rising trend matters more than a single reading.

Alignment should be checked with laser or dial-indicator methods; thermal growth offsets are set at cold alignment.

Darcy-Weisbach head loss hf = f (L/D)(v²/2g); friction factor f depends on Reynolds number and relative roughness.

Reynolds number Re = ρvD/μ; Re < 2000 is laminar, Re > 4000 is turbulent.

Hazen-Williams head loss: hf = 10.67 L Q^1.852 / (C^1.852 D^4.87) in SI units.

Water hammer pressure surge ≈ ρ c Δv, where c is the pressure-wave speed in the pipe.

ASME B31.1 covers power piping; B31.3 covers process piping; B31.5 covers refrigeration piping.

Pipe schedule number ≈ 1000 × P/S, where P is internal pressure and S is allowable stress.

Gate valves are for isolation, globe valves for throttling, check valves for one-way flow, and relief valves for overpressure protection.

A valve's flow coefficient Cv is the flow of water in US gpm at 1 psi drop; use the choked-flow check for gases.

Sensible heat Q = 1.08 × cfm × ΔT(°F) for air at standard conditions; Q = 4.5 × cfm × Δh for total heat.

Water heating/cooling Q(Btu/h) = 500 × gpm × ΔT(°F).

Refrigeration coefficient of performance COP = refrigerating effect / work input; heat-pump COP = heating effect / work input.

Carnot COP for cooling = Tc/(Th − Tc) with absolute temperatures; no real cycle exceeds it.

Refrigerant pressure-enthalpy cycle: compression, condensation, expansion, evaporation; superheat and subcooling are measured at evaporator and condenser outlets.

Cooling tower approach = leaving water temperature − entering wet-bulb temperature; range = entering water − leaving water.

Psychrometrics: relative humidity is the ratio of actual vapor pressure to saturation vapor pressure at the same dry-bulb temperature.

ASHRAE Standard 15 governs refrigerant safety classification and machinery-room requirements; Standard 34 defines refrigerant designations.

Air-side pressure drop and fan laws: fan flow ∝ speed, static pressure ∝ speed², power ∝ speed³.

Three-phase power P = √3 × VL × IL × power factor; single-phase P = V × I × power factor.

Motor full-load current is read from NEC Table 430.250; overload protection is sized per NEC Article 430.

Locked-rotor current is typically 5–8 times full-load current for induction motors.

Motor synchronous speed Ns = 120f/P, where f is frequency in Hz and P is the number of poles.

Slip = (Ns − Nr)/Ns; rated slip for standard induction motors is usually a few percent.

A variable-frequency drive controls motor speed by varying voltage and frequency together (V/Hz ratio) to hold flux.

Control loop terms: proportional output depends on error, integral removes offset, derivative responds to rate of change.

A PID controller tuned too aggressively shows oscillation; too much integral causes windup and overshoot.

Instrumentation signals: 4–20 mA is standard for analog transmitters, with 4 mA representing the live zero.

Preventive maintenance follows time or run-hour intervals; predictive maintenance acts on measured condition such as vibration, oil analysis, or thermography.

Non-destructive examination methods include visual, liquid penetrant, magnetic particle, ultrasonic, and radiographic testing.

Magnetic particle testing applies only to ferromagnetic materials; liquid penetrant works on nonporous surfaces of any material.

Ultrasonic thickness testing detects wall loss from corrosion and erosion; readings are compared against minimum required thickness.

Lubricant condition is tracked by viscosity, water content, particle count, and spectrometric wear metals.

Vibration analysis: unbalance shows 1× running speed, misalignment shows 2× and axial 1×, and bearing defects show high-frequency impacts.

A functional test verifies that a device operates as designed; a calibration verifies accuracy against a traceable standard.

Steam trap testing by ultrasonic or temperature methods identifies failed-open and failed-closed traps.

Lockout/tagout requires energy isolation, verification of zero energy, and removal of stored energy before work.

Confined-space entry requires atmospheric testing for oxygen, flammables, and toxics, plus an attendant and entry permit.

Hot work requires a permit, fire watch, and combustible-free area; gas testing precedes ignition.

NFPA 70 is the National Electrical Code; NFPA 85 covers boiler and combustion systems; NFPA 54 covers fuel gas.

OSHA 29 CFR 1910 Subpart H covers hazardous materials; Subpart S covers electrical safety.

ASME Boiler and Pressure Vessel Code establishes design, fabrication, and inspection rules; the National Board governs repairs and stamps.

A pressure-relief valve must be set at or below the maximum allowable working pressure and be tested and sealed.

Personal protective equipment is the last line of defense in the hierarchy of controls; elimination and engineering controls come first.

Incident reporting and root-cause analysis are required elements of a compliant safety management program.

Torque T = F × r; power P = T × ω, with ω in rad/s (ω = 2πN/60 for N in rpm).

Shaft power (kW) = 2πNT/60 000 when torque is in N·m and speed is in rpm.

Shaft horsepower = T(lb·in) × N(rpm) / 63 025.

Mechanical advantage = load / effort; velocity ratio = effort distance / load distance; efficiency = MA / VR.

Belt drive ratio = driver pulley diameter / driven pulley diameter; belt speed v = πDN.

Gear ratio = teeth on driven gear / teeth on driver gear; torque multiplies by the ratio, speed divides by it.

Bearing life L10 = (C/P)^p million revolutions, p = 3 for ball bearings and 10/3 for roller bearings.

Shaft torsional shear τ = 16T/(πd³); combined bending and torsion uses equivalent moment Me = 0.5[M + √(M² + T²)].

Boiler horsepower = 33 475 Btu/h ≈ 9.81 kW; one boiler hp evaporates about 34.5 lb of water per hour at 212 °F.

ASME Section I governs power boilers; Section IV governs heating boilers; Section VIII governs unfired pressure vessels.

Thin-cylinder hoop stress = Pr/t; longitudinal stress = Pr/2t, so hoop stress governs wall thickness.

ASME Section VIII Division 1 shell thickness t = PR/(SE − 0.6P) plus corrosion allowance.

Safety valve capacity must equal or exceed the maximum rated steam-generating capacity of the boiler.

A low-water cutoff is a required protective device; it must be tested and the burner locked out on low water.

Try-cocks and a gauge glass confirm water level; the gauge glass is the primary day-to-day level indicator.

Boiler efficiency = heat absorbed / heat input; stack loss rises with excess air and high flue-gas temperature.

Hydrostatic test pressure for new Section VIII vessels is typically 1.3 × MAWP, adjusted for temperature.

Pump power P(kW) = Q(m³/s) × H(m) × ρ(kg/m³) × 9.81 / efficiency.

Pump head in metres H = (pressure difference in Pa) / (ρ × 9.81).

Affinity laws: flow ∝ N, head ∝ N², power ∝ N³; flow ∝ D, head ∝ D², power ∝ D³ for impeller diameter D.

NPSH available must exceed NPSH required by a margin to avoid cavitation; NPSHa = (ps − pv)/(ρg) + z − hf.

Specific speed Ns = N√Q / H^0.75; low Ns favors radial flow, high Ns favors mixed and axial flow.

Centrifugal pumps are constant-head machines; positive-displacement pumps are essentially constant-flow machines.

Compressor polytropic power depends on n/(n−1) and pressure ratio; intercooling reduces work and discharge temperature.

Vibration severity is judged against ISO 10816/20816 zone limits; rising trend matters more than a single reading.

Alignment should be checked with laser or dial-indicator methods; thermal growth offsets are set at cold alignment.

Darcy-Weisbach head loss hf = f (L/D)(v²/2g); friction factor f depends on Reynolds number and relative roughness.

Reynolds number Re = ρvD/μ; Re < 2000 is laminar, Re > 4000 is turbulent.

Hazen-Williams head loss: hf = 10.67 L Q^1.852 / (C^1.852 D^4.87) in SI units.

Water hammer pressure surge ≈ ρ c Δv, where c is the pressure-wave speed in the pipe.

ASME B31.1 covers power piping; B31.3 covers process piping; B31.5 covers refrigeration piping.

Pipe schedule number ≈ 1000 × P/S, where P is internal pressure and S is allowable stress.

Gate valves are for isolation, globe valves for throttling, check valves for one-way flow, and relief valves for overpressure protection.

A valve's flow coefficient Cv is the flow of water in US gpm at 1 psi drop; use the choked-flow check for gases.

Sensible heat Q = 1.08 × cfm × ΔT(°F) for air at standard conditions; Q = 4.5 × cfm × Δh for total heat.

Water heating/cooling Q(Btu/h) = 500 × gpm × ΔT(°F).

Refrigeration coefficient of performance COP = refrigerating effect / work input; heat-pump COP = heating effect / work input.

Carnot COP for cooling = Tc/(Th − Tc) with absolute temperatures; no real cycle exceeds it.

Refrigerant pressure-enthalpy cycle: compression, condensation, expansion, evaporation; superheat and subcooling are measured at evaporator and condenser outlets.

Cooling tower approach = leaving water temperature − entering wet-bulb temperature; range = entering water − leaving water.

Psychrometrics: relative humidity is the ratio of actual vapor pressure to saturation vapor pressure at the same dry-bulb temperature.

ASHRAE Standard 15 governs refrigerant safety classification and machinery-room requirements; Standard 34 defines refrigerant designations.

Air-side pressure drop and fan laws: fan flow ∝ speed, static pressure ∝ speed², power ∝ speed³.

Three-phase power P = √3 × VL × IL × power factor; single-phase P = V × I × power factor.

Motor full-load current is read from NEC Table 430.250; overload protection is sized per NEC Article 430.

Locked-rotor current is typically 5–8 times full-load current for induction motors.

Motor synchronous speed Ns = 120f/P, where f is frequency in Hz and P is the number of poles.

Slip = (Ns − Nr)/Ns; rated slip for standard induction motors is usually a few percent.

A variable-frequency drive controls motor speed by varying voltage and frequency together (V/Hz ratio) to hold flux.

Control loop terms: proportional output depends on error, integral removes offset, derivative responds to rate of change.

A PID controller tuned too aggressively shows oscillation; too much integral causes windup and overshoot.

Instrumentation signals: 4–20 mA is standard for analog transmitters, with 4 mA representing the live zero.

Preventive maintenance follows time or run-hour intervals; predictive maintenance acts on measured condition such as vibration, oil analysis, or thermography.

Non-destructive examination methods include visual, liquid penetrant, magnetic particle, ultrasonic, and radiographic testing.

Magnetic particle testing applies only to ferromagnetic materials; liquid penetrant works on nonporous surfaces of any material.

Ultrasonic thickness testing detects wall loss from corrosion and erosion; readings are compared against minimum required thickness.

Lubricant condition is tracked by viscosity, water content, particle count, and spectrometric wear metals.

Vibration analysis: unbalance shows 1× running speed, misalignment shows 2× and axial 1×, and bearing defects show high-frequency impacts.

A functional test verifies that a device operates as designed; a calibration verifies accuracy against a traceable standard.

Steam trap testing by ultrasonic or temperature methods identifies failed-open and failed-closed traps.

Lockout/tagout requires energy isolation, verification of zero energy, and removal of stored energy before work.

Confined-space entry requires atmospheric testing for oxygen, flammables, and toxics, plus an attendant and entry permit.

Hot work requires a permit, fire watch, and combustible-free area; gas testing precedes ignition.

NFPA 70 is the National Electrical Code; NFPA 85 covers boiler and combustion systems; NFPA 54 covers fuel gas.

OSHA 29 CFR 1910 Subpart H covers hazardous materials; Subpart S covers electrical safety.

ASME Boiler and Pressure Vessel Code establishes design, fabrication, and inspection rules; the National Board governs repairs and stamps.

A pressure-relief valve must be set at or below the maximum allowable working pressure and be tested and sealed.

Personal protective equipment is the last line of defense in the hierarchy of controls; elimination and engineering controls come first.

Incident reporting and root-cause analysis are required elements of a compliant safety management program.