PE Mechanical cheat sheet

1 ton of refrigeration = 12,000 Btu/h = 200 Btu/min = 3.517 kW; 1 hp = 2,545 Btu/h = 0.746 kW; 1 kWh = 3,412 Btu.

Sensible air load: Qs = 1.08 x cfm x dT (Btu/h). Latent air load: QL = 4,840 x cfm x dW (W in lb/lb), or about 0.68 x cfm x dGrains.

Water circuits and coils: Q = 500 x gpm x dT (Btu/h), derived from 8.33 lb/gal x 60 min/h x cp = 1.0 Btu/lb-F.

Fan and pump affinity laws: flow proportional to speed, head or static pressure proportional to speed squared, power proportional to speed cubed; impeller-trim laws use diameter in place of speed.

Standard air at 70 F and sea level: density 0.075 lb/ft3, cp = 0.240 Btu/lb-F, specific volume 13.3 ft3/lb, gas constant R = 53.35 ft-lbf/lb-R.

Temperature conversion: F = 1.8(C) + 32; a 1 C difference equals a 1.8 F difference; absolute Rankine = F + 459.67.

Darcy-Weisbach: dP = f (L/D)(rho V^2/2); duct friction charts assume 0.075 lb/ft3 air and absolute roughness near 0.0003 to 0.001 ft for galvanized duct.

Frequently cited ASHRAE standards: 62.1 (ventilation), 90.1 (energy), 15 (refrigerating system safety), 55 (thermal comfort), 34 (refrigerant designation and safety classification).

Humidity ratio W = 0.622 x p_w / (P - p_w) lb water per lb dry air; sensible heating or cooling at constant pressure does not change W.

Moist air enthalpy h = 0.240T + W(1061 + 0.444T) Btu/lb dry air, with T as dry-bulb temperature in F.

Specific volume v = 0.3705 x T(R) x (1 + 1.6078W) / P(psia) ft3/lb dry air; moist-air density = (1 + W)/v.

Relative humidity = p_w / p_ws x 100% at the same dry bulb; dew point is the saturation temperature corresponding to the current humidity ratio.

For air-water vapor, thermodynamic wet-bulb temperature equals adiabatic saturation temperature; constant wet-bulb lines fall between constant-enthalpy and constant-W lines on the chart.

Coil relation: h_leaving = h_ADP + BF(h_entering - h_ADP); BF = (h_leaving - h_ADP)/(h_entering - h_ADP); contact factor = 1 - BF.

Sensible heat ratio SHR = Qs/(Qs + QL); the room process line slope on the chart is set by SHR and the supply-air condition lies on that line.

Chart orientation per ASHRAE: constant dry-bulb lines are vertical, constant humidity-ratio lines horizontal, and the saturation curve bounds the chart at upper left.

Air density correction: rho = 1.325 x P(in. Hg)/T(R) lb/ft3; capacity corrections run roughly 1% per 1,000 ft of altitude and about 1% per 10 F at fixed cfm.

Envelope conduction: Q = U x A x dT, with U = 1/R_total; R = thickness/k plus film resistances (about 0.17 inside and 0.68 outside, ft2-F-Btu/h).

CLTD/CLF method: Q = U x A x CLTD_corrected, with corrections for latitude and month, wall color, attic or duct location, and indoor design temperature.

Fenestration solar gain: Q = A x SHGC x incident solar irradiance; west glass peaks mid-to-late afternoon even though solar noon is earlier.

Thermal mass delays and attenuates conduction, so peak space load lags peak outdoor temperature; cooling load factors (CLF) account for storage, greatest for floors, roofs, and heavy walls.

Ventilation and infiltration: Qs = 1.08 x cfm x dT and QL = 4,840 x cfm x dW; minimum outdoor airflow is set by ASHRAE 62.1.

Internal gains: people about 250 Btu/h sensible and 200 Btu/h latent for light office work; lighting 3.412 Btu/h per watt; equipment from nameplate with a diversity factor.

Heating degree days: HDD = sum of (65 F - daily mean temperature) over the season; annual heating energy scales with 24 x HDD x UA divided by efficiency.

Design margins of roughly 5 to 10% are commonly applied to the block equipment load rather than added item by item to each room load.

Sensible effectiveness = (T_OA,in - T_OA,out)/(T_OA,in - T_EA,in), referenced to the airstream with the smaller capacity rate; total effectiveness uses enthalpy in place of temperature.

Latent effectiveness = (W_OA,in - W_OA,out)/(W_OA,in - W_EA,in); total effectiveness combines sensible and latent performance and governs enthalpy-wheel selection.

Counterflow and close-coupled arrangements yield higher effectiveness than parallel flow; rotary wheels typically achieve 50 to 80% total effectiveness.

Sensible-only devices (heat pipes, runaround coils, plate sensible exchangers) transfer no moisture and prevent cross-contamination between airstreams.

Enthalpy wheels transfer moisture and may carry trace contaminants; purge sections limit carryover, and frost forms when exhaust-side surface temperature drops below freezing.

Runaround coil loops circulate a glycol solution with a pump and three-way valve, and are used when supply and exhaust ducts are far apart.

ASHRAE 90.1 requires exhaust-air energy recovery above specified supply-airflow and outside-air-fraction thresholds, typically with a minimum of 50% enthalpy recovery effectiveness.

Energy recovery lowers coil loads but adds fan and wheel pressure drop; the resulting leaving-air condition must still be checked against the required supply condition.

VAV systems modulate supply airflow at a fixed supply temperature; CAV systems hold constant airflow and vary supply temperature, reheat, or coil capacity.

Cooling tower range = entering water temperature - leaving water temperature; approach = leaving water temperature - entering wet-bulb temperature; smaller approach requires more fill and fan power.

Chiller efficiency conversions: kW/ton = 12/EER = 3.517/COP; COP = EER/3.412.

Duct velocity pressure VP = (V/4005)^2 in. w.g. for standard air; total pressure = static pressure + velocity pressure.

Equal-friction duct sizing holds a constant friction rate, commonly 0.08 to 0.10 in. w.g. per 100 ft; the static-regain method trades higher initial velocity for lower total pressure loss.

Air-side economizer is available when outside-air enthalpy (or dry bulb) is below the return-air value; it requires modulating dampers, changeover control, and fault-detection shutdown.

AHU coil face velocity is typically held to 400 to 500 fpm to prevent condensate carryover; rows, fin spacing, and bypass factor determine the achievable apparatus dew point.

Total fan static pressure must cover filters, coils, dampers, ductwork, and terminal boxes; selection uses a dirty-filter allowance because pressure drop rises as filters load.

Boiler combustion (stack) losses dominate efficiency; a 40 F reduction in stack temperature improves efficiency by roughly 1 percentage point.

Vapor-compression cycle: isentropic compression, constant-pressure desuperheating and condensation, isenthalpic expansion, then constant-pressure evaporation.

COP = refrigeration effect / compressor work; Carnot COP = T_L/(T_H - T_L) with absolute temperatures, and real machines reach roughly 40 to 60% of Carnot.

Mass flow = capacity / refrigeration effect (Btu/lb); required compressor displacement = mass flow x suction specific volume.

Evaporator superheat protects the compressor from liquid slugging; condenser subcooling increases refrigeration effect and prevents flash gas at the expansion valve.

Zeotropic blends have temperature glide between bubble and dew points, which affects charging method, leak detection, and evaporator and condenser selection.

ASHRAE 34 safety groups: A1 indicates lower toxicity and no flame propagation; A2, A2L, A3, and B classes indicate flammability or higher toxicity.

Condensing temperature tracks the cooling medium: roughly 10 to 15 F above ambient for air-cooled units and 5 to 10 F above leaving condenser water for water-cooled units.

Compressor selection: reciprocating and scroll for small and medium capacities, screw for medium and large, centrifugal for large; surge is the low-flow limit of centrifugal machines.

PID output = Kp(e) + Ki(integral of e dt) + Kd(de/dt); proportional acts on present error, integral removes offset, derivative damps the rate of change.

Proportional band (%) = 100/Kp; a narrow band gives fast response with possible cycling, a wide band gives stable control with larger offset.

Proportional-only control leaves a steady-state offset; integral action shifts the output until the error returns to zero.

Direct-acting controllers increase output as the measured variable rises; reverse-acting controllers decrease it. Valve and damper fail positions are set by actuator spring return.

Typical fail positions: heating valves and outdoor-air dampers fail closed, while cooling-coil valves and return dampers fail open to protect coils in freezing weather.

Sensor comparison: RTDs (platinum) are stable and near-linear; thermistors are more sensitive but nonlinear and range-limited; thermocouples span wide ranges with low output and need cold-junction compensation.

Accuracy is closeness to the true value; precision is repeatability. Transmitter error is usually stated as percent of span rather than percent of reading.

BACnet and Modbus are common building automation protocols; BACnet objects and services support scheduling, trending, and alarm and event reporting.

Static-pressure reset lowers the supply-fan setpoint as VAV boxes open, and supply-air-temperature reset raises discharge temperature at low load, both reducing fan and reheat energy.