PE Mechanical HVAC cheat sheet

1 ton of refrigeration = 12,000 Btu/h = 200 Btu/min = 3.517 kW; kW/ton = 12/EER = 3.517/COP.

Sensible air heat: Q (Btu/h) = 1.08 x cfm x delta-T (F), based on standard air at 0.075 lbm/ft3 and cp = 0.24 Btu/(lbm-F).

Sensible water heat: Q (Btu/h) = 500 x gpm x delta-T (F) for water near 60 F.

Pressure conversions: 1 psi = 2.31 ft H2O = 27.7 in. H2O; 1 in. w.c. = 0.0361 psi = 249.1 Pa.

Standard atmosphere: 14.696 psia = 101.325 kPa = 29.92 in. Hg = 33.9 ft H2O.

Power conversions: 1 hp = 550 ft-lbf/s = 2545 Btu/h = 0.7457 kW; 1 kW = 3412 Btu/h.

Air horsepower = (cfm x total pressure in in. w.c.) / (6356 x efficiency); pump horsepower = (gpm x psi) / (1714 x efficiency).

EER = Btu/(W-h); COP = EER/3.412. SEER and HSPF are seasonal part-load ratings and are not interchangeable with design-point COP.

Affinity laws: flow proportional to speed, head proportional to speed squared, power proportional to speed cubed; same exponents apply to impeller diameter.

Closed-system first law: Q - W = delta-U. For a steady-flow control volume: q - w = delta-h + delta-KE + delta-PE.

Carnot COP with absolute temperatures: refrigerator = TL/(TH - TL); heat pump = TH/(TH - TL).

Ideal gas: pv = RT and cp - cv = R. For air, R = 53.35 ft-lbf/(lbm-R) = 287 J/(kg-K), cp = 0.240 Btu/(lbm-R), k = 1.4.

Isentropic ideal-gas relations: T2/T1 = (p2/p1)^((k-1)/k) = (v1/v2)^(k-1).

A throttling device is adiabatic and produces no work, so enthalpy is constant across it while pressure, temperature, and availability drop.

Rankine cycle: pump work is approximately v x delta-p; turbine work is h-in minus h-out; boiler and condenser duties use latent enthalpy.

Saturated mixture enthalpy: h = hf + x hfg, so quality x = (h - hf)/hfg.

Second-law (exergy) efficiency of a cycle is actual COP divided by the reversible COP between the same source and sink temperatures.

Entropy: delta-s = integral of dQ/T along a reversible path; delta-s = 0 for isentropic and greater than zero for any real adiabatic process.

Humidity ratio W = 0.621945 x pw / (p - pw); W does not change during sensible heating or cooling.

Relative humidity phi = pw / psat(Tdb); degree of saturation mu = W / Wsat at the same dry-bulb temperature.

Moist-air enthalpy per lbm of dry air: h = 0.240 T + W (1061 + 0.444 T), with T in F.

Humid volume v = 0.3705 T(R) (1 + 1.607 W) / p(psia), in ft3 per lbm dry air.

Dew point lies at constant W: solve pw = W p / (0.621945 + W), then take the saturation temperature at pw.

Sensible heat ratio SHR = Qs / (Qs + Ql); on the chart it sets the slope of the room process line from the room condition.

Coil bypass factor BF = (h2 - hADP) / (h1 - hADP), and coil SHR = (h1 - h2) / (h1 - hADP), where point 2 lies on the line from 1 to the apparatus dew point.

For air-water mixtures the thermodynamic wet-bulb temperature equals the adiabatic saturation temperature, so the constant wet-bulb line is nearly a constant-enthalpy line.

Standard air at sea level is 0.075 lbm/ft3 (13.33 ft3 per lbm), roughly 70 F dry air at 14.696 psia.

Reynolds number Re = rho V D / mu = V D / nu; pipe flow is laminar below about 2300 and turbulent above about 4000.

Darcy-Weisbach: hf = f (L/D)(V^2/2g), with f = 64/Re in laminar flow.

Colebrook / Swamee-Jain: 1/sqrt(f) = -2 log10( roughness/(3.7D) + 2.51/(Re sqrt(f)) ).

Minor losses: h = K V^2/(2g); when K is unknown, use an equivalent length added to the pipe length.

Energy equation: p1/gamma + V1^2/2g + z1 + hpump = p2/gamma + V2^2/2g + z2 + hloss.

For standard air, velocity pressure VP (in. w.c.) = (V/4005)^2, and V (fpm) = 4005 sqrt(VP).

Hydraulic diameter Dh = 4A/P (four times flow area over wetted perimeter) extends round-duct friction and Reynolds correlations to rectangular ducts.

NPSH available = (p_atm - p_vapor)/gamma + z - hloss; it must exceed the pump NPSH required to avoid cavitation.

Pump and fan laws: Q proportional to N, H proportional to N^2, P proportional to N^3; the system curve is H = K Q^2.

Fourier conduction: q = k A delta-T / L, so conduction resistance R = L/(k A).

Convection: q = h A delta-T with resistance R = 1/(h A); radiation: q = epsilon sigma A (Ts^4 - Tsurr^4).

Stefan-Boltzmann constant sigma = 0.1714e-8 Btu/(h-ft2-R4) = 5.67e-8 W/(m2-K4).

Overall coefficient: 1/(U A) = sum of series resistances (wall layers, fouling, inside and outside films); U is referred to a stated area.

LMTD = (dT1 - dT2)/ln(dT1/dT2) and q = U A LMTD; counterflow yields the largest LMTD for given terminal temperatures.

Effectiveness-NTU: epsilon = q/qmax and NTU = UA/Cmin; epsilon increases with NTU and with Cmin/Cmax approaching 1.

Critical insulation radius r_c = k/h; adding insulation to a small pipe increases heat loss until the outer radius exceeds r_c.

Fin efficiency for a straight rectangular fin: eta = tanh(mL)/(mL) with m = sqrt(h P/(k Ac)).

Biot number Bi = h Lc/k; when Bi < 0.1, internal gradients are negligible and the lumped-capacitance method applies.

ASHRAE 62.1 breathing-zone outdoor airflow: Vbz = Rp Pz + Ra Az; uncorrected total Vou = sum of Vbz, and system intake Vot = Vou / Ev.

Low-velocity duct design commonly uses 0.1 in. w.c. per 100 ft of supply duct, with roughly 0.08 in. w.c. per 100 ft on return.

Fan total static pressure equals the sum of the external system static plus internal losses from coils, filters, and accessories that the rating point excludes.

Typical design air quantities: about 400 cfm per ton, corresponding to roughly a 20 F supply-to-room temperature difference.

Chilled-water plants commonly run 42-45 F supply, 55-58 F return, giving a design delta-T of about 12-16 F.

ASHRAE 90.1 economizer requirements are triggered above a capacity threshold that varies with climate zone; air economizers use outdoor air when its temperature or enthalpy is below the return air.

VAV systems reduce system ventilation efficiency Ev as boxes throttle toward minimum, so the outdoor-air intake must be based on the worst-case (lowest) Ev.

Coil leaving-air conditions are set by the apparatus dew point and bypass factor; a lower ADP removes more latent heat and lowers the coil sensible heat ratio.

Fan heat gain raises supply-air temperature and is roughly 0.5-1.5 F at typical system static pressures, and must be included in the space cooling load.

Ideal vapor-compression cycle: 1-2 isentropic compression, 2-3 constant-pressure condensation, 3-4 isenthalpic expansion, 4-1 constant-pressure evaporation.

Refrigerating COP = (h1 - h4)/(h2 - h1); evaporator capacity = m_dot (h1 - h4).

Added suction superheat improves compressor protection but lowers suction density and slightly reduces capacity and COP.

Liquid subcooling ahead of the expansion valve increases refrigerating effect and COP by lowering h4.

TXV and EEV control evaporator outlet superheat; too little superheat risks liquid floodback, too much starves the coil.

R-410A is a near-azeotropic HFC blend with negligible temperature glide; R-407C is zeotropic with a glide of roughly 10 F that affects charging and coil performance.

Chiller efficiency: kW/ton = 3.517/COP = 12/EER; centrifugal machines commonly rate about 0.5-0.6 kW/ton at design.

Condenser approach = leaving condensing temperature minus entering cooling-water temperature; 1-3 F indicates a clean water-cooled condenser, and a rising approach signals fouling.

Compressor selection by capacity: reciprocating and scroll for small systems, screw for mid-range, centrifugal for large chillers.