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Fluid Mechanics, HVAC & Refrigeration: formula sheet

Fluids, pumps, psychrometrics & plant rooms · 103 formulas · metric edition 1

The full study guide: modules, problems, answer key
Module 1 · Fluid Statics & Flow Fundamentals
Fluid Mechanics, HVAC & Refrigeration-1 Density
ρ=mV\rho = \tfrac{m}{V}
Mass per unit volume.
Fluid Mechanics, HVAC & Refrigeration-2 Specific Gravity
SG=ρρwaterSG = \frac{\rho}{\rho_{water}}
Density expressed as a multiple of water's 1000 kg/m³.
Fluid Mechanics, HVAC & Refrigeration-3 Hydrostatic Pressure (P = ρgh)
P=ρghP = \rho g h
Gauge pressure at depth h in a fluid of density ρ, using g = 9.80665 m/s².
Fluid Mechanics, HVAC & Refrigeration-4 Pressure Head (h = P/ρg)
h=Pρgh = \frac{P}{\rho g}
Converts a pressure into the equivalent height of a fluid column, with g = 9.80665 m/s².
Fluid Mechanics, HVAC & Refrigeration-5 Gauge and Absolute Pressure
Pabs=Pgauge+PatmP_{abs} = P_{gauge} + P_{atm}
Absolute pressure is the gauge reading plus the surrounding atmospheric pressure.
Fluid Mechanics, HVAC & Refrigeration-6 Volumetric Flow Rate (Q = Av)
Q=AvQ = A v
Flow through a duct or pipe: cross-sectional area times average flow velocity.
Fluid Mechanics, HVAC & Refrigeration-7 Continuity Equation (A₁v₁ = A₂v₂)
A1v1=A2v2A_1 v_1 = A_2 v_2
For incompressible flow, the same volume per second passes every cross-section of the pipe.
Fluid Mechanics, HVAC & Refrigeration-8 Pipe Velocity from Flow and Diameter
v=4QπD2v = \frac{4Q}{\pi D^{2}}
Average velocity in a full round pipe from volumetric flow and inside diameter: the first check on…
Fluid Mechanics, HVAC & Refrigeration-9 Dynamic Pressure (q = ½ρv²)
q=12ρv2q = \tfrac{1}{2} \rho v^{2}
The kinetic energy per unit volume of a moving fluid: the pressure of motion itself.
Fluid Mechanics, HVAC & Refrigeration-10 Velocity Head (h = v²/2g)
hv=v22gh_v = \frac{v^{2}}{2g}
The kinetic energy of a flow expressed as an equivalent column height, with g = 9.80665 m/s².
Fluid Mechanics, HVAC & Refrigeration-11 Bernoulli's Equation (Two Points)
P1+12ρv12+ρgz1=P2+12ρv22+ρgz2P_1 + \tfrac{1}{2}\rho v_1^{2} + \rho g z_1 = P_2 + \tfrac{1}{2}\rho v_2^{2} + \rho g z_2
Conservation of mechanical energy along a streamline: pressure, velocity and elevation trade…
Fluid Mechanics, HVAC & Refrigeration-12 Torricelli's Law (v = √(2gh))
v=2ghv = \sqrt{2 g h}
Speed of fluid jetting from an opening a depth h below the free surface, with g = 9.80665 m/s².
Fluid Mechanics, HVAC & Refrigeration-13 Reynolds Number
Re=ρvDμRe = \frac{\rho v D}{\mu}
The dimensionless ratio of inertial to viscous forces that decides laminar versus turbulent flow.
Fluid Mechanics, HVAC & Refrigeration-14 Laminar Friction Factor (f = 64/Re)
f=64Ref = \frac{64}{Re}
In laminar pipe flow the Darcy friction factor depends only on Reynolds number: roughness plays no…
Fluid Mechanics, HVAC & Refrigeration-15 Buoyant Force (Archimedes' Principle)
Fb=ρVgF_b = \rho V g
The upward force on a submerged body equals the weight of the fluid it displaces, with g = 9.80665…
Module 2 · Pipe Flow & Head Loss
Fluid Mechanics, HVAC & Refrigeration-16 Darcy–Weisbach Head Loss
hf=f LD v22gh_f = f \, \frac{L}{D} \, \frac{v^{2}}{2g}
The rigorous pipe friction equation: head loss from friction factor, length-to-diameter ratio and…
Fluid Mechanics, HVAC & Refrigeration-17 Swamee–Jain Friction Factor
f=0.25[log⁡10 ⁣(ε3.7D+5.74Re0.9)]2f = \frac{0.25}{\left[\log_{10}\!\left(\frac{\varepsilon}{3.7D} + \frac{5.74}{Re^{0.9}}\right)\right]^{2}}
An explicit turbulent friction factor within about 1% of the implicit Colebrook–White equation,…
Fluid Mechanics, HVAC & Refrigeration-18 Colebrook–White Friction Factor
1f=−2log⁡10 ⁣(ε3.7D+2.51Ref)\frac{1}{\sqrt{f}} = -2 \log_{10}\!\left(\frac{\varepsilon}{3.7 D} + \frac{2.51}{Re \sqrt{f}}\right)
The reference equation for turbulent friction in a rough pipe, and the curve every Moody diagram is…
Fluid Mechanics, HVAC & Refrigeration-19 Hazen–Williams Head Loss
hf=10.67 L Q1.852C1.852D4.8704h_f = \frac{10.67 \, L \, Q^{1.852}}{C^{1.852} D^{4.8704}}
The waterworks head-loss equation in SI form, with Q in m³/s and D in m; the 10.67 constant is…
Fluid Mechanics, HVAC & Refrigeration-20 Hazen–Williams Velocity
v=0.849 C R0.63S0.54v = 0.849 \, C \, R^{0.63} S^{0.54}
Mean water velocity from hydraulic radius and hydraulic gradient; the 0.849 SI constant becomes…
Fluid Mechanics, HVAC & Refrigeration-21 Minor Loss from K Factor
hL=K v22gh_L = K \, \frac{v^{2}}{2g}
Head lost through a valve or fitting as a multiple of velocity head, with g = 9.80665 m/s² and K…
Fluid Mechanics, HVAC & Refrigeration-22 Equivalent Length of a Fitting
Leq=KDfL_{eq} = \frac{K D}{f}
Converts a fitting's K factor into the length of straight pipe that would cause the same friction…
Fluid Mechanics, HVAC & Refrigeration-23 Valve Flow Coefficient (Cv)
Q=CvΔPSGQ = C_v \sqrt{\frac{\Delta P}{SG}}
The US valve-sizing relation: Cv is the gpm of 60 °F water a valve passes at 1 psi drop, so Q is in…
Fluid Mechanics, HVAC & Refrigeration-24 Valve Flow Coefficient (Kv, metric)
Q=KvΔpSGQ = K_v \sqrt{\frac{\Delta p}{SG}}
The metric valve-sizing relation: Kv is the m³/h of water a valve passes at 1 bar drop, related to…
Fluid Mechanics, HVAC & Refrigeration-25 Orifice Plate Flow
Q=Cd1−β4⋅πd242 ΔPρQ = \frac{C_d}{\sqrt{1 - \beta^{4}}}\cdot\frac{\pi d^{2}}{4}\sqrt{\frac{2\,\Delta P}{\rho}}
Volumetric flow through a square-edged orifice plate from the differential pressure across it.
Fluid Mechanics, HVAC & Refrigeration-26 Venturi Meter Flow
Q=C1−β4⋅πD2242 ΔPρQ = \frac{C}{\sqrt{1 - \beta^{4}}}\cdot\frac{\pi D_2^{2}}{4}\sqrt{\frac{2\,\Delta P}{\rho}}
Flow through a classical Venturi tube from the inlet-to-throat differential pressure.
Fluid Mechanics, HVAC & Refrigeration-27 Barlow's Formula (Pipe Pressure Rating)
P=2StDP = \frac{2 S t}{D}
Internal pressure a pipe can hold from wall stress, wall thickness and outside diameter: the…
Fluid Mechanics, HVAC & Refrigeration-28 Water Hammer Surge (Joukowsky Equation)
ΔP=ρ a Δv\Delta P = \rho \, a \, \Delta v
Peak pressure surge from a sudden change in flow velocity: fluid density times pressure-wave…
Fluid Mechanics, HVAC & Refrigeration-29 Pipe Internal Volume
V=πD24LV = \frac{\pi D^{2}}{4} L
The liquid a run of pipe holds, from inside diameter and developed length: the starting point for…
Fluid Mechanics, HVAC & Refrigeration-30 Partially Filled Horizontal Cylindrical Tank
V=L[r2cos⁡−1 ⁣(r−hr)−(r−h)2rh−h2]V = L \left[ r^{2} \cos^{-1}\!\left(\frac{r-h}{r}\right) - (r-h)\sqrt{2rh - h^{2}} \right]
Liquid volume in a horizontal cylinder from the wetted depth, using the circular segment area times…
Module 3 · Pumps, Fans & Affinity Laws
Fluid Mechanics, HVAC & Refrigeration-31 Total Dynamic Head
TDH=hs+hf+hvTDH = h_s + h_f + h_v
The head a pump must develop: static lift plus friction losses plus velocity head, all expressed in…
Fluid Mechanics, HVAC & Refrigeration-32 Hydraulic Power (P = ρgQh)
P=ρgQhP = \rho g Q h
Power needed to lift a flow Q through a head h, with g = 9.80665 m/s².
Fluid Mechanics, HVAC & Refrigeration-33 Pump Water Horsepower
WHP=Q H SG3960WHP = \frac{Q \, H \, SG}{3960}
Useful power delivered to the liquid; the 3960 divisor assumes US gallons per minute, feet of head…
Fluid Mechanics, HVAC & Refrigeration-34 Pump Brake Horsepower
BHP=Q H SG3960 ηBHP = \frac{Q \, H \, SG}{3960 \, \eta}
Shaft power the motor must actually supply; the 3960 constant assumes gpm, feet of head and…
Fluid Mechanics, HVAC & Refrigeration-35 Pump Efficiency from Hydraulic and Shaft Power
η=PhydPshaft\eta = \frac{P_{hyd}}{P_{shaft}}
Pump efficiency is the ratio of hydraulic power delivered to the liquid over the mechanical power…
Fluid Mechanics, HVAC & Refrigeration-36 Net Positive Suction Head Available (NPSHa)
NPSHa=hatm+hs−hf−hvpNPSH_a = h_{atm} + h_s - h_f - h_{vp}
Absolute head available at the pump suction above the liquid's vapour pressure: the margin that…
Fluid Mechanics, HVAC & Refrigeration-37 Cavitation Number (Margin above Vapour Pressure)
σc=p−pv12ρv2\sigma_c = \frac{p - p_v}{\tfrac{1}{2} \rho v^{2}}
How much pressure margin a flow has above the vapour pressure of its own liquid, measured in…
Fluid Mechanics, HVAC & Refrigeration-38 Pump Affinity Law: Flow vs Speed
Q2Q1=N2N1\frac{Q_2}{Q_1} = \frac{N_2}{N_1}
First affinity law: a centrifugal pump's capacity changes in direct proportion to shaft speed when…
Fluid Mechanics, HVAC & Refrigeration-39 Pump Affinity Law: Head vs Speed
H2H1=(N2N1)2\frac{H_2}{H_1} = \left(\frac{N_2}{N_1}\right)^{2}
Second affinity law: pump head varies with the square of shaft speed, so a 20% speed cut costs 36%…
Fluid Mechanics, HVAC & Refrigeration-40 Pump Affinity Law: Power vs Speed
P2P1=(N2N1)3\frac{P_2}{P_1} = \left(\frac{N_2}{N_1}\right)^{3}
Third affinity law: absorbed power varies with the cube of shaft speed, the single relation that…
Fluid Mechanics, HVAC & Refrigeration-41 Pump Affinity Law: Flow vs Impeller Diameter
Q2Q1=D2D1\frac{Q_2}{Q_1} = \frac{D_2}{D_1}
Capacity scales directly with trimmed impeller diameter at constant speed, the classic way to…
Fluid Mechanics, HVAC & Refrigeration-42 Pump Affinity Law: Head vs Impeller Diameter
H2H1=(D2D1)2\frac{H_2}{H_1} = \left(\frac{D_2}{D_1}\right)^{2}
Developed head falls with the square of the trimmed impeller diameter, so a 10% trim sheds about…
Fluid Mechanics, HVAC & Refrigeration-43 Pump System Curve
H=Hst+kQ2H = H_{st} + k Q^{2}
Head a piping system demands at any flow: the static lift, which never changes, plus a friction…
Fluid Mechanics, HVAC & Refrigeration-44 Pump Operating Point
Qop=H0−Hstk+cQ_{op} = \sqrt{\frac{H_{0} - H_{st}}{k + c}}
Flow at which a pump actually runs: the crossing of its own head curve, H = H₀ − cQ², with the…
Fluid Mechanics, HVAC & Refrigeration-45 Fan Affinity Law: Airflow vs Speed
Q2Q1=N2N1\frac{Q_2}{Q_1} = \frac{N_2}{N_1}
Fan airflow in CFM changes in direct proportion to wheel speed, the first law used when re-sheaving…
Fluid Mechanics, HVAC & Refrigeration-46 Fan Affinity Law: Static Pressure vs Speed
SP2SP1=(N2N1)2\frac{SP_2}{SP_1} = \left(\frac{N_2}{N_1}\right)^{2}
Fan static pressure rises with the square of wheel speed, the reason a modest re-sheave can…
Fluid Mechanics, HVAC & Refrigeration-47 Fan Affinity Law: Power vs Speed
P2P1=(N2N1)3\frac{P_2}{P_1} = \left(\frac{N_2}{N_1}\right)^{3}
Fan brake power varies with the cube of wheel speed: the law behind variable-air-volume energy…
Fluid Mechanics, HVAC & Refrigeration-48 Fan Brake Horsepower
BHP=Q⋅SP6356 ηBHP = \frac{Q \cdot SP}{6356 \, \eta}
Shaft power a fan absorbs; the 6356 divisor assumes cubic feet per minute, inches of water gauge…
Fluid Mechanics, HVAC & Refrigeration-49 Pump Specific Speed (Ns)
Ns=NQH0.75N_s = \frac{N \sqrt{Q}}{H^{0.75}}
The dimensional index that classifies impeller type, evaluated in US units with N in rpm, Q in gpm…
Module 4 · Psychrometrics
Fluid Mechanics, HVAC & Refrigeration-50 Saturation Vapour Pressure (Magnus / Alduchov–Eskridge)
pws=610.94exp⁡ ⁣(17.625 tt+243.04)p_{ws} = 610.94 \exp\!\left(\frac{17.625\,t}{t + 243.04}\right)
The vapour pressure of water at saturation, from temperature alone, by the Alduchov–Eskridge Magnus…
Fluid Mechanics, HVAC & Refrigeration-51 Relative Humidity from Vapour Pressure
φ=pvpws\varphi = \frac{p_v}{p_{ws}}
Relative humidity as what it actually is: the vapour pressure present divided by the saturation…
Fluid Mechanics, HVAC & Refrigeration-52 Humidity Ratio from Vapour Pressure
W=0.62198 pvp−pvW = 0.62198\,\frac{p_v}{p - p_v}
Kilograms of water vapour per kilogram of dry air, from the vapour pressure and the barometric…
Fluid Mechanics, HVAC & Refrigeration-53 Dew Point (Magnus Approximation)
Td=c γb−γ,γ=ln⁡ ⁣RH100+b Tc+TT_d = \frac{c\,\gamma}{b - \gamma}, \quad \gamma = \ln\!\frac{\mathrm{RH}}{100} + \frac{b\,T}{c + T}
Dew point from air temperature and relative humidity by the Magnus formula with the WMO's Sonntag…
Fluid Mechanics, HVAC & Refrigeration-54 Dew Point from Humidity Ratio
Td=243.04 γ17.625−γ,γ=ln⁡ ⁣pv610.94,pv=W p0.62198+WT_d = \frac{243.04\,\gamma}{17.625 - \gamma}, \quad \gamma = \ln\!\frac{p_v}{610.94}, \quad p_v = \frac{W\,p}{0.62198 + W}
The temperature at which air of a given humidity ratio and barometric pressure starts to condense,…
Fluid Mechanics, HVAC & Refrigeration-55 Wet-Bulb Temperature (Stull 2011)
Tw=T arctan⁡ ⁣[0.151977RH+8.313659 ]+arctan⁡(T+RH)−arctan⁡(RH−1.676331)+0.00391838 RH3/2arctan⁡(0.023101 RH)−4.686035T_w = T\,\arctan\!\left[0.151977\sqrt{\mathrm{RH} + 8.313659}\,\right] + \arctan(T + \mathrm{RH}) - \arctan(\mathrm{RH} - 1.676331) + 0.00391838\,\mathrm{RH}^{3/2}\arctan(0.023101\,\mathrm{RH}) - 4.686035
Wet-bulb temperature from dry-bulb temperature and relative humidity in a single closed-form…
Fluid Mechanics, HVAC & Refrigeration-56 Relative Humidity from a Sling Psychrometer
φ=pws(twb)−A p (tdb−twb)pws(tdb)\varphi = \frac{p_{ws}(t_{wb}) - A\,p\,(t_{db} - t_{wb})}{p_{ws}(t_{db})}
Relative humidity from a dry-bulb and a wet-bulb reading, using the psychrometric equation with A =…
Fluid Mechanics, HVAC & Refrigeration-57 Moist Air Enthalpy (per kg DRY air)
h=1.006 t+W (2501+1.86 t)h = 1.006\,t + W\,(2501 + 1.86\,t)
Total heat content of moist air per kilogram of DRY air: the sensible term for the air plus the…
Fluid Mechanics, HVAC & Refrigeration-58 Moist Air Specific Volume (per kg DRY air)
v=0.287042 (t+273.15) (1+1.6078 W)pv = \frac{0.287042\,(t + 273.15)\,(1 + 1.6078\,W)}{p}
Cubic metres of moist air per kilogram of DRY air, from temperature, humidity ratio and barometric…
Fluid Mechanics, HVAC & Refrigeration-59 Moist Air Density at Altitude (and the 1.08 Correction)
ρ=pz (1+W)Rda T (1+1.6078 W),pz=101 325 (1−2.25577×10−5z)5.25588\rho = \frac{p_z\,(1 + W)}{R_{da}\,T\,(1 + 1.6078\,W)}, \quad p_z = 101\,325\,(1 - 2.25577 \times 10^{-5} z)^{5.25588}
Density of moist air from altitude, temperature and humidity ratio, and the correction factor it…
Fluid Mechanics, HVAC & Refrigeration-60 Mixed Air Temperature
Tm=f Toa+(1−f) TraT_m = f \, T_{oa} + (1-f) \, T_{ra}
Temperature of the blend leaving a mixing box, weighted by the outdoor air fraction: the reading…
Fluid Mechanics, HVAC & Refrigeration-61 Degree of Saturation (Moist Air)
μ=WWs\mu = \frac{W}{W_s}
The humidity ratio present divided by the humidity ratio at saturation for the same temperature and…
Fluid Mechanics, HVAC & Refrigeration-62 Cooling Coil Bypass Factor and Apparatus Dew Point
BF=tla−tadptea−tadp\mathrm{BF} = \frac{t_{la} - t_{adp}}{t_{ea} - t_{adp}}
The fraction of the air that leaves a cooling coil as though it never touched it, and the apparatus…
Fluid Mechanics, HVAC & Refrigeration-63 Air Total Heat (4.5 Rule)
Q˙t=ρaV˙ Δh\dot{Q}_t = \rho_a \dot{V} \, \Delta h
Total (sensible plus latent) heat carried by an airstream from airflow and enthalpy change: the…
Module 5 · Air Systems & Hydronics
Fluid Mechanics, HVAC & Refrigeration-64 Air Sensible Heat (1.08 Rule)
Q˙s=ρacaV˙ ΔT\dot{Q}_s = \rho_a c_a \dot{V} \, \Delta T
Sensible heat carried by an airstream from CFM and dry-bulb ΔT, assuming standard air: the trade…
Fluid Mechanics, HVAC & Refrigeration-65 Air Latent Heat (0.68 Rule)
Q˙l=ρaV˙hfg ΔW\dot{Q}_l = \rho_a \dot{V} h_{fg} \, \Delta W
Latent heat from dehumidifying an airstream, set by airflow and the change in humidity ratio: the…
Fluid Mechanics, HVAC & Refrigeration-66 Sensible Heat Ratio (SHR)
SHR=Q˙sQ˙s+Q˙l\mathrm{SHR} = \frac{\dot{Q}_s}{\dot{Q}_s + \dot{Q}_l}
The fraction of a cooling coil's total load that is sensible, the number that decides whether a…
Fluid Mechanics, HVAC & Refrigeration-67 Round Duct Air Velocity
v=4V˙πd2v = \frac{4 \dot{V}}{\pi d^{2}}
Air velocity in a round duct from the volume flow and the duct diameter, the check that keeps…
Fluid Mechanics, HVAC & Refrigeration-68 Equivalent Round Duct Diameter
De=1.30(ab)0.625(a+b)0.25D_e = 1.30 \frac{(ab)^{0.625}}{(a+b)^{0.25}}
Huebscher's equation for the round duct that has the same friction loss and airflow as a given…
Fluid Mechanics, HVAC & Refrigeration-69 Air Velocity Pressure (the 4005 Rule)
VP=(V4005)2\mathrm{VP} = \left(\frac{V}{4005}\right)^{2}
The pressure a pitot tube reads as air is brought to rest, and the velocity that reading implies:…
Fluid Mechanics, HVAC & Refrigeration-70 Air Changes per Hour (ACH)
ACH=3600 V˙Vroom\mathrm{ACH} = \frac{3600 \, \dot{V}}{V_{room}}
How many times per hour a ventilation rate replaces the air in a room, the ventilation yardstick…
Fluid Mechanics, HVAC & Refrigeration-71 Hydronic Heat Transfer (Water)
Q˙=ρwcwV˙ ΔT\dot{Q} = \rho_w c_w \dot{V} \, \Delta T
Heat carried by a water loop from flow rate and supply-to-return ΔT: the SI form of the trade rule…
Fluid Mechanics, HVAC & Refrigeration-72 Glycol Loop Heat Transfer (Capacity Derate)
Q˙=ρcV˙ ΔT\dot{Q} = \rho c \dot{V} \, \Delta T
Heat carried by a glycol loop using the actual mix density and specific heat, which is how the 500…
Fluid Mechanics, HVAC & Refrigeration-73 Loop Water Expansion Volume
ΔV=V0 β ΔT\Delta V = V_0 \, \beta \, \Delta T
Volume a hydronic loop's water gains when heated, from the starting volume, the volumetric…
Fluid Mechanics, HVAC & Refrigeration-74 Expansion Tank Acceptance Volume
Vt=Vs e1−P1P2V_t = \frac{V_s \, e}{1 - \dfrac{P_1}{P_2}}
Diaphragm expansion tank size for a closed hydronic loop from system volume, water expansion and…
Fluid Mechanics, HVAC & Refrigeration-75 Hydronic Static Fill Pressure
P=ρwgH+PmarginP = \rho_w g H + P_{margin}
Cold fill pressure a closed loop needs to lift water to its highest point plus a safety margin, the…
Fluid Mechanics, HVAC & Refrigeration-76 Radiator Output at Non-Rated Temperature
Q˙=Q˙r(ΔTΔTr)n\dot{Q} = \dot{Q}_r \left(\frac{\Delta T}{\Delta T_r}\right)^{n}
Corrects a radiator or baseboard's catalogue output to the actual water-to-air temperature…
Fluid Mechanics, HVAC & Refrigeration-77 Seasonal Heating Energy (Degree-Day Method)
E=Q˙d ΔTm tΔTd ηE = \frac{\dot{Q}_d \, \Delta T_m \, t}{\Delta T_d \, \eta}
Estimates seasonal fuel energy by scaling the design heat loss with the average temperature…
Fluid Mechanics, HVAC & Refrigeration-78 Boiler or Furnace Output from Input
Q˙out=Q˙in η\dot{Q}_{out} = \dot{Q}_{in} \, \eta
Usable heat delivered by a boiler or furnace from its fuel input rate and its efficiency rating,…
Fluid Mechanics, HVAC & Refrigeration-79 Energy Cost from a Utility Rate
Ce=E peC_e = E \, p_e
Cost of the energy a system consumes: kilowatt-hours or fuel BTUs times the utility rate, for tower…
Module 6 · Refrigeration, Boilers & Cooling Towers
Fluid Mechanics, HVAC & Refrigeration-80 Tons of Refrigeration from BTU/hr
T=Q˙12,000 BTU/hrT = \frac{\dot{Q}}{12{,}000\ \text{BTU/hr}}
Converts a cooling load in BTU/hr (or kW) to tons of refrigeration, where one ton is 12,000 BTU/hr…
Fluid Mechanics, HVAC & Refrigeration-81 Coefficient of Performance (COP)
COP=Q˙W˙\mathrm{COP} = \frac{\dot{Q}}{\dot{W}}
Efficiency of a heat pump or chiller: useful heating or cooling delivered divided by the electrical…
Fluid Mechanics, HVAC & Refrigeration-82 Energy Efficiency Ratio (EER)
EER=Q˙ [BTU/hr]W˙ [W]\mathrm{EER} = \frac{\dot{Q}\ [\text{BTU/hr}]}{\dot{W}\ [\text{W}]}
Cooling efficiency as BTU/hr of capacity per watt of electrical input, a deliberately mixed-unit…
Fluid Mechanics, HVAC & Refrigeration-83 EER to COP Conversion
EER=3.412×COP\mathrm{EER} = 3.412 \times \mathrm{COP}
Converts between the two efficiency scales, since one watt of input equals 3.412 BTU/hr and both…
Fluid Mechanics, HVAC & Refrigeration-84 Chiller Efficiency (kW per Ton)
kW/ton=W˙ [kW]Q˙ [tons]\mathrm{kW/ton} = \frac{\dot{W}\ [\text{kW}]}{\dot{Q}\ [\text{tons}]}
The chiller-plant efficiency metric: kilowatts drawn per ton of cooling produced, where lower is…
Fluid Mechanics, HVAC & Refrigeration-85 Refrigeration COP from Enthalpies
COP=h1−h4h2−h1COP = \frac{h_1 - h_4}{h_2 - h_1}
Coefficient of performance of a vapour-compression cycle read straight off a pressure-enthalpy…
Fluid Mechanics, HVAC & Refrigeration-86 Compressor Isentropic Efficiency
ηs=h2s−h1h2−h1\eta_{s} = \frac{h_{2s} - h_{1}}{h_{2} - h_{1}}
How much of the work a compressor actually consumes went into raising the refrigerant's enthalpy,…
Fluid Mechanics, HVAC & Refrigeration-87 Refrigerant Superheat
SH=Tsuction−Tsat\mathrm{SH} = T_{suction} - T_{sat}
Degrees of superheat at the compressor suction: how much warmer the vapour is than its saturation…
Fluid Mechanics, HVAC & Refrigeration-88 Refrigerant Subcooling
SC=Tsat−Tliquid\mathrm{SC} = T_{sat} - T_{liquid}
Degrees of subcooling at the condenser outlet: how much colder the liquid is than its saturation…
Fluid Mechanics, HVAC & Refrigeration-89 Refrigerant Mass Flow Rate
m˙=Q˙Δh\dot{m} = \frac{\dot{Q}}{\Delta h}
Refrigerant circulated per unit time from the cooling capacity and the enthalpy change across the…
Fluid Mechanics, HVAC & Refrigeration-90 Chiller Heat Rejection
Qr=Qe HRFQ_r = Q_e \, \mathrm{HRF}
Heat a chiller's tower has to reject: the evaporator load times the heat rejection factor that adds…
Fluid Mechanics, HVAC & Refrigeration-91 Condenser Water Flow Rate
V˙=Q˙⋅HRFρwcw ΔT\dot{V} = \frac{\dot{Q} \cdot \mathrm{HRF}}{\rho_w c_w \, \Delta T}
Tower water flow needed to reject a chiller's load plus compressor heat, the physics behind the 3…
Fluid Mechanics, HVAC & Refrigeration-92 Cooling Tower Range
ΔT=Th−Tc\Delta T = T_h - T_c
Cooling tower range: the temperature drop the tower achieves between the hot water returning from…
Fluid Mechanics, HVAC & Refrigeration-93 Cooling Tower Approach
A=Tc−TwbA = T_c - T_{wb}
Cooling tower approach: how many degrees the cold basin water sits above the ambient wet-bulb…
Fluid Mechanics, HVAC & Refrigeration-94 Cooling Tower Heat Rejection
Q=500 R ΔTQ = 500 \, R \, \Delta T
Heat a cooling tower rejects from flow and range using the trade constant 500 = 8.34 lb/gal × 60…
Fluid Mechanics, HVAC & Refrigeration-95 Cooling Tower Evaporation Rate
E=0.001 R ΔTE = 0.001 \, R \, \Delta T
Evaporation loss from a cooling tower using the industry rule of 0.1% of recirculation per degree…
Fluid Mechanics, HVAC & Refrigeration-96 Cycles of Concentration (COC = M/B)
COC=MB\text{COC} = \frac{M}{B}
Cycles of concentration for a cooling tower from the makeup and blowdown flows: the master number…
Fluid Mechanics, HVAC & Refrigeration-97 Blowdown Rate from Cycles
B=ECOC−1B = \frac{E}{\text{COC} - 1}
Blowdown a cooling tower must bleed to hold a target cycles of concentration, given its evaporation…
Fluid Mechanics, HVAC & Refrigeration-98 Cooling Tower Makeup Water Rate
M=E+B+DM = E + B + D
Total makeup water a cooling tower needs: the sum of evaporation, blowdown to drain, and drift…
Fluid Mechanics, HVAC & Refrigeration-99 Boiler Horsepower to Heat Output
Q=33,475  BHPQ = 33{,}475 \; \text{BHP}
Converts boiler horsepower to heat output using the ASME definition of 33,475 BTU per hour per…
Fluid Mechanics, HVAC & Refrigeration-100 Boiler Horsepower to Steam Rate
S=34.5  BHPS = 34.5 \; \text{BHP}
Steam output of a boiler from its horsepower rating, at the ASME definition of 34.5 lb/h of steam…
Fluid Mechanics, HVAC & Refrigeration-101 Boiler Blowdown Rate from Steam Rate
B=SCOC−1B = \frac{S}{\text{COC} - 1}
Continuous blowdown a steam boiler must carry, in pounds per hour, from its steam production rate…
Fluid Mechanics, HVAC & Refrigeration-102 Condensate Return Percentage
%CR=ScS×100\%CR = \frac{S_c}{S} \times 100
Percentage of generated steam that comes back to the boiler house as condensate: the headline…
Fluid Mechanics, HVAC & Refrigeration-103 Boiler Makeup from Condensate Return
M=S(1−%CR100)M = S\left(1 - \frac{\%CR}{100}\right)
Fresh makeup water a steam plant must treat, from the steam production rate and the fraction of…