I have been approached by lot of people to teach them system design
for the HVAC&R product development and I thought it fit for them
to start from basics as without solid foundation there can be
no building.So I thought of compiling the basic formulae first and
then go for the system design aspects.It has taken me considerable
time to compile these formulae.
I would like to thank Ms. Ashima Saxena for helping me in editing the list of the compilation.
I would like to thank Ms. Ashima Saxena for helping me in editing the list of the compilation.
| Thermodynamic Design Formulae | ||
| Sr. No. | EQUATION | FORMULAE |
| 1 | F = m a | Newton's law of motion |
| 2 | P = F / A | Pressure |
| 3 | ρ = m / V | Density |
| 4 | W = F d | Work |
| 5 | PE = m g H | Potential energy |
| 6 | KE = ½ m V2 |
Kinetic energy |
| 7 | Q = m Cp( t2 - t1 ) |
Sensible heat |
| 8 | Q = m ( h2 - h1 ) |
Total heat |
| 9 | W - Q = dE | 1st law of thermodynamics |
| 10 |
Cpa =
1.005 kJ/kgK
|
Heat capacity of dry air |
| 11 |
Cpw =
4.193 kJ/kgK
|
Heat capacity of water |
| 12 |
Cpv =
1.884 kJ/kgK
|
Heat capacity of water vapor |
| Heat Transfer Formulae | ||
| 13 | Q = - k A dt/dx | Conduction |
| 14 | Q = hc A ( ts - tf ) |
Convection |
| 15 | Q=σ A Fε FA (t1⁴-t2⁴) | Radiation |
| 16 | Re = ρ V Dh / µ |
Reynolds number |
| 17 | Pr = µ Cp / k |
Prandtl number |
| 18 | Nu = hc D / k |
Nusselt number |
| 19 | Nu = 0.023 Re0.8 Pr0.4 |
Dittus-Boelter |
| Moist Air Phase Formulae | ||
| 20 | P = Pa + Pv |
Dalton's Law of partial pressure |
| 21 | Pv = R T | Perfect gas law |
| 22 | Ra = 0.287 kJ/kgK |
Gas constant of dry air |
| 23 | Rv = 0.4615 kJ/kgK |
Gas constant of water vapor |
| 24 | W = 0.622 Pv / (P - Pv) |
Humidity |
| 25 | Pv =
P / [1+0.622/W] |
Vapor pressure from humidity |
| 26 | r = (1+W) / v | True density of moist air |
| 27 | Ps =
0.6105 exp [ 17.27 t / (237.3+t) ] |
Magnus saturation pressure |
| 28 | t = 237.3 / [17.27 / Ψ -
1] where Ψ = ln (Ps / 0.6105) |
Dew point temperature using the Magnus equation |
| 29 | f = Pv
/ Ps |
Relative humidity |
| 30 | Pv = Psw - 1.8( P- Psw )( db - wb )/( 2800 - 1.3 wb ) |
Carrier vapor pressure |
| 31 | H = 1.005 db + W [ 2500.6 + 1.85 db - 0.023 wb] | Enthalpy |
| 32 | hfg = 2501.9 - 2.4189 t |
Latent heat of water vapor |
| Air Psychometric Formulae | ||
| 33 | ma =
ρ Qa |
Mass flow of dry air |
| 34 | Qs = ma Cpm ( t2 - t1 ) |
Sensible duty |
| 35 | Cpm = 1.023 kJ/kgK |
at typical air-conditioning conditions |
| 36 | Qt = ma (h2 - h1 ) |
Total duty |
| 37 | SHR = Qs / Qt |
Sensible heat ratio |
| 38 | b = ( db0 - adp ) / ( dbi - adp ) |
Bypass factor |
| 39 | Qs = h A (db - wb) |
Sensible heat at wet wick |
| 40 | Ql = hd A (Ws,w - W) hfg,w |
Latent heat at wet wick |
| 41 | hd = hc / Cpm |
Mass transfer coefficient |
| Room Heat Formulae | ||
| 42 | Q = Uo Ao ( to - ti ) |
Heat conduction through a wall |
| 43 | r = ro
+ Σ t/K + ri |
Wall resistance |
| 44 | Qsg = SHGF SC
A CLF |
Solar heat gain |
| 45 | Q = U A CLTD | Cooling load temperature difference method |
| Cold Room Formulae | ||
| 46 | Qpulldown = m C dT |
Pull down load |
| 47 | Qlatent
= m ∆W λ |
Latent load |
| 48 | Qrespiration
= m R |
Heat of respiration |
| Solar Angle Formulae | ||
| 49 | d = 23.45 sin ( 360 (284+n) / 365) | Solar Declination |
| 50 | LST = CT + (Lstd - Lloc)/15 + E + DT |
Local Solar Time |
| 51 | E = 0.165 sin 2B - 0.126 c os B - 0.025 sin B | Equation of Time |
| 52 | B = 360 (n- 81) / 364 | Parameter in E |
| 53 | h = 15 (LST - 12) | Hour angle |
| 54 | sin β = cos l c osh cos d + sin l sin d | Altitude angle |
| 55 | cos φ = (cos d sin l cos h - sin d cos l) / cos β | Solar Azimuth |
| 56 | cos θ = cos β cos λ sin Σ + sin β cos Σ | Angle to surface normal |
| Solar Radiation Formulae | ||
| 57 | IDN =
A e -B / sin β |
Direct Normal Solar Flux |
| 58 | IdH = C IDN |
Diffuse Horizontal Solar Flux |
| 59 | ID = IDN cos θ |
Direct Solar Flux on Surface |
| Coil Calculation Formulae | ||
| 60 | dQ = hd dA ( ha - hi ) |
Heat flow on the c oil air side |
| 61 | dQ = hr
dAi ( ti - tr ) |
Heat flow on the c oil fluid side |
| 62 | dQs = hc dA ( ta - ti ) |
Air sensible heat |
| 63 | Q = U A lmtd | Duty from UA LMTD method |
| 64 | Lmtd = (dti - dto) / Ln( dti / dto ) |
Log mean temperature difference |
| 65 | Q = e Qmax |
Effectiveness method |
| 66 | e = (1 - exp(- Ntu (1- Cr)) / (1 - Cr exp(- Ntu (1-Cr)) |
Counter-flow effectiveness |
| 67 | Cr = Cmin / Cmax |
Capacity ratio |
| 68 | Ntu = U A / Cmin |
Number of transfer units |
| Steam Formulae | ||
| 69 | λ = 2164 kJ/kgK | Latent heat of vaporization at 2 bar gauge pressure |
| 70 | λ = 333.6 kJ/kg | Latent heat of freezing |
| Fluid Flow in Pipes Formulae | ||
| 71 | dPfriction = ½ ρ ƒ L V2
/ Dh |
D'Arcy Weisbach friction equation |
| 72 | 1/√ƒ = -2 Log [ ε / (3.7 Dh) + 2.51 / (Re √ƒ) ] |
Colebrook friction factor |
| 73 | Dh = 4 A / P |
Hydraulic diameter |
| Duct Design Calculation Formulae | ||
| 74 | P + ½ ρ V2 + ρ g H = constant |
Bernoulli equation |
| 75 | P1 + ½ ρ V2 + r g H1 = P1 + ½ ρ V2 + ρ g H1 + Ploss |
Modified Bernoulli |
| 76 | dP = ½ ρ Vd2 [ 0.4 ( 1 - Vd/Vu)2 ] |
Branch straight through dp |
| 77 | Def = 1.3 (ab)0.625 / (a+b)0.25 |
Effective diameter of rectangular duct |
| 78 | dP = ½ ρ V2 [ (A1/A2)2 - 1 ] |
dP for ideal flow through a nozzle |
| 79 | dP = ½ ρ V2 [ 1 - (A1/A2) ]2 |
dP for sudden enlargement |
| 81 | Re ≈ 67 V Dh |
standard air with V (m/s)
and Dh (mm) |
| Fan Laws | |||||
| 82 | Law 1 | ρ = const | Q ~ ω | SP ~ ω2 |
Pw ~ ω3 |
| 83 | Law 2 | ω = c onst | Q = const | SP ~ ρ | Pw ~
ρ |
| 84 | Law 3 | ω ~ 1/√ρ | Q ~ 1/√ρ | SP = const | Pw ~ 1/√ρ |
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