The heating, ventilation, and air conditioning (HVAC) equations.
AIR EQUATIONS
Velocity
U.S. UNITS
or for standard air (d = 0.075 lb/cu ft)
To solve for “d”:
V = Velocity (fpm)
Vp = Velocity Pressure (in. w.g.)
d = Density (lb/cu ft)
Pb = Absolute Static Pressure (in. Hg)
(Barometric pressure + static pressure)
T = Absolute Temp. (460° + °F)
METRIC UNITS
or for standard air (d = 1.204 kg/m3)
To solve for “d”:
V = Velocity (m/s)
Vp = Velocity Pressure (Pascals or Pa)
d = Density (kg/m3)
Pb = Absolute Static Pressure (kPa)
(Barometric pressure + static pressure)
T = Absolute Temp. (273° + °C = °K)
Heat Flow
U.S. UNITS
Q (sens.) = 60 x Cp x d x cfm x Δt
or for standard air (Cp = 0.24 Btu/lb – °F):
Q (sens.) = 1.08 x cfm x Δt
Q (lat.) = 4750 x cfm x ΔW (lb.)
Q (lat.) = 0.67 x cfm x ΔW (gr.)
Q (total) = 4.5 x cfm x Δh
Q = A x U x Δt
R = 1/U
Q=Heat Flow (Btu/hr)
Cp = Specific Heat (Btu/lb · °F)
d = Density (lb/cu ft)
At = Temperature Difference (°F)
AW = Humidity Ratio (lb or gr H2O/lb dry air)
Ah = Enthalpy Diff. (Btu/lb dry air)
A = Area of Surface (sq ft)
U = Heat Transfer Coefficient (Btu/sq ft · hr * °F)
R = Sum of Thermal Resistances (sq ft· hr · °F/Btu)
P = Absolute Pressure (lb/sq ft)
V = Total Volume (cu ft)
T = Absolute Temp. (460° + °F = °R)
R = Gas Constant (ft/°R)
M = Mass (lb)
METRIC UNITS
Q (sens.) = 60 x Cp x d x l/s x Δt
or for standard air (Cp = 1.005 kJ/kg – °C):
Q (sens.) = 1.23 x l/s x Δt
Q (lat.) = 3 x l/s x ΔW (lb.)
Q (total) = 1.2 x l/s x Δh
Q = A x U x Δt
R = 1/U
Q=Heat Flow (watts or kW)
Cp = Specific Heat (kJ/kg – °C)
d = Density (kg/m3)
At = Temperature Difference (°C)
AW = Humidity Ratio (g H2O/kg dry air)
Ah = Enthalpy Diff. (kJ/kg dry air)
A = Area of Surface (m2)
U = Heat Transfer Coefficient (W/m2 . °C)
R = Sum of Thermal Resistances (m2 . °C/W)
P = Absolute Pressure (kPa)
V = Total Volume (m3)
T = Absolute Temp. (273° + °C = °K)
R = Gas Constant (kJ/kg °R)
M = Mass (kg)
Total Pressure
U.S. UNITS
TP = Vp + SP
cfm = A x V
TP = C x Vμ
TP = Total Pressure (in. w.g.)
Vp = Velocity Pressure (in. w.g.)
SP = Static Pressure (in. w.g.)
V = Velocity (fpm)
Vm = Measured Velocity (fpm)
d = Density (lb/cu ft)
A = Area of duct cross section (sq ft)
C = Duct Fitting Loss Coefficient
METRIC UNITS
TP = Vp + SP
l/s = 1000 x A x V
TP = C x Vμ
TP = Total Pressure (Pa)
Vp = Velocity Pressure (Pa)
SP = Static Pressure (Pa)
V = Velocity (m/s)
Vm = Measured Velocity (m/s)
d = Density (kg/m3)
A = Area of duct cross section (m2)
C = Duct Fitting Loss Coefficient
FAN EQUATIONS
U.S. UNITS
cfm = Cubic feet per minute
rpm = Revolutions per minute
P = Static or Total Pressure (in. w.g.)
bhp = Brake horsepower
d = Density (lb/cu ft)
METRIC UNITS
I/s = Litres per second
m3/s = Cubic metres per second
P = Static or Total Pressure (Pa)
kW = Kilowatts
d = Density (kg/m3)
PUMP EQUATIONS
U.S. UNITS
gpm = Gallons per minute
rpm = Revolutions per minute
D = Impeller diameter
H = Head (ft. w.g.)
bhp = Brake horsepower
HYDRONIC EQUIVALENTS
- a. One gallon water = 8.33 pounds
- b. Specific heat (Cp) water = 1.00 Btu/lb °F (@ 68°F)
- c. Specific heat (Cp) water vapor = 0.45 Btu/lb °F (@ 68°F)
- d. One ft. of water = 0.433 psi
- e. One ft. of mercury (Hg) = 5.89 psi
- f. One cu.ft. of water = 62.4 lb = 7.49 gal.
- g. One in. of mercury (Hg) = 13.6 in.w.g. = 1.13 ft. w.g.
- h. Atmospheric Pressure = 29.92 in.Hg = 14.696 psi
- i. One psi = 2.31 ft. w.g. = 2.04 in.Hg
METRIC UNITS
I/s = Litres per second
m3/s = Cubic metres per second
rad/s = Radians per second
D = Impeller diameter
H = Head (kPa)
BP = Brake horsepower
HYDRONIC EQUATIONS
U.S. UNITS
gpm = Gallons per minute
Q = Heat flow (Btu/hr)
Δt = Temperature diff. (°F)
ΔP = Pressure diff. (psi)
Cv = Valve constant (dimensionless)
whp = Water horsepower
gpm = Gallons per minute
bhp = Brake horsepower
H = Head (ft w.g.)
Sp. Gr. = Specific gravity (use 1.0 for water)
Ep = Efficiency of pump
NPSHA = Net positive suction head available
Pa = Atm. press. (use 34 ft w.g.)
Ps = Pressure at pump centerline (ft w.g.)
V2/2g = Velocity head at point Ps (ft w.g.)
Pvp = Absolute vapor pressure (ft w.g.)
g = Gravity acceleration (32.2 ft/sec2)
h = Head loss (ft)
f = Friction factor (dimensionless)
L = Length of pipe (ft)
D = Internal diameter (ft)
V = Velocity (ft/sec)
Converting pressure in inches of mercury to feet of water at various water temperatures
Water Temperature degrees
F
F
F |
60
∘
60
∘
60^(@) |
150
∘
150
∘
150^(@) |
200
∘
200
∘
200^(@) |
250
∘
250
∘
250^(@) |
300
∘
300
∘
300^(@) |
340
∘
340
∘
340^(@) |
Ft. head differential per in. Hg. differential |
1.046
1.046
1.046 |
1.07
1.07
1.07 |
1.09
1.09
1.09 |
1.11
1.11
1.11 |
1.15
1.15
1.15 |
1.165
1.165
1.165 |
METRIC UNITS
Q = Heat flow (kilowatts)
Δt = Temperature diff. (°C)
ΔP = Pressure diff. (Pa or kpa)
Cv = Valve constant (dimensionless)
m3/s = Cubic metres per second
l/s = Litres per second
WP = Water power (kW) or (W)
m3/s = Cubic metres per second
I/s = Litres per second
Sp. Gr. = Specific gravity (use 1.0 for water)
BP = Brake power (kW)
E, = Efficiency of Pump
H = Head (Pa) or (m)
NPSHA = Net positive suction head available
Pa = Atm. press. (Pa – Std. Atm. press. = 101,325 Pa)
Ps = Pressure at pump centerline (Pa)
V2/2g = Velocity head at point Ps (m)
Pvp = Absolute vapor pressure (Pa)
g = Gravity acceleration (9.807 m/sec2)
h = Head loss (m)
f = Friction factor (dimensionless)
L = Length of pipe (m)
D = Internal diameter (m)
V = Velocity (m/sec)
ELECTRIC EQUATIONS
U.S. UNITS
I = Amps (A)
E = Volts (V)
P.F. = Power factor
R= ohms (Ω)
P = watts (W)
Bhp = Brake horsepower
METRIC UNITS
kW = Kilowatts
I = Amps (A)
E = Volts (V)
P.F. = Power factor
R = ohms (Ω )
P. = watts (W)
