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)
FREQUENTLY ASKED QUESTIONS
When working with HVAC equations, it’s often necessary to convert between U.S. and Metric units. To do this, you can use conversion factors such as 1 lb/cu ft = 16.02 kg/m³ for air density, 1 ton of refrigeration = 3.516 kW for cooling capacity, and 1 horsepower = 0.7457 kW for fan power. Additionally, you can use online conversion tools or consult a reliable reference source, such as the ASHRAE Handbook, to ensure accurate conversions.
Air velocity and pressure drop are closely related in ducts, as an increase in velocity results in a corresponding increase in pressure drop. The equation for pressure drop (ΔP) in ducts is ΔP = f \* (L/D) \* (ρ \* V^2 / 2), where f is the friction factor, L is the duct length, D is the duct diameter, ρ is the air density, and V is the air velocity. Understanding this relationship is essential for designing and optimizing duct systems to minimize energy losses and ensure efficient airflow.
The cooling capacity of an HVAC system can be calculated using the equation Q = m \* Cp \* ΔT, where Q is the cooling capacity, m is the mass flow rate of air, Cp is the specific heat capacity of air, and ΔT is the temperature difference between the supply and return air. This equation is a fundamental principle in HVAC engineering and is used to size cooling coils, select equipment, and optimize system performance.
Humidity plays a critical role in HVAC calculations, as it affects the comfort, health, and safety of building occupants. The equation for relative humidity (RH) is RH = (Pv / Ps) \* 100, where Pv is the vapor pressure and Ps is the saturation pressure. Accurate calculations of humidity are essential for designing and operating HVAC systems, particularly in applications such as hospitals, laboratories, and data centers, where precise control of humidity is crucial.
To apply HVAC equations to real-world design problems, you need to understand the specific requirements of the project, including the building’s occupancy, climate, and load characteristics. By selecting the relevant equations and inputting the necessary parameters, you can perform calculations to size equipment, design duct systems, and optimize system performance. It’s essential to consider factors such as safety, energy efficiency, and cost-effectiveness when applying HVAC equations to ensure that the designed system meets the project’s requirements and constraints.
