Hvac Equations (U.S./Metric)

The heating, ventilation, and air conditioning (HVAC) equations.

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3.2 HYDRONIC EQUIVALENTS

3.3 METRIC UNITS

4 HYDRONIC EQUATIONS

4.1 U.S. UNITS

4.2 Converting pressure in inches of mercury to feet of water at various water temperatures

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)

P_b = 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)

P_b = Absolute Static Pressure (kPa)
(Barometric pressure + static pressure)

T = Absolute Temp. (273° + °C = °K)

Heat Flow

U.S. UNITS

Q (sens.) = 60 x C_p x d x cfm x Δt

or for standard air (C_p = 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)

C^p = 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 C_p x d x l/s x Δt

or for standard air (C_p = 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)

C_p = 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 = V_p + SP

cfm = A x V

TP = C x V_μ

TP = Total Pressure (in. w.g.)
Vp = Velocity Pressure (in. w.g.)
SP = Static Pressure (in. w.g.)
V = Velocity (fpm)
V_m = Measured Velocity (fpm)
d = Density (lb/cu ft)
A = Area of duct cross section (sq ft)
C = Duct Fitting Loss Coefficient

METRIC UNITS

TP = V_p + SP

l/s = 1000 x A x V

TP = C x V_μ

TP = Total Pressure (Pa)
Vp = Velocity Pressure (Pa)
SP = Static Pressure (Pa)
V = Velocity (m/s)
V_m = 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)
C_v = 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
P_a = Atm. press. (use 34 ft w.g.)
P_s = Pressure at pump centerline (ft w.g.)

V²/2g = Velocity head at point P_s (ft w.g.)
P_vp = 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 $F F F$	$60 \circ 60 \circ 60^(@)$	$150 \circ 150 \circ 150^(@)$	$200 \circ 200 \circ 200^(@)$	$250 \circ 250 \circ 250^(@)$	$300 \circ 300 \circ 300^(@)$	$340 \circ 340 \circ 340^(@)$
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)

C_v = 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
P_a = Atm. press. (Pa – Std. Atm. press. = 101,325 Pa)
P_s = Pressure at pump centerline (Pa)

V²/2g = Velocity head at point P_s (m)
P_vp = 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)