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

**Contents**hide

## 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/m^{3})

To solve for “d”:

V = Velocity (m/s)

Vp = Velocity Pressure (Pascals or Pa)

d = Density (kg/m^{3})

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 H_{2}O/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/m^{3})

At = Temperature Difference (°C)

AW = Humidity Ratio (g H_{2}O/kg dry air)

Ah = Enthalpy Diff. (kJ/kg dry air)

A = Area of Surface (m^{2})

U = Heat Transfer Coefficient (W/m^{2} . °C)

R = Sum of Thermal Resistances (m^{2} . °C/W)

P = Absolute Pressure (kPa)

V = Total Volume (m^{3})

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/m^{3})

A = Area of duct cross section (m^{2})

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

m^{3}/s = Cubic metres per second

P = Static or Total Pressure (Pa)

kW = Kilowatts

d = Density (kg/m^{3})

## 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

m^{3}/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.)

V^{2}/2g = Velocity head at point P_{s} (ft w.g.)

P_{vp} = Absolute vapor pressure (ft w.g.)

g = Gravity acceleration (32.2 ft/sec^{2})

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)

C_{v} = Valve constant (dimensionless)

m^{3}/s = Cubic metres per second

l/s = Litres per second

WP = Water power (kW) or (W)

m^{3}/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)

V^{2}/2g = Velocity head at point P_{s} (m)

P_{vp} = Absolute vapor pressure (Pa)

g = Gravity acceleration (9.807 m/sec^{2})

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)