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)

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)

## 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.