Hvac Equations (U.S./Metric)

()

The heating, ventilation, and air conditioning (HVACequations.

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)

How useful was this post?

Click on a star to rate it!

Average rating / 5. Vote count:

No votes so far! Be the first to rate this post.

We are sorry that this post was not useful for you!

Let us improve this post!

Tell us how we can improve this post?