Hvac Constants 72i59

Derivation of the Nine Major HVAC Constants Bill Greco Trident3 2-16-07 [email protected]

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Introduction On a Daily basis the following nine numbers 500, 3960, 6356, 1.08, 0.68, 4.45, 4005 1096 and 12,000 are used by HVAC engineers and designers as constants in their calculations. The importance of having a complete understanding of how these constants are constructed cannot be over stressed. If any calculations are outside of normal operating ranges with regard to temperature, pressure, specific volume or other variables that make up these constants, the resulting calculations will be in error. Adjustments in the constants value are often required, however many HVAC professionals fail to make those changes. Another reason for knowing how these “constants” were established is that our calculations could be called into question by someone from another discipline. If for instance someone asks “Why are you using the number 1.08 in this equation ?” we need a better expalanation than “Because we always use that number”. Definition of a Constant The definition of a constant is: 1.

A number that is part of an algebraic expression.

2.

An expression represented literally, not having a specific numerical value for example: If A is proportional to B, then A / B is a constant. This is also known as a dimensionless number or a literal constant.

3.

A quantity that is regarded as fixed and unchanging for the purpose of a particular calculation.

4.

A specific invariant whose properties and relationships are unaltered by mathematical transformation of coordinates. Examples of this are pi and e. (e = The base of the natural logarithms.)

5.

The value of a specific physical quantity that is determined by the laws of nature and the choice of units. Categorization of Constants Constants are categorized as follows: Absolute constants – Such that the numerical value is fixed and unchanging. ( This only occurs in mathematics and not in the physical world. ) Conditional constants – All physical quantities that are determined by the laws of nature are conditional. No fixed values exist in nature. Example: The speed of light can be altered by conditions. Logical constants – Connectives of a given system of logic. Examples- If....Then....Not....Or. Literal constants – As discussed above in the second definition.

The nine major HVAC constants are conditional constants. The fact that these nine numbers are conditional is very important. If a calculation is being made that is not within average physical variants which are outside of the normal HVAC boundaries such as temperature, humidity level, elevation above sea level, or other parameters, the relationship of specific heat or specific volume quantities could cause an error on the entire calculation. If abnormal conditions are encountered it then becomes critical that the constant be recalculated. An example of such a situation is the calculation of a process involving high temperature air and high pressures. Another example is an HVAC calculation being required for a space that is at a higher than normal elevation.

Derivation of the Nine Major HVAC Constants Bill Greco 2-16-07

[email protected]

page 2 of 6

500 Constant The 500 Constant is used in the calculation of Gallons per minute (GPM) as it relates to BTUH and delta temperature ( Delta temperature = discharge water temperature minus entering water temperature).

The 500 constant is simply derived as : 8.34 pounds per gallon of water x 60 minutes per hour = 500 The 8.34 pounds per gallon of water occurs at 54 degrees F. 3960 Constant The 3960 constant is used in the calculation of pump horsepower.

Where: BHP = Brake Horsepower GPM = Gallons per minute TDH = Total Dynamic Head, feet SP_GRAV = Specific Gravity of the fluid being pumped Pump_Eff = Pump Efficiency expressed as a decimal, less than unity (1<) The 3960 constant is derived by :

Normally rounded off to 3960. Where: 33,000 = Foot pounds per minute per horsepower. 8.34 pounds per gallon of water, the 8.34 pounds per gallon of water occurs at 54 degrees F.

6356 Constant The 6356 constant is used in the calculation of air or fan horsepower.

Where: BHP = Brake Horsepower CFM = Cubic Feet (of specified gas) Per Minute SP_inwg = Static Pressure, inches of water gage Gas_Sp_Grav = Specific gravity of gas being transported by fan Fan_Eff = Combined efficiency of motor and fan and drive The 6356 constant is derived in the following way: Water weighs 62.30 pounds per cubic foot at 70 degrees F. 33,000 foot pounds / horsepower / per minute

where: 12 = inches per foot and 33,000 = foot pounds/minute/horsepower

Derivation of the Nine Major HVAC Constants Bill Greco 2-16-07

[email protected]

page 3 of 6

1.08 Constant

The 1.08 constant is used in the calculation of CFM in relation to sensible heat and delta temperatures when expressed in BTUH and degrees Fahrenheit.

Where: CFM = Cubic feet per minute of air being delivered BTUH_Sens = BTU’s per hour of sensible heat Delta_T = Temperature difference in degrees F. The 1.08 constant is derived the following way:

Where: 0.243 = Specific heat of moist air at standard conditions 60 = minutes per hour 13.5 = Specific volume of air in cubic feet per pound at 69 degrees F. and 50% RH at sea level A note about the 0.243 used as a specific heat constant. The specific heat of moist air at constant pressure (a) is defined as the heat required to raise one pound (mass) of air one degree F. at a constant pressure. And : a = d + (w s) Where: a = Specific heat of moist air, s= Specific heat of saturated air, d= Specific heat of dry air w=ratio of dry air to saturated air lb/lb It has been substantiated that the d for a temperature range of 0 to 100 Deg F can be taken to be 0.240 btu/lb : deg F, the specific heat of moist air = 0.444, and the average for w = 0.0075 lb/lb therefore: a = 0.240 + (0.0075 x 0.444) = 0.243 Btu/lb:degF. 0.68 Constant The 0.68 constant is used in the calculation of BTU’s per hour ( BTUH ) of latent heat. Where: BTUH_Latent = BTU’s per hour of latent heat CFM_OA = Cubic feet per minute of outside air W_RM = Room or space moisture content W_OA = Outside air moisture content The 0.68 constant is derived the following way:

Where: 1076 = BTU’s required to condense one pound of water from room air 60 = 60 minutes per hour 13.5 = Specific volume of air in cubic feet per pound at 69 degrees F. and 50% RH at sea level 7000 = Grains per pound of water

Derivation of the Nine Major HVAC Constants Bill Greco 2-16-07

[email protected]

page 4 of 6

4.45 Constant The 4.45 constant is used to determine pounds of air being delivered or moved per CFM per Hour. 4.45 lbs air / cfm / hour is derived from:

Where: 60 = 60 minutes per hour 13.47 = Specific volume of air in cubic feet per pound at 68 degrees F. and 50% RH at sea level 4005 Constant The 4005 constant is used in the calculation of velocity pressure in relation to inches water gage pressure and velocity when expressed as feet per minute.

Where: hv = inches water gage velocity pressure V = velocity in feet per minute The 4005 constant is derived by the following procedure: Water weighs 62.3 pounds per cubic foot at 70 degrees. Air at 70 degrees F. and 14.6963 lbs/sqin. Pressure occupies 13.344 cuft of space per pound.

g = acceleration due to gravity at 0 degrees latitude = 32.088 ft_sec_squared at 40 degrees latitude = 32.158 ft_sec_squared at 90 degrees latitude = 32.258 ft_sec_squared 2 x g at 40 degrees latitude = 64.316 ft_sec_squared

where: 60 = seconds per minute the 4005 “constant” can vary due to gravity alone by as much as +/- 11 from the poles to the equator with everything else remaining equal. The constants 1096.2 and 4005 are connected mathematically and physically by : Specific volume of air = 13.344 cuft per pound of air at 70 degrees F. and 14.6963 psi pressure

Derivation of the Nine Major HVAC Constants Bill Greco 2-16-07

[email protected]

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1096 Constant Like the 4005 constant the 1096 constant is also used in the calculation of velocity pressure expressed as inches of water and velocity of air in feet per minute, however the added variable of weight of air in pounds per cubic foot (specific density) is involved in the calculation. The constant is more accurately calculated as 1096.2.

Where: hv = inches water gage velocity pressure V = velocity in feet per minute W = density of air in lbs per cubic feet The 1096 constant is derived by the following procedure: Water weighs 62.3 pounds per cubic foot at 70 degrees.

g = acceleration due to gravity = at 40 degrees latitude = 32.158 ft_sec_squared 2 x g at 40 degrees latitude = 64.316 ft_sec_squared

and 18.27 x 60 seconds per minute = 1096.2 Usually found rounded off to 1096 12000 Constant The 12000 constant is used in the calculation of tons of refrigeration in relation to BTU’s per hour. The amount of heat to melt one ton of ice in one 24 hour day expressed in BTU’s per hour. 1 ton of ice = 2,000 pounds The heat of fusion = 144 BTU’s are required to produce a change of phase in one pound of ice (solid) to water (liquid). 2,000 pounds x 144 BTU/LB = 288,000 BTU’s.

Derivation of the Nine Major HVAC Constants Bill Greco 2-16-07

[email protected]

page 6 of 6

Conclusion Example of how a constant incorrectly used can effect an HVAC calculation: Assume a system that has terminal reheat and supplies air after it es the reheat coil at 110 deg F DB and 50% RH, at these conditions the density of air is 15.03 cuft/lb, this changes the constant to 0.97.

If the reheat coil above is designed to condition a space needing 40,000 Btuh, and a design temperature of 70 degrees, using the constant 1.08 the calculated CFM required will be:

Using an adjusted constant of 0.97 the actual CFM required would be calculated as:

That could lead to an error of 1031- 926 = 106 CFM. Constants are fine for quick ball park calculations, however adjustments should be made when accurate calculations are required.

References:: Kent, R.T. Kent’s Mechanical Engineers Handbook Carrier Air Conditioning Company McGraw-Hill Compnay 1965

Wiley 1936

Handbook of Air Conditioning System Design

Baumeister, T. Marks Standard Handbook for Mechanical Engineers, McGraw-Hill sixth edition, 1967