Presure Differentials Considering Aspect Ratios

Room Pressurization Differentials Accounting for Aspect Ratio: The Missing Variable

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William Greco July, 2009 2404 Greensward N. Warrington, Pa. [email protected] Introduction: The equations used at present by all known sources, and Consulting A and E firms fail to take aspect ratio of an opening into consideration during calculation of CFM pressurization requirements. Modern digital control systems, VFD motor controllers and modulating dampers are the only reason that our pressurization systems work well, too much air is being assumed and designed into our systems for doorways and opening differentials when using the general velocity head equation. This report and the equations contained herein addresses and theorizes a solution to the aforementioned problem. Premise: All pressurization calculations performed up to this date (including the calculations performed by the author) have used a general, widely known velocity pressure formula which is good for general work if an opening aspect ratio of between 1:1 and 1:5 is assumed, however due to the fact that we are dealing with doorways, autoclave openings and other long and very narrow openings between pressurized areas which are between 50 and 1500 to 1, the general equation in general use is not valid (and many, HVAC spread sheets are based on this invalid equation). A 7’ high x 3’ doorway with a 1/8” opening at both door jambs and head with a ½” undercut has an aspect ratio of (door fame and head length) = 36"84"84" aspect ratio aspect ratio  36"   1, 632 :1 and   = 72:1 0.125" head and jambs door undercut  0.5" 

Such huge aspect ratios render standard velocity head equations useless due to the fact that air is in fact flowing at low velocities due to high reynolds numbers caused by a high friction coefficient of entry at the doorways and openings between areas, and not because the differentials are low. A high aspect ratio produces a high friction coefficient of entry due to the huge linear distance of the entry edge of a doorway crack opening as compared to a square opening, high aspect ratios also produce high surface friction area as opposed to square openings.

Room Pressurization Differentials Accounting for Aspect Ratio: The Missing Variable

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William Greco July, 2009 2404 Greensward N. Warrington, Pa. [email protected] An autoclave opening that is 30 feet long and ½” wide yields the following: A total of (30 feet x 12 sides) = Linear Entry edge of 360 inches An aspect ratio of (30 x 12)/0.5 = 720 to 1 and an area of (360 x 0.5)/144 = 1.25 square feet or (360 x 0.5) = 180 in2. The same area under consideration using only the general velocity head equation would be considered as a square opening with a 1:1 ratio. This would include (4) sides of only 180 = 13.416 inches (each side of square opening) .13.416 inches, A linear entry edge of (13.416 x 4) = 53.66 inches instead of the actual entry edge of 360 inches. Duct sizing is based on what is known as an equivalent diameter, not on rectangular area. The reason for this is that there is more surface area creating more friction on a high aspect ratio duct than on a circular duct of the same area. Ductalators and all sizing charts are based on equivalent diameter, and it is this equivalent diameter that we should be using to determine our required capacity differentials for pressurization purposes.

The general velocity head equation: V=

H  1   13.35   

where: V = Velocity in feet per minute H = Velocity Head  inches water gage 13.35 = specific volume of air at 700 F and 29.92 hg (Cubic Feet Per Pound) substituting CFM and AREA for velocity  CFM CFM Then V=   13.35 1096.2 = 4005   = 4005 H  AND Area Area

   CFM = 4005  H Area 

Room Pressurization Differentials Accounting for Aspect Ratio: The Missing Variable

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William Greco July, 2009 2404 Greensward N. Warrington, Pa. [email protected]

Most engineering offices usea 0.75 factor to account for friction thus : CFM = 4005

 H Area 0.75

(equation-1)

and this is the equation that most engineering offices use to calculate pressure differences between conditioned spaces. Example-1: Calculate the CFM required to maintain a 0.06 inwg differential with a 30 linear foot long x ½ inch wide opening between the an Autoclave Load side and the Mechanical space. using the General Velocity Head Equation. (360 x 0.5)/144 = 1.25 square feet 4005

 0.06 1.250.75 = 919.7 CFM

920 cfm would be the standard calculated capacity required. This means that 920 cfm must be made available to be transferred. Equivalent Diameter Equation- based on Aspect Ratio Dr. Willis Carrier years ago established the following equation which is found in the Carrier System Design Manual (which was in it’s 10th printing in 1974) pg 2-340.625

de

ab  = 1.3 0.25 a+b 

(equation-2)

where: a = the height of an opening or duct b = the width of an opening or duct d e = the equivalent diameter of opening or duct It is this equation that determines the equivalent diameter of differing aspect ratios of openings or conduits on all ductalators used by HVAC designers and engineers. To determine the area that we should be considering for these large aspect ratio openings, Equation-2 should be used first to account for Aspect Ratio then the resultant area plugged into the the general velocity head equation-1 .

Room Pressurization Differentials Accounting for Aspect Ratio: The Missing Variable

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William Greco July, 2009 2404 Greensward N. Warrington, Pa. [email protected]

Example-2 (same problem as Example-1) Calculate the CFM required to maintain a 0.06 inwg differential with a 30 linear foot long x ½ inch wide opening between the Autoclave Load side and the Mechanical spaceusing the Equivalent Diameter (eq-2) and General Velocity Head (eq-1) equations.

Using equation-2 0.625

de

360 0.50  = 1.3

0.25

360+0.50 

= 7.661 inches equivalent diameter

Calculating the area = 2

 7.661      2   Area = = 0.32 square feet 144 and substituting the results into equation-1

and substituting the resultsinto equation  1 4005

 0.06 0.32 = 314 CFM

314 cfm is computed with the geometry of the opening being taken into consideration. 920 cfm is computed using the assumption that Nature would allow us to use a “one equation fits all” approach, and generally Nature is not that cooperative.

The above example indicates that two thirds more CFM would be required from the AC system than is actually needed.

Room Pressurization Differentials Accounting for Aspect Ratio: The Missing Variable

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William Greco July, 2009 2404 Greensward N. Warrington, Pa. [email protected] Required Reynolds Numbers Reynolds number: From “Engineering Formulas” by Frank Sims published by Industrial Press 1999 page-10 The equation for the Reynolds number of airflow is: Using equation-2: 2.07 V d w  (equation-3) u where : NR  Reynolds number V  velocity in FPM NR =

D  inside diameter of conduit inches  w  specific weight of air lbs / cubic foot   1/ 13.35  0.075 u  absolute viscosity of air 0.018 centipoise Example-3 (our Autoclave again)= Calculate the Reynolds number required to maintain a 0.06 inwg differential with a 30 linear foot long x ½ inch wide opening between an Autoclave Load side and the Mechanical space assume a non-dimensional instantaneous (velocity) = (Volume per unit time, area) cross section velocity of 314 cfm / 0.32 sqft (calculated equivalent) = 981 fpm Reynolds number =

2.07 9817.6610.75  = 64821 0.018

Indicating that even using the proposed equivalent flow method an Autoclave opening, is in the turbulent flow region, a good indication that entry coefficient and friction is high enough to make things uncomfortable for air entering the opening. When comparing this to the General accepted (incorrect) calculation method of simply using the General Velocity Head equation the velocity works out to 920/1.25 = 736 fpm the reynolds number still falls above the >33,000 * number which determines Laminar vs Turbulent flow. * = 1985 ASHRAE Fundamentals Handbook, pg. 2.10 fig 13.

Room Pressurization Differentials Accounting for Aspect Ratio: The Missing Variable

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William Greco July, 2009 2404 Greensward N. Warrington, Pa. [email protected]

Conclusion: The entire HVAC industry uses a widely accepted general equation. continuing to use the presently accepted general equation for classified spaces in Pharmaceutical, Biological and critical Electronic Manufacturing work is nothing less than a gross misuse of energy. As I stated at the beginning of this report Modern digital control systems, VFD motor controllers and modulating dampers are the only reason that our pressurization systems work well, too much air is being assumed and designed into systems for doorways and opening differentials when using the general velocity head equation which does not account for differing geometry’s of various openings. Respectfully, William Greco 2404 Greensward N. Warrington, Pa. [email protected]