Pressure Drop in Air Piping Systems Series of Technical White Papers from Ohio Medical Corporation

Transcription

1 Pressure Dro in Air Piing Systems Series of Technical White Paers from Ohio Medical Cororation Ohio Medical Cororation Lakeside Drive Gurnee, IL 600 Phone: (800) Fax: (847) Rev

2 TERMINOLOGY ACFM Actual Cubic Feet er Minute CFM Cubic Feet er Minute GPM Gallons er Minute NOMENCLATURE Constants: g Acceleration Due to Gravity (../sec ) γ - Secific Weight (lb/ ) ρ - Density of Fluid (slugs/ ) µ - Dynamic Viscosity (lb*s/ ) ε - Equivalent Roughness ( for Galvanized Pie) K L Loss Coefficient for Fittings (Found in Industrial Literature or College Text) Variables: z n Height at Position n (.) V - Velocity of Fluid (/sec.) D - Diameter of Pie (in. or.) A Cross Sectional Area of Pie (in. ) L Pie Length (.) h L Head Loss (.) n Pressure at Node n f Friction Factor

3 INTRODUCTION Ever since the develoment of iing systems throughout civilization there has been the need to analyze ie size for otimal flow. In 78 Daniel Bernoulli had develoed an equation to reresent all variables within a iing system, as shown below: V V + + z = + + z + hl γ g γ g () From Bernoulli s equation, we can see how ressure, velocity and osition relate to one another, and many derivations can be created from this equation. Deending on the assumtions made and under certain conditions, some of the variables become negligible and can be removed to simlify the equation, and result in a simler solution. The nature of this aer is to solve for the ressure dro (or commonly referred to the back ressure) which is essentially the ressure difference between two oints in a iing system. The ressure dro is critical when sizing ie. A um that is integrated within a iing system is designed such that it will withstand certain forces at the inlet and exhaust. If the um is subjected to forces greater than the ones rescribed, there is a high otential for damage to the internal um comonents, and thus the designed flow will be affected. This aer will focus on the flow of air, although it can be shown that other fluids can also be modeled using the same methodology. Like other media that flows within a iing system, air has its own characteristics which benefit and hinder the rocess. There are numerous ways in which to solve for the ressure dro of iing system. That is to say, one can incororate the use of a comuter with a lethora of soware available. However, the underlying equations used in these rograms follow the same fundamental laws of hysics found in any collegiate Fluid Mechanics textbook. In addition, sound engineering judgment should be used when sizing ie. While a cost-effective solution may look good on the bottom line, a safe and reliable system should have recedence in any design. For our discussion the following assumtions can be made: Assumtions:. Air Flow will be turbulent.. The temerature for the ambient air will be 70 o F. Air flow will be defined using ACFM. With these assumtions we can model our system.

4 BACKGROUND: As we all have either exerienced, or heard about, the henomenon referred to as turbulence. Essentially turbulence is a random ositioning of the flow of air. Whereas in a laminar condition, the flow of air is uniform and follows a smooth, organized ath. For air iing, we assume that the air flow will be turbulent due to surface randomness in the iing fabrication and/or ower fluctuation in the air source equiment. A visual deiction of laminar and turbulent flow is shown below: Laminar Flow Figure Turbulent Flow Figure To see if the flow of air will be turbulent or laminar, we solve for a arameter referred to as the Reynolds number. The Reynolds number is a dimensionless number which is obtained from the following equation: ρ V D Re = µ () The conditions for if the flow is turbulent or laminar is as follows: If Re < 00 then the flow is Laminar If Re > 4000 then the flow is Turbulent If 00 < Re < 4000 then the flow is classified as in Transition. 4

5 To determine if the flow rate is laminar or turbulent, the Reynolds number should be calculated. The combination of the Reynolds number, equivalent roughness and ie diameter we can determine the friction factor from the Moody chart. (Moody charts can be found in industrial literature and in college text books.) The friction factor is used in the equations below. OTHER EQUATIONS: Some of the other equations used to determine the ressure dro are in this section. We can solve for the velocity of the flow by dividing the ACFM by the cross sectional area: Volumetric Flow Rate( Velocity ( / s) = Area( ) / s) () Where the area is solved by: A = π r (4) Once the velocity is found, we can then check to see if the flow is turbulent, or laminar, by utilizing the Reynolds equation (as mentioned reviously). The ressure dro in a iing system can be broken down into two () equation forms:. Major Pressure Losses (Pie Losses). Minor Pressure Losses (Losses through fittings, valves, etc.) The Equation for Major Losses: The Equation for Minor Losses: = f l D = γ ρ V h L (5) (6) Where h L is found by: h L = K L V g (7) And the constant K L is found in tables of either college text, or industrial references. Combining Equations (6) and (7) we can solve the ressure differential directly: V = γ K L g (8) 5

6 Once the ressure dro has been calculated for the ie length and all of the fittings/valves, the total ressure dro can be found by the summation of all comonents. In Equation form: = + + Total Fittings Pie Valves (9) COMPRESSIBLE VERSUS INCOMPRESSIBLE: The reader might be wondering that since air is a gas, shouldn t the flow be characterized as comressible? The answer to this question is deendent on many conditions. Deending on the length of the ie and the comlexity of the arrangement of fittings and valves, the ressure dro may, or may not, be small relative to the initial ressure. If the ressure dro is small enough, then you can assume the fluid is incomressible. Otherwise, the flow is Comressible, and comlicates the analysis. An examle to find the ressure ratio is as follows: We have a ie length of 7-0 and the ressure dro should be no greater than.0 si er 7-0. The ressure at the beginning is 4.7 si. ( ) (0) si si ( 7 ) =.068 = 6.8% This ratio is small enough to assume an incomressible flow. Sound judgment and exerience should be used when alying this equation. In different industries, different values are used to make the difference. 6

7 EXAMPLE: Given: A Squire-Cogswell S750TR-T system needs to have an exhaust line sized roerly. The customer needs to ie the system to the outside the building. The customer knows that there will be 00. of ie, three 90 o elbows, and two 45 o elbows. All Piing will be galvanized (ε = ). Air temerature is 60 o F and atmosheric ressure is 4.7 si. Find: The roer exhaust ie diameter for this system. Known: The given flow rate is 6.8 ACFM er um. The exhaust for the um is - /. (It is always advisable to check with the manufacturer of the um for a back ressure allowance. Deending on the manufacturer of the um, the allowable back ressure may vary.) The back ressure should not be greater than si. Solution: First we solve for the major losses- Find the velocity of the fluid from the flow rate using equation (): min V = 6.8 =.7 min 60sec sec V =.7 sec Cross Sectional Area of Pie Let s assume a -/ (0.065.) Cross Sectional Diameter: Therefore: V =.7 =.6 sec (0.065 ).4 sec The next variable we look for is the Reynolds Number using equation (): ρvd Re = µ slugs Re s = 7 lb s.74 0 ( 0.5. ) = 76,47 7

8 Once the Reynolds number is found then the flow can be determined as either turbulent or laminar. In this examle, the flow is turbulent. The frictional factor can be found from knowing the Reynolds number, relative roughness and diameter of the ie. From the Moody Chart f = 0.09 Using equation (5) to solve for the major losses: 00. slugs = sec lb = 68. lb = in = si Second we solve for the minor losses (i.e. through fittings and valves) using equation (8): V = γ K L g = lb.6 s.5. s.6 s +.4. s = lb 59 lb = 59 44in =. 50 si = + Total Fittings Pie 8

9 Total = 9.49 si si Total =. 99 si As we can see from this solution, the ressure dro is much higher than what should be observed in the ums. Therefore, other iterations of the examle are shown in Table : Iteration Pie Size (in.) Major Losses Pressure Dro in Pie (si) Minor Losses Pressure Dro in Fittings (si) Total Pressure Dro (si) / / EXPERIMENT: Table The above theory was tested in our lab to see if the data correlated with the solutions. The exeriment was set u as seen in the following ictures: 9

10 Pressure Measuring Device: Merical DP000I (Accuracy 0.05%R) Pum: 45 lm Volumetric Free Flow, VDC, 4.0 Am Pie Size: /8 (.69ID) Fittings: /8 Tee s (Qty. ) /8 Pie Niles (as aroriate) /8 Pie Coulings (as aroriate) Conditions for the test: Ambient conditions at Sea Level: Flow Rate: Temerature - 70 o F Pressure 4.7 PSIA 45 lm (Aroximately.6 ACFM) The ressure dro was measured at different ie lengths. Refer to the data below. Length Major Losses Calculated (si) Minor Losses Calculated (si) Tee Branch Flow: 0.05() = 0.0 Elbow: 0.04() = 0.04 Tee Branch Flow: 0.05() = 0.0 Elbow: 0.04() = 0.04 Couling: 0.00() = 0.00 Tee Branch Flow: 0.05() = 0.0 Elbow: 0.04() = 0.04 Coulings: 0.00() = Tee Branch Flow: 0.05() = 0.0 Elbow: 0.04() = Coulings: 0.00(5) = 0.00 Tee Branch Flow: 0.05() = 0.0 Elbow: 0.04() = Coulings: 0.00(7) = 0.04 Table P Calculated (si) P Measured (si)

11 Pressure Dro Exeriment Pressure Dro (si) Calculated Measured Pie Length (Inches) Figure As we can see from the data above, the calculated and measured data oints correlate with each other. The average difference is 0.0 si between the calculated and measured data oints. The non-linear behavior of the measured values is attributed to the random behavior of air. From Figure, one can see that the ressure data searates from the oint. The searation of data oints can be attributed to leaks or irregularities in the ie (i.e. burrs, surface irregularities from galvanizing etc.) The leaks in the iing system will decrease the flow rate, this in turn decreases the ressure. It is also interesting to note that as the ie length increases, so does the ressure. This is both demonstrated in the measured and calculated values.

12 CONCLUSION: Otimization of iing is essential in today s new construction of building systems. Due to ever increasing costs of steel and coer, there is no other alternative but to take a closer look at the iing system. In the ast, a rule of thumb gave a large margin of safety. However, the Engineer, Contractor and Architect must understand that the margin of safety can be held while decreasing the excess size of the ie. As long as the ressure dro is within the um manufacturer s secifications, the erformance will not be affected. The ressure dro in the iing system directly affects the erformance of the um. Essentially the ressure dro roduces additional forces that directly and indirectly affect the internal arts. It should be noted that having an excess size diameter of ie can be detrimental as well (i.e. oversized). If the area is increased, the excess (stagnant) air will act as an obstruction to the flow and therefore create a greater turbulence. Another detrimental effect, besides damage to the internal comonents of the um, is the reduction of air caacity the um removes. The back ressure acts as an obstruction to the flow, therefore hindering caacity. The examle could be solved in different ways. In fact we could have different ie sizes in this line. That is to say, we could have calculated for a run 50-0 of ½ Dia. and 50-0 of Dia. The calculation above is good for aroximating the ie size for the entire length of the ie, and it is also good for solving for smaller sections of ie. In addition, this aer makes lot of assumtions regarding the condition of the air flow and the ambient conditions. It can be argued that a more detailed analysis would be aroriate, and in other cases a more general solving aroach would be aroriate. As shown in the examle, there are many stes that need to be followed to give us an otimized ie size. There are many oortunities to overlook error by using these equations. Therefore, it is recommended to use sound industry judgment when solving for the ressure dro and interreting the results.