TOTAL AIR PRESSURE LOSS CALCULATION IN VENTILATION DUCT SYSTEMS USING THE EQUAL FRICTION METHOD DOMNIA Flori*, HOUPAN Aca, POPOVICI Tudor Techical Uiversity of Cluj-Napoca, *e-mail: floridomita@istautclujro (correpodig author) A B S T R A C T This method may be applied i two situatios: whe the total air pressure drop for the system is give ad whe some values for the so-called ecoomical velocity are imposed alog the successive ducts I the first case, the method cosists i determiig the ecessary diameters for some ducts ad for all the system Thus, i this case, the total available pressure is divided to the total legth of the mai duct, givig as result the frictio loss per meter of duct, also kow as frictio loss factor or specific liear pressure drop [Pa/m], which icludes both major ad mior losses Received: March 0 Accepted: March 0 Revised: April 0 Available olie: May 0 Keywords: air pressure loss, vetilatio duct system, airflow rate, equivalet resistace, omogram INTRODUCTION The preseted method gives a simplified approach for determiig both the major ad mior head losses for air distributio etworks Through the method, these losses are evaluated simultaeously, which allows, o oe had to obtai low eergetic cosumptio, ad o the other had, a fast balacig of the braches i order to attai the desiged airflow rates At a global level, the etire air trasportig etwork offers the same specific pressure drop, measured i Pa/m ad which icludes both major ad mior losses Whe air is movig alog the air pipe etwork, it ca be accepted that the coditios for cosiderig air as a icompressible gas are fulfilled; therefore the perfect gas laws are applicable For makig the computig easier, a certai equivalece coefficiet is itroduced by multiplyig the expoet of air flow volume, obtaiig a result which is proportioal to the total head loss Therefore, this coefficiet is a hydraulic similitude factor [] By the meas of this coefficiet, o more iterative calculatios will be used for the pressure balacig throughout the system For applyig the method, three diagrams were proposed, combiig together the ecessary data for dimesioig a vetilatio etwork MATERIALS AND METHODS Determiatio of total air pressure loss H The applicability rage of the method icludes situatios which ca be reduced to two distict cases: -the value of total air pressure loss for the etwork is give or is imposed; -some particular values of so-called ecoomical velocity are requested for the cosecutive ducts alog the etwork[] Whether i the situatios correspodig to the first case, the framework of the method determies the ecessary diameter for each duct, the secod case situatios are solved by determiig the diameters ad the air pressure loss for each sector ad i the etire etwork
Thus, i the first case, the available pressure H (which must overcome the major ad mior losses) is divided to the legth of the mai brach (cosidered usually as beig the logest brach ad havig the biggest local pressure drops) [], [3] H R = ; [Pa/m] () where: meas the total duct legth of the mai brach O a certai brach, the duct, havig l legth, will geerate a total pressure loss H, as follows: H = R ; [Pa] () The air pressure losses i juctios result from balacig the pressure at the kots Kowig the air pressure drop for each idividual duct, the legth of the ducts, the ecessary airflow volume ad the sum of local pressure drop coefficiets, the desig diameter of the duct may be determied [], [4] The total air pressure H for the mai brach is: λ ρ v H = ; [Pa]; (3) d where: λ is the frictio coefficiet; the duct legth; d the equivalet diameter; the local pressure drop coefficiet; ρ air desity; v average air velocity Kowig that the duct has circular sectio ad trasports the airflow rate D, from the cotiuity equatio comes: 4D v = ; π ρ d [m/s]; (4) Replacig this expressio of the velocity i (3) we fid: λ H = A D ; 5 4 d d [Pa]; (5) where: 6 A = ; π ρ [m 3 /kg]; (6) is a quatity which ca be cosidered as costat for a certai etwork The coefficiet is itroduced: therefore relatioship (5) becomes: λ = ; [m -4 ]; (7) 5 4 d d
H = A D ; [Pa] (8) To a certai value of the coefficiet may correspod differet combiatios of the quatities, d ad, whereas for D=ct i = ct, the air resistace of the etwork is costat So, air ducts havig differet legths, diameters ad local pressure drop coefficiets but providig the same value for the coefficiet, are called similar I other words, the coefficiet is a hydraulic criterio (or dimesioless group) of similarity [5], [6] By the meas of this coefficiet, it is o loger eed to make tedious repetitive calculatios i order to balace the pressure i juctios, whe dimesioig a vetilatio etwork [5], [6] The equal frictio method Total air pressure loss calculatio usig the equivalet resistace Whe the head loss correspodig to a certai airflow rate is kow, the followig equatios may be writte i the case of a juctio where two braches ad meet: H = H ; (9) D = D D where: D is the resultig airflow, from the summatio of the braches airflows [], [7] or: Therefore: D = D ; (0) D D = () The relatioship () may be writte as follows: D D = D ; () At the cosidered juctio we may write: (D D )A = D A; (3) p where: p is the equivalet coefficiet of the two ducts coected i parallel The relatioship (3) becomes: Based o () i (4), it follows: D p = (4) D D = p (5)
By geeralizatio, for ducts coected i parallel, the equivalet coefficiet p is: = p i= i (6) The relatioship (6) presets a aalogy with the coectio i parallel of the electrical resistors Whe two cosecutive ducts ad trasportig the same airflow rate are discussed (series coectio), the followig equatios may be writte: D = D = Ds ; (7) Hs = H H where: H s is the total head loss for the two ducts ad D s is the airflow rate which passes through the ducts Thus: sa Ds = A D A D; (8) becomes: s = ; (9) where: s is the equivalet coefficiet of the two ducts coected i series By geeralizatio, for ducts coected i series, the equivalet coefficiet s is: = (0) s The relatioship (0) presets a aalogy with the coectio i series of the electrical resistors The total head loss of the etire air distributio etwork is the mai value used for the calculatio of the fa ecessary pressure Whe the values D, ad are kow for each duct, the equivalet diameters of the ducts are determied by the meas of omograms [] I the relatioship (7), for the similarity coefficiet, we substitute the frictio coefficiet λ by its value give by Pradtl, vo Karma ad Nikuradse: =,4 lg ε ; () λ d ad the result is:,4 lgε lgd = () 5 4 d d i= For vetilatio ducts made of steel plate, the absolute roughess is ε = 0, mm, so we obtai: 9,4 lgd = (3) 5 4 d d where: d is the equivalet diameter of the sectio, [m] i
For circular pipes, the equivalet diameter is the same with the geometrical diameter, but for rectagular ducts havig the sides ratio a/b 0, the equivalet diameter must be calculated with the followig formula: 5 5 a b =,3 ; [m] (4) (a b) d 8 The relatioship (3) is preseted below uder a omogram form (Figure ), i which three idepedet variables are combied:, d ad The mass airflow rate D is added, too The variables ivolved i this graphical represetatio have the followig rages: - airflow: 00 50000 kg/h; - head loss: 6 300 mmh O; - similarity coefficiet: 0,0 000; - legth of a pipe: 40 m; - local pressure drop coefficiet: 0,5; - air velocity: 40 m/s Fig Total air pressure loss calculatio usig the equivalet resistace
3 Example of usig the omogram for air pressure loss calculatio Followig, we give a example how to use this omogram If it is kow that a vetilatio duct havig a legth of 30 m trasports 3000 kg/h air with total pressure losses of 70 mmh O ad the local pressure drop coefficiet is,05, fid the equivalet diameter of the duct ad air velocity through the duct Usig diagram o I (Figure ), for D=3000 kg/h (poit A) ad the head loss 70 mmh O (poit B), we obtai poit C, from which results the equivalet coefficiet =0 From the same diagram, for =30 m ad D = 3000 kg/h, we obtai poit D, which is projected o the vertical axis to the right of the diagram, i poit E I diagram o II (Figure ), joiig the poit E with poit F (correspodig to local pressure drop coefficiet =,05), we obtai o curve = 0, the G poit which gives the vetilatio duct diameter, d=40 mm From diagram o III (Figure ), for D=3000 kg/h (poit I) ad d = 40 mm (poit H) results the air velocity i the duct, v=8,5 m/s CONCLUSIONS This calculatio method allows a more simple ad rapid determiatio of total loss of pressure i a vetilatio duct etwork, just by usig a omogram Is a very useful tool for the desigers of vetilatio systems i order to make a accurate calculatio of vetilatio ducts ad total pressure drops alog the air route The method is easier to use tha the classical method of calculatio (pressure balacig method) ad therefore is recommeded for air ducts quick calculatios ad for makig techical ad ecoomic estimates of the vetilatio systems It ca be used both to calculate the logest ad loadig air route ad to balace the secodary braches of the vetilatio etworks Pressure losses i braches will be determied by imposig the pressure balace i the juctios Kowig the head loss for each idividual duct, the legth of the ducts, the ecessary air flow volume ad choosig the sum of local pressure drop coefficiets, the desig diameter of the duct may be determied The method respects the romaia regulatios regardig the desigig ad the executio of vetilatio duct systems [8], [9], therefore it ca be easily used REFERENCES POPOVICI T, DOMNIA F, HOUPAN A (00), Istalaii de vetilare i codiioare (Vetilatio ad air coditioig systems), Vol I Ed UTPress Cluj-Napoca ASHRAE HANDBOOK (008), HVAC Applicatios 3 CHRISTEA A, NICULESCU N (97), Vetilarea i codiioarea aerului (Vetilatio ad air coditioig); Vol I Ed Tehic Bucureti 4 DU G, COLDA I, STOIENESCU P, ENACHE D, ZGAVAROGEA M, HERA D, DU A (00), Maualul de istalaii; Istalaii de vetilare i climatizare (Buildig Services Hadbook; Vetilatio ad air coditioig systems) Ed Arteco Bucureti 5 ETHERIDGE D, SANDBERG M (996), Buildig vetilatio Theory ad measuremet, EdWiley 6 NICULESCU N, DU G, STOENESCU P, COLDA I (983), Istalaii de vetilare i climatizare (Vetilatio ad air coditioig systems), Ed Didactic i Pedagogic Bucureti 7 GRIMM NR, ROSALER RC (997), HVAC Systems ad Compoets Hadbook Ed McGraw-Hill 8 *** I-5 (00), Normativ privid proiectarea i executarea istalaiilor de vetilare i climatizare (Regulatios regardig the desig ad the executio of vetilatio ad air coditioig systems), Idicativ I 5/ 9 *** STAS 9660 Istalaii de vetilare i climatizare Caale de aer Forme i dimesiui (Vetilatio ad air coditioig systems Air ducts Dimesios ad shapes)