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570 CHAPTER 31 1965 Guide And Data Book Table 5.... Ratio of Pressure Loss to Branch Velocity Pressure fta&o of Vetoed)' m Branch to VelocitjTm Main Dud 0.4 04 04 1.0 1.5 2J) 3J> 90-deg 6.5 3.1 2.0 l;5 . 0.95 0.74 0.62 60-deg 1 5.0 2.2 1.3 0.77; 0.47 0.47 0.58 45-deg . 3.5 1.3 0.64 0.43. 0.40 0.45 0.54 where " pressure loss due to gradual enlargement, inches of water. Cr =* coefficient of loss, as ratio of Iras to loss for. abrupt . expansion, dependent upon the total included between the sides of the duct. ;The loss for a:sudden symmetrical contraction can be ex pressed as: B. - c, f-^-V - C, (-^-V - C.(--V (10) V.400S/ \4005/ V.4005/ 1 ' where -- pressure toss due to sudden contraction (Fig. 11).- ..; C = loss coefficient based on orifice area A*. . _ ,r . ., y " velocity of air through orifice, feet per minute. The loss for a gradual symmetrical contraction cab be similarly expressed as: where the coefficient of loss C* depends on the.included angl* of the sides of the duct and the sharpness of the edges at the junction of taper to the following duct section! DUCT DESIGN The following discussion refers to ducts for commercial and industrial heating, ventilating, and air-conditioning sys tems of the central'station type. The.design :methods given yield the static pressure required to overcome the resistance of the ductwork, including-the supply outlets and return in takes. The .fan selected, for the duct system must not only produce this pressure but also the additional pressure 'required by the central equipment such as washers or spray chambers, heating or cooling' coils, and filters. Pressure losses of these components should be obtained from the manufacturers' catalogs. Special duct design procedures for heating ducts used in residences can be found in Chapter 7, Warm Air Hearing Systems, of the 1964 Guide And Data Book. The design of ducts in industrial exhaust systems is digniiawd in Chapter 35 of the 1964 Guide And Data Book. General rules which should be followed in the rfoaign 0f ducts are: 1. The air should be conveyed aa directly as possible at the permissible velocities to obtain the desired results with mini mum noise and greatest economy of power, material, and space. 2. Sudden changes in the direction or velocity of the air should be avoided, when sudden changes are necessary at benda turning vanes should be used to minimize the pressure Iran 3. Diverging transition pieces should be made as gradual.as practicable. As shown in the section on area 'Knw| losses in abrupt enlargements are high, and therefore such transitions' should be avoided. The included angle of divergence for enlarge, ment should not exceed 20 deg. Leases b contractions are low but the bcluded angle of convergence should not be greater than 60 deg. 4. Where the greatest air carrying capacity per square foot of sheet metal is desired, rectangular ducts should he M nearly square as posable. Aspect ratios (ratio of width to depth) greater than 8 to 1 should be avoided. Where possible, a ratio of 4 to 1 or less should be maintained. 5. Ducts should be constructed of smooth material, uch as steel or aluminum sheet metaL For ducts made from other materials, proper allowance for the change in roughness should be made.* 6. Through the design procedures which follow, a reasonably precise estimate of the flow resistances offered by. the system can be obtained. However, it should be recognized that, m actual installations, resistances may vary considerably from the cal culated values because of variation b the smoothness of ma terials, types of jointe used, and the ability of workmen to fabricate the system b accordance with the design. Fans and motors should therefore be selected to provide atleaet a slight factor of safety, and dampers should be installed b each branch outlet for halftncing the system. 7. Avoid obstructing ducts with piping, conduits, or structural members. Unavoidable duct obstructions must be streamlined with an easement or a (ear-drop, the length of which should be at least three times the thickness of the tear-drop. Procedure for Duct Design The general procedure is as follows: L Study the plan of the building and arrange the positions of the supply outlets to provide proper distribution of air within each space. Select outlet sizes from manufacturers' catalog data. 2. Draw a sketch of the most convenient duct system, con necting the supply outlets and' return btakes with the central station apparatus, taking cognizance of the building construc tion, avoiding all obstructions in steel work and equipment, and at the same time maintaining a simple design. 3. Calculate the sizes of aU mab and branch ducts by one of the methods given b the following section. 4. Determine the total pressure requirement of the supply and return duct systems. Although the toss b total presssure of each duct run connecting the fan and each supply outlet (or return intake) should be calculated and made tne same for all runs, ordinarily only tbe pressure loss of the duct run apparently having the greatest resistance is referred to as tbe pressure loss of the duct system. Dampers are relied upon for hnlnneing the system. 5. However, the more self-balancing the duct system is, tbe less expensive b the long run is the overall system from tbe standpoint of engineering, duct fabrication and ntidUt.innl and balancing of the duct system. 6. If the ducts are of recommended construction and are air tight, one can assume that approximately 75 percent of the difference between the initial and final velocity heads will be available for conversion to statio pressures. This applies to duct systems designed by any of the three methods described b this fig. 11.... Air Row at Abrupt Enlargement or - Contraction of Air Stream , .... Design Velocities It is not possible to give specific rules for selecting duct velocities, but tbe velocities listed in Table 6 have given satis factory results in designing conventional systems. Since the fan horsepower increases approximately as the square of the velocity, and noise generation increases with static pressure, velocities should be kept low for quiet and economical opera tion. On the other, hand, as evident from Equation 3, at a Air Duct Design 571 Table 6 ... Recommended and Maximum Dud Velocities for Conventional Systems SicoMMfldid Velocities, Fpa Dee'gncfioe Outdoor Air Intakes* Filters* Heating Coils** Cooling Coils* Air Washers* Fan Outlets Branch Risers*1 Outdoor Air Intakes* Cooling Coils* Fan Outlets Branch Risers* Residence* Sdioob, Theaters, Public Buildings Industrial ftufldtngs 500 500 600 250 300 350 450 500 600 450 500 600 500 1000-1600 700-900 600 500 500 1300-2000 1000-1300 600-900 600-700 500 1600-2400 1200-1800 800-1000 800 Maximum Velocities, fpa 800 300 500 450 500 1700' 800-1200 700-1000 650-800 900 600 500 . 1500-2200 1100-1600 800-1300 800-1200 1200 600 500 1700-2800 1300-22001000-1800' 100CF1600 The rebeiti*re for total (see ewe, not the act free am; other vriooitk* * For low ralodty systems oobr. Far lecoauaeadetiope eo high Telocity tvttenm, see eeetion on deatea af hub velocity duct* tn this chapter, and eee lUfe 9 in Chapter S at tbe 1964 Gvtn An Data Book. the main at each branch duct. For the selected velocities and known air-flow rates, the various duct diameters may be read directly from Figs. 2 or 3, and the equivalent rectangular sizes are obtained from Table 2. The pressure loss of the run having apparently the highest resistance is determined by nriHing the straight pipe, elbow, and transition losses; this total value represents the fan static pressure required for the supply-duct system. The return-air system is sized simi larly, starting with the lowest velocities at the return intakes and increasing them progressively in the direction of the fan inlet. Dampers are relied upon for balancing the system. A refinement of this method involves sizing the branch ducts to dissipate the pressure available at the entrance to each. The pressure loss of the ductwork between the fan and first branch take-off is subtracted from the now known fan static pressure to obtain the available pressure at each junc tion. By trial and error, a branch velocity is found that results in tiie branch pressure loss being equal to, or somewhat less fhftn, that available. The procedure is repeated for each branch. If the fan is specified so that the static pressure available for the ductwork is known;- the method consists of finding, by trial and error, the velocities in the main duct that will result in a pressure.loss equal to the pressure available. The branch ducts are then sized as previously explained. The merits of the velocity-reduction method are: (1) duct are determined very easily, and (2). velocities can be limited to those known to be safe from causing noise problems. Its disadvantages are: (1) proper choice of velocities requires, experience and judgment, and (2) the designer cannot always determine by inspection which run may have the highest resistance. Equal-Friction Method given flowrate, <the duct size increases with, decreasing ve-. lodty. For multistory buildings,.it is sometimes possible to reduce the height between floors by tiring very small ducts, thereby effecting a considerable reduction in building invest ment cost. The various space-saving systems which are be coming increasingly numerous are discussed in Chapters 2, 3, and 4 of the 1964 Guide And Data Book. The design of high-velocity'ducts is! discussed briefly in a later section, Design of High-Velocity Ducts, in this chapter. .< ` . .DESIGN METHODS ,, In the design fif air duct systems, three methods are em ployed: (1) veiocUy-reduction,. (2) equal-friction, and. (3) static-regain. The three methods and their refinements rep resent different design levels of accuracy and' complexity, and they should be selected to suit the application: Simple duct systems may be designed as quickly and easily as possible. For large installations; the'system static-pressure requirement must be determined as precisely as possible. ./ .. It should.be borne in mind that none of the three duct de? . sign methods will automatically produce the most economical duct system for all conditions. A careful evaluation, and balancing of all cost variables entering into design of a duct system should be madn with each design method.if maximum economy is to be achieved. -The main variables affecting the the owning cost of a.'duct system are: cost of the duetwork, duct insulation,-fan horsepower,-'space requirements, and cost of provisions for sound attenuation. Velocity-Reduction Method , This method consists of dting the velocity- at-the-'fan discharge and designing for progressively lower velocities in The principle of this method is to make the pressure loss per foot of length the same for the entire system. Little bal ancing is required for symmetrical layouts in which all runs have about the same resistance. For layouts having both short and long runs, the shortest run will require considerable dampering. A modification of this method would include designing the longest run at two or more different friction rates. If, due to space limitations, a relatively high' friction rate must be used on the upstream side of the duct system, this rate can-be re duced when space conditions become less critical on the down stream of the system. Usual practice is to select the velocity in tbe'main duct near the fan to provide a satisfactory noise level for the par-' ticular application. Since the flow rate (cfm) i3 known, this establishes a value of friction loss per 100 ft of duct in Fig: 2 or 3. -This same friction loss value is maintained throughout the design. For example, the flow rate in the main after the first branch take-off is reduced by that handled by the branch; Therefore, proceed vertically downward in Fig. 2 or 3 - to the new flow rate value, and read the velocity and diameter. Note that the velocity is reduced. An advantage of this method is that it automatically reduces the duct velocities in the direction of flow, thereby reducing noise' problems. The equivalent rectangular size of any diameter is obtained from Table 2. By continuing the procedure, the designer may size ail sections, including branch' ducts, from Figs. 2 and 3 at-the aarnp. friction loss per foot of actuallength. - - After the system,-the designer should1calculate the pressure loss of the run-which apparently has the highest resistance. The pressure losses of all elbows and transitions are included, and expressed in terms-ofeqitioalerit length' of straight pipe. -- `'s ','c