Document 5LdjaLRL1evGm0DQD9N7BrXy8

848 CHAPTER 42 ' .1949 Guide for duct sizes of square cross-sections from 6 x 6 in. to 48 x 48 in. As an illustration, the dotted lines in the chart show values calculated from Equation 6 which indicate that the slope for this particular material is somewhat different than from the average curves. The curves in Fig. 3, as well as Equation 6, show that the attenuation in decibels is'directly proportional to the length of duct lined, and that the larger the duct the greater will be the length which must be lined, in order to obtain a given noise-reduction. If the length of duct from the main duct to a grille is shorter than the length of lining indicated by the calculations, this duct may be subdivided into smaller ducts, as shown in Fig. 4. The increase in hoise reduction thus obtained may be calculated from Equation 7, provided the splitters are installed parallel to the long side of'the duct: - where a+bn i2a -- R0 o + 6 <7) R, = reduction with splitters, decibels. Re = reduction in same length of duct, without splitters,:decibels.., a = dimension of short side of duct, inches or feet, b = dimension of long side of duct, inches or feet. n = number of channels formed by splitters. . ; Example 1. An air conditioning installation is to be installed in a small theater. Determine the necessary sound treatment for the air distribution system to provide a satisfactory noiBe level in the theater utilizing these conditions: Fan tip speed 4000 fpm, total pressure 1.25 in.................................. 77-. db . I Acceptable room noise level (Table 1). ......................:v................. 40 db Required attenuation.......... ......... ........^.11...'............. 37 db Solution: Natural attenuation of supply duct. ' .. - Sheet metal duct 50 ft long'48 in. x 36 in.. (Table 2) 50 'x 0.01...:. 0:5 db. . ... Elbows, two size 48 in. x 36 in. (Table 3)2x1.---- ,............... 2.0, db-, : ,, -... . Attenuation grilles to theater air change .10 min (Table 5), outlet ' '.' velocity 1000 fpm 1 ........... 1....... ............. ...:.. v .......... -22-0 db'_'^, Total natural attenuation..................... ................................: . . 24.5 dh Difference between required and natural attenuation, 37 minus 24.5, is.l2,5.db. . Tins attenuation must be supplied by sound treatment in the duct, either in the form of duct lining or plate cells. Sound Control " 849 A similar analysis of.the return duct system shows that 15 db attenuation is to be furnished by absorptive material.. An inspection of the installation shows that the lining of the plenum on the'suction side' of the fan would prove the most economical, where it would secure the dual function of heat insulation and sound absorption. Example B. A 10 x 20 in. duct is connected to a private office space in a' quiet loca tion. Determine the length of lining necessary to attenuate average fan noise satisfactorily, using a lining material of a type to which Equation 6 applies; and having an absorption coefficient of 0.40 at 256 cycles. Assume that the duct is only 12 ft long as shown in Fig. 4, and that a 30 db reduction is required in this length. Solution: Case 1. (No splitters), From Equation 6, Ro = 12.6 X12X 0.401-4 = 12.6 db 200 Case B. (Two splitters, three channels), From Equation 7, .10+ (20X3) R, = 12.6 X - 10 + 20 29.6 db AIR SUPPLY OPENING NOISES When air is introduced into a room through a grille''or register at a constant velocity, sound energy is being introduced into the enclosure at a constant rate1*. Due to partial reflection at the boundaries of the en closure, the intensity of sound at any point in the space builds up to some maximum value. In a large room at a point remote from the . source of sound (the supply opening) the intensity can be shown to be substantially proportional to the rate at which sound energy is generated and inversely proportional to the number of sound absorption units (sabins) in the room,. It would thus, appear , that doubling the sound absorption of the room would halve the intensity and result in a noise level decrease of 3 db. Grille noise is similar in character to fan vortex noise. Knowing the noise level at the face of a grille for a given grille blade setting, the noise will vary as given in Equation 8 where V is the velocity of the air through the grille. r(vydb (change) = 55 logs (si For a change in blade setting Equation 9. applies and in . this , case, the total pressure is measured directly behind the face of the grille. "' For a typical air. conditioning grille the noise level , at the grille face may be approximately 48 db with a total pressure behind the grille of 0.1 in. .X