Document Y9g655gZbLrZ2nrjEdJQ2aMQn

426 CHAPTER 17 1956 Guide atmospheric temperature of 62 F, a chimney gas temperature of 500 F; a unit chimney gas weight of 0.09 lb per cu ft, sea level atmospheric pressure, a coefficient of friction of 0.016, and a friction duct length equal to the height of the chimney above the grate level. These curves may be used for general operating conditions. For specific conditions, a new chart may be prepared from Equation 4. DETERMINING INDUSTRIAL CHIMNEY SIZES If the required performance for a proposed chimney is known, and if a chimney-gas velocity is assumed, Equation 3 can be transposed to yield the necessary height, and an equation can be developed for the required diame ter. These operations result in the following equations: U= 2.96B, D, 0.184/pc-BoK* Ted (7) ~ttt Sic.- V >, \ V \ \ \ O l 1,1--1 O 30 60 ------1----- til 90 >20 160 - .1.1 I I ,I 180 210 240 270 300 AMOUNT OF CASES FLOWING ANO DISCHARGED POUNDS PER SEC Fig. 2. Typical Set of Operating Characteristics of a Natural Draft Chimney The weight of gas per second, W = 12.075 --dV7B=e~fic f,rom which c d = V0.288 VoP, (8) where H = required height of chimney above grate, feet. d = required minimum diameter of chimney, feet. V = chimney gas velocity, feet per second. Dr = total required draft, inches of water. For large chimneys, it is usual to assume, that total construction cost is least when the product Hd (height X diameter) is minimum. On this assumption, the product of Equations 7 and 8 can be differentiated, and . the differential set equal to zero to find the minimum. Solution for velocity then yields the following equation: V, (9) Chimneys and Draft Calculations 427: where V, = economical chimney gas velocity, feet per second. Equations 7, 8 and 9 can of course be simplified if values are assumed for some of the factors in it. Some typical figures for boiler plants are: Average chimney gas temperature 500 F......................................... T, = 960 F absolute ' Average atmospheric temperature 62 F............................................T0 = 522 F absolute Average coefficient of friction 0.016.................................................... f = 0.016 Average chimney, gas density, 0 F, 1 Atmosphere...................... ,,,, =0.09 lb per cu ft Barometer reading, sea level.............................................................B0,= 29.92 in. Hg To solve a typical example: Proceed horizontally from a Weight Flow Rate point to intersection with diameter line; from this intersection fol low vertically to chimney height line; from this intersection follow horizontolly to the right to Available Draft scale. Starting from a point of Available Draft, take steps in reverse order. When these values are substituted in Equations 7, 8 and 9, respectively the results are: H = 190Dr (10) d = 1.51F*'s (ii) = 13 7jyi/6 (12) These, equations should be used for general operating conditions only, or where the required data necessary for an exact determination are difficult or impossible to secure. Whenever it is possible to obtain accurate data, or the anticipated operating conditions are fairly well known, the required size should be determined from Equations 7, 8, and 9. Additional construction data for large industrial chimneys, whether