Document zow977gyjNOBXOK7kJMRMao8m

Y Heating Ventilating Air Conditioning Guide 1938 of the kind of material used in the construction, varies as the volume of material in the structure, -the cost criterion then may be represented by the approximate equation: Q = TciHD ' (9) where Q = volume of material, cubic feet. t = average wall thickness, feet. ' For all practical purposes, the value of irf-may be taken as a constant regardless of the size of the structure. Hence, in general, the volume, and consequently the cost, of a chimney structure may be based on the factor HD as a criterion. Therefore, the value of the chimney gas velocity which will result in the least value of HD for any one set of operating con ditions will produce a structure which will be the most economical to use, because its cost will be least. The problem at. hand is to. deduce an equation for the chimney gas velocity which will result in a combination of a height and a diameter whose product HD'will'be least.. The solution is obtained by equating, the product of Equations 7 and 8 to HD, differentiating this product with respect to V and equating , the resulting expression to zero. This; pro-' cedure results in the following expression: , where = economical chimney gas velocity, feet per second. , Equation 10 gives the economical velocity of the chimney gases for' any set of operating conditions, and represents the velocity which will result in a chimney the size of which will, cost less than that of any other size as determined by any other velocity for the same operating con ditions. After the value of the economical velocity has been determined, the corresponding height arid, diameter can then be determined from Equations 7 and 8, respectively, and the economical size will then be attained. Equations 7, 8 and 10 may be simplified considerablys for average operating conditions in ari average size steaih plant by assuming typical conditibrisi.; w ; -Average; chimney gas temperature, 500 F....... ....... .........-Tc = 960 Mean atmospheric temperature, 62 F............................ ,:...T0 = 522 Average coefficient of friction, 0.016 ............................... ./ = 0.016 Average chimney, gas'density, 0.09.:______ ....................... Wc = 0.09 . ! Sea level elevation, with: barometer of 29.92._______ :------B0 = 29.92 -V . Substituting these values in Equations 10, 8 and. 7, respectively;, and reducing, the results are substantially: , ; ' , '. - Fe = 13.7 IF1/5 ' ., d = \:wV6 . : H = 190Dr ' (n> a2* (13)' 188 Chapter 10. Chimneys and Draft Calcuijvtions Fig. 7 gives the economical chimney sizes for various amounts of gases flowing and for required draft intensities as computed from Equations 11, 12 and 131 They are based on the operating factors' used in reducing Equations 7, 8 and 10 to their simpler form. The sizes shown by the curves in the chart should be used for general operating conditions only, or for installations where the required data necessary for an exact deter- Height of Chimney, ft Fig. 7., Economical Chimney Sizes ^Diameter values also for gas temperatures of 400, 500 and 600 F > iriination are'difficult or impossible to secure. Whenever'it is pbssible to secure accurate data, or' the anticipated operating conditions are fairly well known,-the required size should be deteriniried from Equations 7, 8-and-10. The recommended minimum inside dimensions and heights of chimneys for small and medium size installations are given-in Table 1. GENERAL EQUATION The'general draft equation for a steam prodiidrig plant may be; stated as follows: ' ' . . Dt -- if = Af + hi If hid + he + hBr + hv + ho + hs + Ar . ..:.(14) 189