Document jyoy2VvMyenY2q7Epj8ynkz32

Heating Ventilating Air Conditioning Guide 1939 Chapter 10. Chimneys and Draft Calculations 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: where Q = -etHD (9) Q = volume of material, cubic feet. t = average wall thickness, feet. For all practical purposes, the value of itl 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: ! Fe (10) j- 1 where Ve = economical chimney gas velocity, feet per second. 1 -s 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 and 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 considerably for average operating conditions in an average size steam plant by assuming typical conditions. x >, . | 4? 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 J* s Substituting these values in Equations 10, 8 and 7, respectively, and reducing, the results are substantially: F. = 13.7 W1/s (U) D = 1.5 W2/s (12) . 77,= 190Pr (13) 194 it- 7 gives the economical chimney sizes for various amounts of gases * and for required draft intensities as computed from. Equations 11, flowing a ^ are based on the operating factors used in reducing 12 K ns 7 8 and 10 to their simpler form. The sizes shown by the Equatio ^ chart shouid be used for general operating conditions only, CU^^installations where the required data necessary for an exact deter- Heightof Chimney, ft. Fig. 7. Economical Chimney Sizes3 *Diameter values also for gas temperatures of 400. 500 and GOO F mination are difficult or impossible to secure. Whenever it is possible to secure accurate data, or the anticipated operating conditions are fairly well known, the required size should be determined 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 producing plant may be stated as follows: -- hi = ftp + Ab + h-BA + he + hBi + hv + ho + hE + hR 195 (14)