Document 3MQL2rBz4NxnxZoK62LLeonJ

American Society of Heating and Ventilating Engineers Guide, 1932 corresponding to the various assumed velocities, there is one size which will cost least. Since the cost of a chimney structure, regardless 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 = tIIID (8) where Q = volume of material, cubic feet. t = average wall thickness, feet. Height of Chimney, ft. For all practical purposes, the value of %t may be taken as a constant regardless.of the size of the structure, Hence, in general, the voltmie, 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 whose cost will be least and, as a result, will be the most economical to use. The.problem at hand is to deduce an equation for the chimney gasvelocity 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 3 and 4 to HD, differentiating; this product with 240 Chapter 15--Draft and Chimneys respect to V and equating the resulting expression to zero. This pro cedure results in the following expression : where Ve = economical chimney gas velocity, feet per second. Equation 9 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 conditions. After the value of the economical velocity has been determined, the corresponding height and diameter can then be determined from Equa tions 6 and 7, respectively, and the economical size will then be attained. Equations 6, 7 and 9 may be simplified considerably for average operating conditions in an average size steam plant by assuming the following conditions: 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 Substituting these values in Equations 2, 3 and 5, respectively, and reducing: Ve = 13.7 Wl/i D = 1.51F2/s H = 190Dr (10) (11) (12) Fig. 7 gives the economical chimney sizes for various amounts of gases flowing and required draft intensities as computed from Equations 10, 11 and 12, and are based on the operating factors used in reducing Equations 6, 7 and 9 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 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 6, 7 and 9. The recommended minimum inside dimensions and heights of chimneys for small and medium size installations are given in Table 1, which is taken from the A.S.H.V.E. Code of Minimum Requirements for the Heating and Ventilation of Buildings (edition of 1929). GENERAL DRAFT EQUATION AND DRAFT LOSSES The general draft equation for a steam producing plant may be stated as follows: Dt -- hi -- hF + h-B + hBr + hv + hBd + he + ho + Ae + hR ^241 (13)