Document jmmOp7LyY61LbrnGojQMkyN59

X American Society of Heating and Ventilating Engineers Guide, 1934 - chimney sizes based only on boiler horsepowers. After the ultimate horsepower of the projected plant had been determined, the chimney size in the table corresponding to this figure was then selected as the proper size required. Generally, no further attempt was made to determine if the height thus selected was sufficient to help create the required draft demanded by the entire installation, or the diameter sufficiently large to enable the chimney quickly, efficiently and economically to dispose of the gases. Since the operating characteristics of a natural draft chimney are similar in all respects to those of a centrifugal pump, or a centrifugal fan, it is no more possible to select a proper size chimney from such a table, even with correction factors appended, than it is to select the proper size pump from tables based only on the amount of water to be delivered. DETERMINING CHIMNEY SIZES The required diameter and height of a natural draft chimney are given by the following equations: _____ Dr . (6) where JD = 0 288 WTc B0WCV (7) H'= required height of chimney above grate bar level, feet. D = required minimum diameter of chimney, feet. V = chimney gas velocity, feet per second. Dr = total required draft demanded by the entire installation outside of the chimney, inches of water. Equations 6 and 7 give the required size of a natural draft chimney with all of the operating factors taken into consideration. Values for all of the factors with the exception of the chimney gas velocity may be either observed or computed. It is, of course, necessary to assume an arbitrary value for the velocity in order to arrive at some definite size. For any one set of operating conditions there will be as many sizes of chimney as there are values of reasonable velocities to assume. Of the number of sizes 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: <2 = -*tHD (8) where Q -- volume of material, cubic feet. t = average wall thickness, feet. For all practical purposes, the value of r.t 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 354 Chapter 26--Chimneys 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 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 3 and 4 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 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 355