Document zbx02wpyQbbBq8wQnzadr690m

424 CHAPTER 17 1956 Guide -the chimney and, with the large amount of gases that are exhausted to the atmosphere through the industrial chimney, downwash can be very ob jectionable.1 AVAILABLE DRAFT FOR THE INDUSTRIAL CHIMNEY The available draft, Z)a, for large chimneys and stacks has been estimated with apparent satisfaction in the past by means of formulas which in effect deduct an estimated friction loss from a theoretical draft determined as in Equation 1. The friction loss can be estimated by means of one of the formulas available for ducts, such as the Fanning equation. This pro cedure results in formulas for the available draft as follows: For a cylindrical stack: D. = 2.96 BB0 p. \ 0.00126WTMrc/L tJ (PBoPo (3) and for a rectangular stack: D, 2.96 HB0 Pc T0 Pc \ 0.000388^7', fLlx + y) To) (xyYBcPc (4) where Do = available draft, inches water gage. H = height of chimney above inlet, feet. Bo = existing barometric pressure, inches of mercury. Po = density of air at 0 F, 1 atmosphere pressure. p0 = density of flue gas at 0 F, 1 atmosphere pressure. To -- temperature of atmosphere, Fahrenheit, absolute. To = temperature of flue gas, Fahrenheit, absolute. W = flue gas flow rate, pounds per second. f = coefficient of friction. h = length of friction duct (approximately equal to H), feet. d - minimum diameter of round chimney, feet. x and y = length and width of cross-section of rectangular chimney, feet. The following notes facilitate the use of Equations 3 and 4. 1. The barometric pressure, represented by Bo, is the actual pressure at the site of the chimney and not the pressure reduced to sea level datum. In general, the barometric pressure decreases approximately 0.1 in. Hg per 100 ft increase in elevation. 2. The unit weight of a cubic foot of chimney gases at 0 F and sea level barometric pressure is given by the equation: Po = 0.131(70, + 0.0950, + 0.0831V, (5) In this equation CO,, Oj.and IV, represent the percentages of the parts by volume of. the carbon dioxide, oxygen and nitrogen content, respectively, of the gas analysis: For ordinary operating conditions, the value of Po may be assumed at 0.09. The density effect on the chimney gases, due to superheated water vapor resulting from moisture and hydrogen in the fuel, or due to any air infiltration in the chimney proper, is disregarded. Though water vapor content is not disclosed by Orsat analy sis, its presence tends to reduce the actual weight per cubic foot of chinmey gases. 3. The atmospheric temperature is the actual observed temperature of tlje outside air at the time the analysis of the operating chimney is made. The mean atmospheric temperature in the temperate zone is approximately 62 F. 4. The chimney gas temperature decreases from the breeching connection to the top of the stack. Tins drop in temperature depends upon the material and construction Chimneys and Draft Calculations 425 of the stack, its tightness or freedom from leaks, its area, its height, and the velocity of the gases through it. The same chimney will suffer different temperature losses depending upon the capacity under which it is working, and the variable atmospheric conditions. No general equation covering all these variables has been suggested, but from observations on chimneys varying in diameter from 3 to 16 ft, and in height from 100 to 250 ft. Equation 6 was deduced :* To = (6) where Ti = temperature at the center of the connection from the breeching, Fahrenheit degrees, absolute. Ht, = height of the stack above center line connection to breeching, feet. 5. The coefficient of friction between the chimney gaseB and a sooted surface has been taken by many workers in this field as a constant value of 0.016 for the condi tions involved. Tins value, of course, would be less for a new unlined steel stack than for a brick or brick-lined chimney, but in time the inside surface of all chimneys, re gardless of the materials of construction, becomes covered with a layer of soot, and thus the coefficient of friction has been taken the same for all types of chimneys and generally constant for all conditions of operation. For reasons of simplicity and convenience-to the reader, this constant value of 0.016 has been employed in the de velopment of the various special equations and charts shown in this chapter. In important large chimney design, especially when the construction or the mate rials are unusual, it is recommended that use be made of the Reynolds number1 in determining the friction factor,/. The following problem illustrates the use of Equation 3: Example 1: Determine the available draft of a natural draft chimney 200 ft in height and 10 ft in diameter, operating under the following conditions: atmospheric temperature, 62 F; chimney gas temperature, 500 F; sea level atmospheric pressure. Bo = 29.92in. Hg; atmospheric and chimney gas density, 0.0863 and 0.09, respectively; coefficient of friction, 0.016; length of friction duct, 200 ft. The chimney discharges 100 lb of gases per second. Solution: Substituting these values in Equation 3 and reducing, Do = 2.96 X 200 X 29.92 X /0.0863 _ 0.09\ \ 522 960 / 0.00126 X 1001 X 960 X 0.016 X 200 10s X 29.92 X 0.09 = 1.27 - 0.14 = 1.13 in. Fig. 2 shows the variation in the available draft of a typical 200 ft by 10 ft chinmey operating under the general conditions noted in Example 1. When the chimney is under static conditions and no gases are flowing, the available draft is equal to 1.27 in. of water, the theoretical intensity. As the amount of gases flowing increases, the available draft decreases until it becomes zero at a gas flow of 297 lb per second, at which point the.draft loss, due to friction, is equal to the theoretical intensity. The point of maximum draft and zero capacity is called shut-off draft, or point of im pending delivery, and corresponds to the point of shut-off head of a centrif ugal pump. The point of zero draft and maximum capacity is called the wide open point, and corresponds to the wide open point of a centrifugal pump. . A set of operating characteristics may be developed for any size chimney operating under any set of conditions by substituting the proper values in Equation 3, and then plotting the results in the manner shown in Fig. 2. Fig. 3 is a typical chimney performance chart giving the available draft for various gas flow rates and sizes of chimney. This chart is based on an