Document RJDqyVgO3X6vDOdNYrz3bKvLv

366 CHAPTER 19 1948 Guide To = temperature of air surrounding the chimney, Fahrenheit degrees.absolute. Tq = average or effective temperature of the gases in the chimney, Fahrenheit de grees absolute. "The quantity Dt, yielded by' the' formula, is the pressure difference between the gas inside and air outside of the chimney, in inches of. water, when no flow occurs in the chimney. The quantity is variously known as'the theoretical draft, the static draft or the computed draft. It is very useful in predicting and analyzing chimney performance, but it is seldom if ever attained in an actual, chimney because of the friction incident to gas flow, wind effects, etc. AVAILABLE DRAFT The available draft, Da,for large chimneys and slacks 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 deter mined.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 procedure results in formulas for the available draft'as follows: For a cylindrical stack: Da = 2.96 HBo IFC\ To) 0.00126 H-TTc/Z, D`BqWc (2) and for a rectangular stack: Da = 2.96 HBo WA _ 0.000388 W* TcfL ( -1- y) Tc) xy*B0Wc (3) where Do = available draft, inches water gage. H = height of chimney above grate, feet. Bo = existing barometric pressure, inches of mercury. W0 = density of air at 0 F, 1 atmosphere pressure. We = density of flue gas at 0 F, 1 atmosphere pressure. To = temperature of atmosphere, Fahrenheit degrees absolute. Tc = temperature of flue gas, Fahrenheit degrees absolute. W = flue gas flow rate, pounds per second. / = coefficient of friction. L = length of friction duct ( = H approximately), 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 2 and 3. 1. The barometric pressure, represented by B0, 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 fool of chimney gases at 0 F and sea level barometric, pressure is given by the equation: Wc = 0.131 CO, + 0.0950, + 0.083N, (4) In this equation COt, 0, and Nt 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 Wc 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 infiltrations in the chimney proper is disregarded. Though water vapor content is not disclosed by Orsat analysis, its presence tends to reduce the actual weight per cubic foot of chimney gases. 3. The atmospheric temperature is the actual observed temperature of the outside air Chimneys and Draft Calculations 367 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. This drop in temperature depends upon the material and construction 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 observa tions on chimneys varying in diameter from 3 to 16 ft and in height from 100 to 250 ft Equation 5 was deduced *: 3,3 r, [(f)- ' where .ffb - 3 (5) T\ = absolute temperature at the center of the connection from the breeching, , Fahrenheit degrees. Hb = the height of the stack above center line connection to breeching, feet. 5. The coefficient of friction between the chimney gases and a sooted surface has been taken by many workers in this field as a constant value of 0.016 for the conditions in volved. This value, of course, would be less for a new uiilined steel stack than- for a brick or brick-lined chimney, but in time the inside surface of all chimneys regardless of the materials of construction becomes covered with a layer of soot, and thus the coef ficient of friction has been taken the same for all types.of chimneys and in general 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 development of the various special equations and charts shown in this chapter. In important chimney design, especially when the construction or the materials are unusual, it is recommended that use be made of the' Reynolds number * in determining the friction factor, f. The following problem illustrates the use of Equation 2: 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 tempera ture, 62 F; chimney gas temperature, 500 F; sea level atmospheric pressure, B0 = 29.92 in. 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. Substituting these values in'Equation 2 and reducing: rt Da - 2.96 X 200 X 29.92 X /0.0863 ~ w0.09 \j---0-.-0-0-1-2-6---X101*0X0* 2X9.99260XX0.00.90-1-6--X--2--0-0 = 1.27-0.14 = 1.13 in. Fig. 1 shows the variation in the available draft of a typical 200 ft by 10 ft chimney 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 impending delivery, and corresponds to the point of shut-off head of' a centrifugal 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 2 and then plotting the results in the manner shown in Fig. .1.