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516 CHAPTER 36 1959 Guide for a given inlet temperature and flow rate, to the ideal draft that would be observed if the same quantity of flue gases traversed the chimney without cooling and without friction. The chimney efficiency may be calculated as follows: . ______________final measured draft ideal draft calculated from the inlet temperature REQUIRED DRAFT Before the proper chimney for a particular installation can be selected or designed, the required draft of the combustion unit must be known. The required draft is equal to the sum of all of the resistances' to gas flow from the point at which combustion air enters the unit to and including the chimney connection. This is based on the assumption that air for combustion is available without restriction (such as would be caused by tightly enclosed building construction) at that dustrial chimney class, and their requirements should be treated accordingly. The majority of industrial chimneys op erate under induced or forced draft, resorting to natural draft operation only in the case of emergencies. They are built of brick, concrete, or steel, depending upon economy and the type of installation needed. Proper height is of importance because of removal of waste products, inasmuch as the prod ucts of combustion are often deflected downward around the chimney and, with the large amount of gases that are ex hausted to the atmosphere through the industrial chimney, downwash can be very objectionable.1 AVAILABLE DRAFT FOR THE INDUSTRIAL CHfMNEY The available draft, Da, for large chimneys and stacks has been estimated with apparent satisfaction in the past by means of formulas which in effect deduct an estimated fric tion 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 procedure results in formulas for the available draft as follows: For a cylindrical stack: Q.QOmW'TJL D, (3) d*Btpe and for a rectangular stack: for Various Kinds of Coal point of entrance to the unit. Particularly in residences, un restricted supply of combustion air must be assured. fig. 1 presents information on the fuel-bed draft loss for various kinds of coal burned at different rates. Rough gen eralisations can be given for the losses in the flue passages of boiler or furnace but, on account of the great differences in such devices, more reliable data on their flue-gas volume, temperature, and flue resistance should be obtained for de sign purposes from their respective manufacturers. Flue gases encounter resistance to flow in breechings or smoke pipes, and this can probably be treated with sufficient accuracy by means of the method used for air ducts. (See Chapter 21.) The friction in straight ducts can be estimated by means of the last term of Equations 3 and 4. Abo, the temperature of flue gases falls during passage through breechings or flue pipes. For uninsulated surfaces this probably can be adequately estimated by assuming a loss of heat from the flue gas of 3 Btu per (hr) (sq ft) (Fahr enheit deg temperature difference between the gases and surrounding air). INDUSTRIAL CHIMNEYS . Chimneys can be classified as residential and industrial, the chief difference being their sizes and the types of draft. Chim neys over approximately lYz ft in diameter are in the in where Dm ~ available draft, inches water gage. H = height of chimney above inlet, feet. B, *= existing barometric pressure, inches of mercury. pt = density of air at 0 F, 1 atmosphere pressure. density of flue gas at 0 F, 1 atmosphere pressure. T, temperature of atmosphere, Fahrenheit, abso lute. Tm * temperature of flue gas, Fahrenheit, absolute. W ** flue gas flow rate, pounds per second. / = coefficient of friction. L ~ length of frictioo duct (approximately equal to H), feet. d *= minimum diameter of round chimney, feet. z 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 B,, 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 unitwexght of a cubic foot of chimney gases at 0 F and sea level barometric preaure is given by the equation: p. ~ 0.131CO, + 0.0950, + 0.083#, (5) In this equation CO,, 0, and #, 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 p, may be assumed at 009. The effect on the chimney gas density, of superheated water vapor resulting from moisture and hydrogen in the fuel, or of any air infiltration in the chimney proper, is disregarded. Al though water vapor content is not disclosed by Orest analysis. Chimneys and Draft Calculations its presence tends to reduce the actuai weight per cubic foot . chimney gases. 3. The atmospheric temperature is the actual observed tem perature of the outdoor air at the time the analysis of the op erating chimney is made. `Hie 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 tignfrTM>CQ or freedom from leaks, its area, its height, and the velocity of the 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 ou chimneys varying in diameter from 3 to 16 ft, and in height from 100 to 250 ft, Equation 6 was de duced :* rcr-i -3 (6) Tt *= temperature at the center of the connection from the breeching, Fahrenheit, absolute'. Hk *= height of the stack above center line connection to breeching,feet. 5. The coefficient of friction between the chimney gases and a gooted surface has been taken by many workers in this field as a constant value of Oj016 for the conditions involved. This value, of course, would be less for a new unlined steel stack (v>gn for a brick or brick-lined chimney, but in time the inside surface of all chimneys, regardless of the materials of construc tion, becomes covered with a layer of soot, and thus the co efficient 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 0316 has been employed in the development of the various special equations and charts shown in this chap- In important large chimney design, especially when the con struction or the materials are unusual, it is recommended -that use be made of the Reynolds number* in determining the fric tion factor, f. 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; chim ney gas temperature, 500 F; sea level atmospheric pressure, B, = 2932 in. Hg; atmospheric and chimney gas density, 00863 nH 0.09, respectively; coefficient-of friction, 0016; length of friction duct, 200 ft. The chimney discharges 100 lb of gases per second. Solution; Substituting these values in Equation 3 and reducing, D. = 2.96 X 200 X 29.92 X /(0".0J8g63- ~ 0.09\ 517 Noturol-Draft Chimney 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 tiie wide open point of a centrifugal pump. A set of operat ing 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 chim ney. This chart is based on an atmospheric temperature of 62 F, a chimney gas temperature of 500 F, a unit chimney gas 000126 X 100* X 960 X 0.016 X 200 10* 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 chimney operating under the general condi tions noted in Example 1. When the chimney is under static conditions and no gases are flowing, the available draft is equal to 127 in. of water, the theoretical intensity. As the amount of gases flowing increases, the available draft de creases until it becomes zero at a gas flow of 297 lb per sec ond, at which point the draft loss, due to friction, is equal to the theoretical intensity. The point of maximum draft and s' To solve a typical example: Proceed horizontally from a Weight Flow Rate point to intersection with diameter line; from this intersection follow vertically to chimney height line; from this intersection follow horizontally to the right to Avail able Draft scale. Starting from a point of Available Draft, take steps in reverse order. fig. 3___ Chimney Performance Chart