Document mp8oaDeLeM7eYYpJNR8Gwwr5O

W 296 CHAPTER 21 1960 Guide respectively. These charts were developed by the ASHAJ3 Research Laboratory.1 The charts, Figs. 2 and 3, were constructed from the basic flow equation for the pressure loss in circular ducts (see Chapter 4): (4) where B/ -- head loss due to friction, inches of water. / -- a nondimensional friction coefficient, which for air- * actuu. o*cun><c c conditioning work depends upon Reynolds number and the relative roughness of the conduit. Appronmate ' Fig. 4 .... Correction Factors for Density and Viscosity values of / were taken from the work of Moody* where e = 0.0005 ft. (See Chapter 4, Fig. 4, Relation Between ductwork.* The correct friction loss for ducts of other than Friction Factor and Reynolds number.) It is numeri-' . standard sheet-metal construction may be determined by cally equal to the reciprocal of the numbel of-duct ' multiplying the losses obtained from figs. 2 and 3 by the diameters required to cause a pressure loss equivalent factors found in Figs. 5 and6i to one velocity pressure. l * length of conduit, feet. . ' D * inside diameter of conduit, feet. - Accurate experimental data on the absolute roughness for flexible .tubing are not yet available. There is also little in formation on the friction loss in ducts lined with acoustical H. -- velocity pressure of mean velocity, inches of water. material. Until definite-information is available, it is recom- The air friction chart is based on standard air with a den -. mended that the correction factor for very rough pipes be sity of 0.075 lb per cu ft, flowing through average, dean,, ' used-for uncovered soft material, and the factor for medium round, galvanized metal ducts having approximately 40 roughness be used for material behind perforated metal. joints per 100 ft. Fig. 2 should not be used to'obtain values Example 1 illustrates the use of Fig. 3 to determine friction below the charts by extrapolation, because critical; flow loss in a galvanized sheet-metal duct. Examples.S, 5, and 4 would occur in this region'and values bo obtained would be . illustrate the use of Figs. 4, 5, and 6 in applying correction unreliable. -' \ - factors for ducts of other than sheet-metal construction and Variations in air temperature of the order'of 20 deg'- .for air at high temperature. ., from 70 F affect duct friction very little. Figs. 2' and 3 can therefore be used for all air systems with temperatures from/ 50 F to 90 F.1 For systems carrying air at.much higher tem Example 1: Determine the friction loss when circulating 10,000 cfm of., air at standard density through 75 ft of 24-in. diameter galvanized duct. peratures, however, the values found in the charts must be - Solution: Find-10,000 cfm on the left scale of Fig. 3 and corrected.* To determine the friction loss in such systems, the / . move horizontally right to the diagonal line marked 24 in. The actual flow rate or velocity existing at the nonstandard con ' other intersecting diagonal shows that'the velocity in the pipe ditions must be used. Changes in humidity, or the changes in barometric is 3200 fpm. Directly below the intersection It is found that the friction per 100.ft is 050 in.; then for 75 ft the friction will be 0.75-X 050 = 058 in. In a like manner, any two variables may pressure or in the pressures required to circulate the air through the systems, have little ;influence on duct friction and can be disregarded in calculating friction losses in-ordi nary air-flow systems.1 For unusual conditions, the friction ' values obtained from Figs. 2 and 3. must be corrected.* For ordinary applications, an excellent approximation for . nonstandard temperatures is where A. = Khc (5) ft* =* friction loss under actual operatiog'conditions,'inches of water. ft* -- friction loss obtained from Figs. 2 and 3 using the ac tual flow rate or velocity existing under the nonstand- . ard conditions, inches of water. .. K friction loss correction factor, obtained from Fig. 4, dimensionless. For ducts of other than standard sheet-metal construction, correction factors may be obtained from Figs. 5 and 6. The correction factors shown in Fig. 5 were computed for the value-of , the roughness in feet, shown' in Table 1.* Most ductwork today is fabricated from galvanized-iron or alumi num'sheet metal, or flexible tubing. Fig. 6 presents in graphi cal form the recommended correction factors for aluminum. Jo correct for pip* rovgfcata vttipfy friction tost obtained from Fig*. 2 and 3 by wnufai factor obtained from Bg. 5. Fig; 5.... Correction Factors for Pipe Roughness Air Duct Design 297 Table 1.... Values of Roughness for Different Pipes* Degree of Rovgfuwa Aovghne** in Foot Drawn Tubing................................ New Steel or Wrought Iron Pipe.. Galvanized Iron.............................. Average Concrete........................... Average Riveted Steel................... Very smooth Medium smooth Average Medium rough Very rough 0.0000015 0.00015 0.0005 0.003 0.01 be determined by the intersection of the lines representing the other two variables. Example t: If the duct in Example 1 is very rough, instead of galvanized, with 40 joints per 100 ft, find the total friction. Solution: On Fig. 5 find (by interpolation between 12-in. and 40-in. pipe) the intersection of the 24-in. very rough pipe line wnd the 3200 fpm velocity ordinate, and at the left margin read a correction factor of 2. The friction loss in the rough duct is therefore 2 X 058 -- 0.76 in. Example S: If the duct in Example l is made of aluminum, instead of galvanized iron, find the total friction. Solution; On Fig. 6 find (by interpolation between 12-in. and 35-in. pipe) the intersection of the 24-in. line and the 3200-fpm velocity ordinate, and at the left margin read a correction factor of 051. The friction log in the aluminum duct is therefore 051 X 058 = 055 in. Example 4` Determine the friction log in.the duct of Ex ample 1, if the temperature of the air transmitted through the duct is 200 F. Solution.- For t -- 200 F, the density of the air is p. -- 0.060 lb per cu ft. Bence, the actual air-flow rate in the duct is 10.000 X 0.075 Q* 0.060 12A)0 cfm .and the actual velocity V0 4. 12500 3.14 4,000 fpm With Q, -- 12500 and D ~ 24 in, find A. = 0.77 in. of water per 100 ft in Fig. 3 and K -- 0535 in Fig. 4. The friction log under actual operating conditions is: ft. = 0535 X 077 = 0.64 in. per 100 ft. The friction log for 75 ft is then 0.75 X 054 = 0.48 in. CIRCULAR EQUIVALENTS OF RECTANGULAR DUCTS * Used in computing values for Fig. 3. (ob)*- d. 150 (a + !>)" (6) where a *= length of one side of rectangular duct, inches. b = length 0! adjacent side of rectangular duct, inches. d, = circular equivalent of a rectangular duct for equal friction and capacity, inches. Table 2 gives the circular equivalents of rectangular ducts for equal friction and flow rate for aspect ratios not greater than 11.7:1 based on Equation 6* Note that the mean velocity in a rectangular duct will be lees than in its circular equivalent. Multiplying or dividing the length of each side of a duct by a constant is the same as multiplying or dividing the equivalent round size by the same constant. Thus, if the cir cular equivalent of an 80 x 24 in. duct is required, it will be twice that of a 40 x 12 in. duct, or 2 x 23.0 = 46.0 in. DYNAMIC LOSSES Wherever eddying flow is present, brought about by sudden changes in the direction or magnitude of the velocity of the air flowing, a greater log in pressure takes place than would occur in a steady flow through a similar length of straight duct having a uniform cross-section. The amount of this loss, in excess of straight-duct friction, is termed dynamic loss. Although dynamic losses may be assumed to be caused by changes in area actually occupied by the air flow, for con.venience they are divided into two general classes: (1) those caused by changes in direction of the duct and (2) those caused by changes in cross-sectional area of the duct. Dynamic losses vary substantially as the square of the mean velocity of (he air, and are therefore(aco+nv6e)*niently ex pressed as a fraction of the velocity head: An air-handling system is usually sized first for round ducts. Then, if rectangular ducts are desired, their sizes are selected to provide flow rates equivalent to those of the round ducts originally selected. A comprehensive study at the ASHAE Research Labora tory proved that for most practical purposes- rectangular' ducts of aspect ratios not exceeding 8:1 will have the same friction pressure loss for equal lengths and mean velocities of flow as a circular duct of the same hydraulic diameter. When duct sizes are expressed in terms of hydraulic diameter, and when equations for friction loss in round and rectangular ducts are equated for equal flow rate and. equal length, Equation 6 giving the circular equivalent of a rectangular duct is obtained* H4 = dynamic pressure log, inches of water. -- -V = mean velocity of air flow, feet per minute. C -- an experimentally determined constant (dynamic loss coefficient). Where different areas are involved, subscripts are used to denote the area to which the coefficient applies, as Ci for inlet area, Ci for outlet area, and C for orifice area. The dynamic log coefficient C is dimensionless and repre sents the number of velocity heads lost at the conduit transi tion or bend- Values of the dynamic loss coefficient for elbows