Document O6QNX2dQnr49N0xOMa11jEQ

730 CHAPTER 32 1955 Guide' appreciable, as in elbows of good design, it is customary to include the dynamic loss with the friction loss, thereby facilitating design calculations. PRESSURE LOSSES IN ELBOWS It is convenient to express the combined dynamic and friction losses due to an elbow as equivalent to the loss in a length L of similar straight duct. -A recent A.S.H.V.E. survey9 of available data has indicated that this method of expressing the loss is justified for design purposes, owing to the relation of the loss to the corresponding friction factor, /. Fig. 5 gives the additional equivalent length of duct in terms of widths W for elbows in rectangular ducts; Fig. 6 gives the equivalent length in terms Air Duct Design 731 the aspect ratio is = g- = 4.0; Fig. 5 gives (L/W), = 6, so Lj = 6 X 6/12 = 3 addi tional equivalent feet. The total length of the straight runs from A to D is I = !a_b + 1b-c + Ic-d = 7 + 20 + 5 = 32 ft and the additional equivalent length due to the elbows is L = In + In = 23 + 3 = 26 ft. Thus the equivalent length of the system from A to D is 1 + L = 32 + 26 = 58 ft of 6 by 24 in. duct. The diameter of a circular duct, equivalent in friction and capacity to this rec tangular duct, is 12.4 in. as given by the table of circular equivalents, Table 2. At a delivery rate of 2000 cfm, the A.S.H.V.E. Friction Chart, Fig. 2, gives a loss of 0.6 in. of water per 100 ft of 12.4 in. diameter duct. Thus the loss from A to D is 0.6 X 58/100 = 0.348 in. of water. The use of elbows of radius ratio, R/W = 1.5, is considered good practice with respect to both installation and operation. In a given rectangular duct 6 by 24 in., for example, the additional equivalent length L necessary to represent the elbow loss will generally be greater for a flat bend where the Fio. 5. Loss in 90-Deg Elbows of Rectangular Cross-Section of diameters D for round ducts. When these curves for additional equiva lent length are used, the straight lengths of duct between elbows should be measured to the intersection of their center lines. The data of Figs. 5 and 6 may be readily converted9 to the loss as a percentage of the velocity head. Example 8: (Use of Fig. 5 for the calculation of elbow losses.) Given the portion of a duct system shown in Fig. 7, it is required to determine the pressure loss between points A and D. Air at standard conditions is being suppheu at the rate of 2000 cfm in a 6 by 24 in. galvanized duct of average construction. Jtibows No. 1 and 2 have centerline radii of 18 and 9 in., respectively. Solution: For elbow No. 1 the radius ratio R 21i8~ 0.75 and the aspect ratio is S} -- ^ = o.25. The additional equivalent length for elbow No. 1 in terms of W' is obtained from Fig. 5: (L/lf), = 11.5. Thus L, = 11.5 X 24/12 = 23 additional equivalent feet. Similarly for elbow No. 2, the ratio radius is ^ = g = l-5 and aspect ratio, H/W -- 1/4, than if the bend of the same radius ratio bad *D p*ane the narrow dimension giving an aspect ratio, Datapresently available for losses in compound bends,10'11 where two or more elbows are close together, do not warrant refinement of design calcuations beyond use of the sum of the additional equivalent lengths L for the individual elbows. Where angles of other than 90-deg bend are enc?VnTMe^> the loss may be considered as directly proportional to the angle oi bend. Losses11 for elbows discharging air directly into a large space are T4 t e , ^ose indicated in Figs. 5 and 6 for elbows within duct systems. A q tt v<r' *osses .branch take-offs are at present quite meager. An -o.tl.V.E. cooperative investigation is underway for the purpose of obtainng more data on losses in typical take-off fittings. j Thtning vanes may be advantageously employed in elbows, both to reuee the pressure loss and to provide a more uniform velocity distribution ownstream from the bend. Vanes and concentric splitters are particularly ecommended where miter elbows are used, because even the simplest vane