available and are detailed in previous editions of this handbook. A rule of thumb by the author is 17 mm/m (0.2 in/ft) of flow path length. This rule only applies in the liquid-loaded froth and emulsion regimes (Ql >50 m3/hm or >5.5 gpm/in of outlet weir length). At lower liquid loads, the hydraulic gradient is less.
As noted, the weir crest how is calculated on an equivalent clear-liquid basis. A more realistic approach is to recognize that in general a froth or spray flows over the outlet weir (settling can occur upstream of the weir if a large "calming zone" with no dispersers is used). Bennett et al. [AlChE J., 29, 434 (1983)] allowed for froth overflow in a comprehensive study of pressure drop across sieve trays; their correlation for residual pressure drop h'L in Eq. (14-100) is presented in detail in the previous (seventh) edition of this handbook, including a worked example. Although more difficult to use, the method of Bennett et al. was recommended when determination of pressure drop is of critical importance.
Example 11: Pressure Drop, Sieve Tray For the conditions of Example 9, estimate the pressure drop for flow across one tray. The thickness of the tray metal is 2 mm. The superficial F-factor is 2.08 m/s(kg/m3)y2.
Solution Equations (14-100), (14-106), and (14-107), where ht = hd + P(hw + how), are used. For FS = 2.08, FB = 2.32 and FH = 16.55. From Example 9, Lw = 1.50 m and hw = 38 mm. For a liquid rate of 22,000 kg/hr, Q = 7.27(10-3) m3/s, and Q/Lw = 4.8(10-3). By Eq. (14-107) or Fig. 14-37, P = 0.48. From Eq. (14-102) or Fig. 14-35, Cv = 0.75. Then, by Eq. (14-101), hd = 29.0 mm liquid. Using Eq. (14-109), how = 18.9 mm. Finally, ht = hd + P(hw + how) = 29.0 + 0.48(38 + 18.9) = 56.4 mm liquid.
When straight or serrated segmental weirs are used in a column of circular cross section, a correction may be needed for the distorted pattern of flow at the ends of the weirs, depending on liquid flow rate. The correction factor Fw from Fig. 14-38 is used directly in Eq. (14-109). Even when circular downcomers are utilized, they are often fed by the overflow from a segmental weir.
Loss under Downcomer The head loss under the downcomer apron, as millimeters of liquid, may be estimated from hda = 165.2
where Q = volumetric flow of liquid, m3/s and Ada = most restrictive (minimum) area of flow under the downcomer apron, m2. Equation (14-112) was derived from the orifice equation with an orifice coefficient of 0.6. Although the loss under the downcomer is small, the clearance is significant from the aspect of tray stability and liquid distribution.
The term Ada should be taken as the most restrictive area for liquid flow in the downcomer outlet. Usually, this is the area under the downcomer apron (i.e., the downcomer clearance times the length of the segmental downcomer), but not always. For instance, if an inlet weir is used and the area between the segmental downcomer and the inlet weir is smaller than the area under the downcomer apron, the smaller area should be used.
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