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Rapid Filtration                                                                                 363


                 2. Volume Criterion for Backwash Water Assume that                  W (in.)
                            2
                         3
                   the 6 m =m criterion applies (from Amirtharajah,   0      4      8     12      16
                   1985, illustrated in Figure 12.31). Therefore,  1200                                   5000
                                                                         B    51 mm (2 in.)
                                                                  1000
               V(backwashwater) ¼ V(loading)   A(filter)   2 filters=bay       W                          4000
                        3
                                       2
                           2
                  ¼ 6:0m =m   (4:27   6:10 m )=filter   2 filters=bay                        B = 610 mm (24 in.)
                                                                   800
                        3
                  ¼ 312 m =bay (82,580 gal=bay)                                                           3000
                                                                 Q (m 3 /h)  600             B = 533 mm (21 in.)  Q (gpm/ft 2 )
              Discussion
              Backwash is usually done on a time basis. The use of a                        B = 457 mm (18 in.)  2000
                                                                   400
              backwash turbidimeter would provide a process that has a
              more focused approach to backwash duration. A plot of                       B = 381 mm (15 in.)
              backwash turbidity versus backwash water volume per  200                                    1000
              unit area of filter bed, similar to Figure 12.31, would be              B = 305 mm (12 in.)
              useful for a given installation. Such a plot should be gen-  0                              0
              erated for each kind of raw water filtration season and  0     100    200    300    400   500
              for different pretreatment conditions. To estimate the frac-           W (mm)
              tion of water produced used in backwash, assume HLR
                                             2
              (filtration) ¼ 12.2 m=h (5.0 gal=min=ft ), and assume  FIGURE 12.32 Flow capacities for washwater troughs. (Adapted
              t(run)   24  h.  V(water  produced=run)   (12.2  m=h)    from ITT Water & Wastewater Leopold Inc., Fiberglass Wash-Water
                                        3
              (24 h)   (4.27 m   6.10 m) ¼ 7626 m (2.015 mg). The back-  Troughs, Product Data Sheet FRP-200; used by permission from ITT
              wash water volume is 312=7626   0.04 fraction of the  Leopold, Zelienople, PA.)
              water produced, which is slightly less than the ‘‘rule of
              thumb’’ value of about 5%.
                                                                  In selecting wash-water troughs, the semicircular bottoms
            12.4.4.4  Backwash Water Troughs                   minimize trapping of air and foam (Kawamura, 1991, p. 199).
            The functions of wash water troughs are as follows: (1) to  A filter bed width of  6 m (20 ft) permits the use of ‘‘off-the-
            collect and convey backwash water to a gullet and then  shelf’’ proprietary type of troughs of fiberglass or other syn-
            through pipes or channels and pipes to a storage pond, and  thetic material.
            (2) to distribute coagulated raw water over the filter bed so  On sizing the troughs, Figure 12.32 gives flow capacities
            that there are no localized high velocities (albeit the filter is  for different sizes for a proprietary fiberglass trough. The
            started with backwash remnant water above the media). Some  troughs should have the hydraulic capacity for the highest
            issues in design are (1) spacing, (2) cross-section dimensions,  backwash flow. The trough discharge into a gullet should
            (3) distance above media, and (4) whether to adopt proprietary  provide an adequate free-fall so that there is no backup. The
            methods of reducing media loss.                    gullet itself requires the same consideration with respect to
              Regarding spacing, the distance selected is arbitrary and  hydraulic capacity. Kawamura (1990, p. 202) gives a formula
            may vary 2–3m(6–9 ft). The distance depends also on the  that relates flow and depth for a flat bottom rectangular
            flow capacity of the backwash water troughs. For example,  channel as
            the maximum backwash water flow, Q(max), is divided by the
                                                                                            0:667
            flow per trough, Q(trough). Therefore, the number of troughs                 Q
                                                                                                          (12:46)
            is n(troughs) ¼ Q(max)=Q(trough), where n(troughs) is                h o ¼  CB
            rounded to the nearest whole number. For a rectangular
            filter of dimensions w(filter)   L(filter), the spacing is then,  where
            w(troughs)   L(filter)=n(troughs). When set up on a spread-  h o is the depth of water at the upstream end of channel (m)
                                                                                        3
            sheet, the procedure may be repeated until satisfactory spa-  Q is the flow in channel (m =s)
            cing and trough size are obtained.                    B is the width of channel (m)
              The distance above the media depends upon the backwash  C is the coefficient
            practice. In the United States, the bed expansion is 20%–50%
            and the vertical distance from the media surface to the crest of  . In SI units, C ¼ 1.38
            the wash-water troughs is 0.7–1.0 m (Cleasby, 1992). In the  . In U.S. Customary units, C ¼ 2.49 and other units
            United Kingdom, with air first and water second, with bed  are ft and s
            expansion <10%, the distance is 0.1–0.2 m. In Europe, with
            air-water first and water second, with bed expansion about  12.4.4.5  Under-Drain Systems
            ‘‘zero’’ percent, the distance is 0.5 m. Kawamura (1999, p. 85)  The under-drain system has two functions: (1) to collect
            recommended about 1.8 m (6 ft) for a concurrent air-water  filtered water while retaining the media, and (2) to distribute
            backwash so that the grains of media do not reach the wash-  backwash water uniformly over the area of the filter bed.
            water troughs.                                     Another requirement is that these functions remain intact
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