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11-3 SINGLE-PASS(INTERMITTENT) PACKED=BED FILTERS 721 graded sieves (i.e., screens) of diminishing size in-the ratio of 20.5 (see Table 11-7). The quantity of sand in the bottom pan and retained on each sieve is weighed and the successive amounts held between adjacent sieves are added to obtain the cumu- lative weight. The cumulative weights are then converted to percentages of weight equal to or less than the size of the overlying sieve. The cumulative percentages are then plotted versus the size of the sieve opening on arithmetic-log or probability- log paper to obtain the size distribution. The analysis of sieve data-is illustrated in Example 11-2. Additional information on the characterization of various filter ma- terials with respect to size, surface area, and chemical properties may be found in Dallavalle (194$). The effective size dlo and uniformity coefficient (UC) are the principal char- acteristics of the filtering material that affect the design and operation of low-rate intermittent and recirculating and high-rate granular and porous medium filters. For solid filtering mediums such as sand, the effective size dio is defined as the 10 per- cent size by weight, determined by a wet-test sieve analysis (ASTM C117-95). The wet-test sieve analysis is the recommended method because the amount of fine ma- terial cannot be determined adequately with the dry-test method. It is interesting to note that the 10 percent size by weight corresponds quite closely to the median value by count. The uniformity coefficient is defined as the 60 percent size divided by the 10 percent size: G UC d6o (11-2) d10 Grain size affects the time of passage of a liquid through the medium.The uniformity coefficient is used to determine whether the individual particles are of similar size or whether there is a wide range of particle sizes. Determination of the effective size and the uniformity coefficient is illustrated in Example 11-2. i EXAMPLE 11-2.-SAND SIZE ANALYSIS. Given the following data, obtained from a wet-test j sieve analysis of washed river sand, determine the effective size and the uniformity co- efficient. I Size of i } Sieve size opening, Percent or number mm retained i i s in 9.53 0 4 4.75 6.2 8 2.38 16.7 i 16 1.18 24.8 30 0.60 24.1 50 0.30 18.2 i 100 0.15 7.5 Pan 2.5 Solution 1. Compute the cumulative percent passing by weight and plot the resulting values ver- sus sieve size opening. II j I