## Q tVs T7

These equations may be solved simultaneously for a and b producing

If the number of data points is more than two, the data may be grouped to form two data points. Using i as the index for the first group and j as the index for the second,

S and Sj refer to the total number of member elements in the respective groups. The previous equations are actually calculating the means of the two groups.

Example 7.3 In order to determine the values of a and b of Equation (7.23), experiments were performed on uniform sands and anthracite media yielding the following results below. Calculate the a's and b's corresponding to the respective diameters.

Uniform Sand

Uniform Anthracite i.0 6.2 0.06

Solution: Uniform sand, diameter = 0.5 mm:

hdi 0.06 ββ_., . a = -t- = - = 0.051 Ans r^u^ (ln 006 yr* ΓΌ 1

Uniform sand, diameter = 0.7 mm:

Jd 1 0.06 nrm* a a = -t- = - = 0.0216 Ans fin^/rin^ (m^yiin^)

lnkf in006

Similar procedures are applied to the rest of the data. The following is the final tabulation of the answers:

Diameter (mm) a b

Anthracite 1.0 0.00114 2.17

From the results of this example, the equations below with the values of b averaged are obtained.

hd = 0.051(q)222 for uniform sand, 0.5 mm diameter hd = 0.022(q)222 for uniform sand, 0.7 mm diameter hd = 0.0133(q)222 for uniform sand, 1.0 mm diameter

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