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Calculations:
First we determine the size of the filter and head loss in normal filtration through the sand and gravel bed.
Then we use two approaches to find the area of the clear well . The first is based upon conventional knowledge that the back wash velocity needs to be 10 times the filter velocity. From there we know that the space between the top of the filter bed and the bottom of the clear well is linked directly to the amount of head loss between those two points (head loss from the pipe, elbows, expansion and contraction, expansion of the bed). To do this, we used information from Schulz and Okun (1992).
The second approach is to use the empirical formula, called the Weber Equation. The velocity for filtration is based on the sand's d60 (this equation is meant only for sand) and the specific weight of both water and sand.
Then the velocity for backwash is based on the filtration velocity, the sand's porosity and the ratio of height of the expanded and unexpanded filter bed.
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{latex} \large $$ V = K_e (\overline \varepsilon )^{n_e } $$ {latex} |
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{latex} \large $$ \overline \varepsilon = 1 - {D \over {D_e }}(1 - \varepsilon ) $$ {latex} |
Once the back wash velocity is determined, solving the clear well and filter dimensions are the same process.
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