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The second approach is to use the empirical formula, called the Weber Equation. The velocity for filtration is based on the sand's d60 (only works with sand) and the specific weight of both water and sand. Then the velocity for back wash is based on the filtration velocity, the sand's porosity and the ratio of height of the expanded and unexpanded filter bed. Once the back wash velocity is determined, solving the clear well and filter dimensions are the same process.
Design Output:
| Conservative | Empirical |
|---|---|---|
Filter Square Side | 1.5m | 1.5m |
Filter Height | 3.95m | 2.56m |
Clear Well Diameter | 6m | 6m |
Clear Well Height | 1.37m | 1.23m |
Mathcad Conclusions:
1) Our design based on simple hydraulics will work. However, it is a very large filter and will not be sustainable economically. The material cost for construction will be too high.
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