MATHCAD Design of Filter and Clear Well

MATHCAD File.

PDF version of our MATHCAD File.

Mathcad Code Explanation:

Target Input:
We are determining the parameters of the plant that we have, and then the basics of the filter design, such as number of filters, backwash time, and the amount of bed expansion.
Condition Input:
These are where the parameters of the construction materials are entered (ex. Media and pipes). The design is for a sand filter resting on about half as much gravel.

Calculations:
First we determine the size of the filter and head loss in normal filtration. Then we use two approachs 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 headloss between those two points (headloss from the pipe, elbows, expansion and contraction, expansion of the bed). To do this, we used information from Okun  and the "Minor Losses in Pipes" Manual.

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:  

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.

2) The design based on the empirical Weber equation (instead of the conservative approach) is much smaller and less expensive. However, the validity of the empirical equations is not yet certain. Therefore testing needs to be done in bench and pilot scale models.

3) If the empirical equations are valid, then we can change parts of the design, by changing the sand parameters. For example, lower BW velocity by lowering the d60 and specific weight of the media.