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Plane Assumption Test
In our initial design, we assumed that as long as the spacing between the filtration tubes in each layer is small in comparison to the depth of a layer of sand, then the flow of water out of the tubes will converge and form a plane of filtration. For our purposes, we assumed that a ratio of 1 to 10 of tube spacing versus filter depth was small enough. Laboratory experiments should be conducted to find the depth which will still allow the tubes to be modeled as a plane. The number of inlet and outlet tubes per plane can also be varied to see if our modeling of the layer of tubes as planes of filtration is accurate. We can decrease the space between the tubes to find the necessary ratio between the sand layer depth and the necessary spacing between the tubes that will allow us to model the layer of tubes as a plane.
Figure 2: Plane Area Concept
Performance Study
A number of parameters will need to be studied in order to find the optimal design conditions for a filtration unit. The variables to be studied experimentally include diameter of sand grains, depth of each filter layer, horizontal spacing between pipes, and filtration velocity. A robust study of all these variables will require a long period of time, and it is thus recommended that we proceed with the design and installation of a filtration unit with conservative design parameters. Once full-scale performance can be analyzed, we can proceed with an exhaustive performance study to further optimize the stacked rapid sand filtration unit design.
Figure 1: Plane Area Concept