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Download the PVC Cap Orifice Design MathCAD file here. These calculations are extremely similar to those in the "Series of Orifices" design as both files require calculations
The head loss in the tube was determined using the equations for major and minor losses. The equations used in these calculations were found in online AguaClara notes and in Frank M. White's Fluid Mechanics (6th Edition).
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Using this information, the necessary flow of alum from the doser based on dimensions given above is determined. Using a stock required dose concentration of 1.5 mg/L in the untreated water, the necessary stock concentration is found as welllocated in the alum doser can be calculated.
The following section calculates the flow of alum given varying alum stock heights (of 5 inches to 25 inches). The final graph depicts results showing that if alum stock height varies greatly, the flow remains generally within the acceptable flow error. This error stems from the fact that we are not using alum for flocculation. Flocculation requires precision whereas merely dosing for improved performance leaves room for some error.
These results prove that this design will not work well with our point-of-use unit either. By playing with the dimensions of the tubing, pvc cap, alum doser itself, and more, the lowest average flow we could obtain was around 6 mL/s. Though this is better than the "Series of Orifices" design, it is still extremely high for our desired system. Given this value, 518 L of alum stock would be used per day. This would require a large holding tank well beyond the size we originally planned to use.