PVC Cap as Orifice Design
Summary
The last proposed design was to use install a PVC cap at the base of a small piece of tubing attached to the alum-doser exit orifice. A small orifice would also be drilled into this PVC cap as another exit orifice. Given the head loss that the tubing and orifice combination would provide, we again needed to determine if the resulting alum flow would be slow enough to dose the water appropriately. We looked at the range of flow based on the given allowable 20-percent error and discovered that the resulting flow of alum from this design was too large for our purposes as well. These calculations are extremely similar to those found in the "Series of Orifices" design as both files require the determination of the resulting range in flow of alum.
Calculations
Download the PVC Cap Orifice Design MathCAD file here.
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).
The flow through the alum doser exit tubing was determined given user-defined parameters for the dimensions of the alum stock tank, such as height of tank (and thus, height of alum level) and diameter of exit orifice (and thus, diameter for the attached plastic tubing). These calculations were completed by simplifying the system to a "hole-in-the-bucket" situation.
Next, using the previously determined flow through the exit tubing, the flow through the orifice drilled at the center of the attached PVC cap is determined. The calculations for flow assumes that flow through the tube was constant and neglects the effect of gravity on the flow. We assumed that the flow was fast enough to support this neglection.
Then, head loss through this system is calculated given the user-inputted value for the wall thickness of the desired PVC cap. These calculations utilize the fluids functions found at the top of this page. This head loss is composed of major losses, and hence shear losses, only. It should be noted that the head loss through the system did not include the head loss through the attached tubing. The diameter of the tube was relatively large and the length was generally short; therefore, we concluded that the head loss experienced through the tube would be negligible compared to that through the PVC cap orifice.
Using this information, the necessary flow of alum from the doser based on dimensions given above is determined. Using a required dose concentration of 1.5 mg/L in the untreated water, the necessary stock concentration located 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.