Calculating Orifice Sizes and the Dual Scale for the Lever Arm.
Abstract:
During the fall semester of 2009, the Non-linear Chemical Alum Doser Team calculated the two orifice sizes and developed the dual scale for the lever arm. Our goal was to meet the alum needs of the upcoming AGALTECA plant, which has a maximum flow rate of 6.3 L/s, maximum alum stock dosage of 125 gm/L, and a maximum target alum target rate of 100 mg/L. We determined that a nonlinear alum doser with a scale arm length of 0.5m, total lever length of .75m, tube diameter of 3/8 inch, and orifice sizing of .082 inch and .044 inch can meet the needs of the AGALTECA Plant. Other lever arm parameters can be found along with the calculations deriving them on the embedded Mathcad file "2009 NCDC Lever Arm Calculations"
Methods:
Our method consisted of 1)establishing the relationship between plant flow rate, alum dosage, delta h between the constant head pump, and the dual scale 2)utilization of Mathcad
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Array function to link them 3)Trial and Error process to determine orifice size and the dual arm scale.
We first link the plant flow to the target alum flow rate via the mass balance equation. We then utilized the orifice equation to link the alum float rate to the different delta h's. Delta h divided by the sin(angle deflection) gives us the points along the lever which is our dual scale.
We utilized the array calculation ability of Mathcad to link the plant flow rate to the dual scale. The Mathcad file first asks the user to input all the necessary plant parameters to include target alum dosage scale as an array. It then develops another arrary of alum flow rate necessary to meet those target alum dosage given the plant's flow rate and the alum concentration of the stock tank. We then created an array of delta H for each alum flowrate utilizing the orifice equation. The Mathcad then created another array indicating points along the scale that would correspond to each delta H.
Given a set maximum angle deflection and other specified plant parameters, we would vary the orifice diameter through a trial and error process until we are able to both achieve the desired array of alum dosage and the corresponding array of dual scale that fully utilized the entire length of the scale arm.
Results/Discussion
The two orifice sizes that we calculated were .082 inch and .044 inch. Because the dosage tube is so wide(3/8 inch), these two orifices control the flow of alum from the constant head tank to the entrance tank. Given these two diameters and other plant parameters we are able to utilize the entire length of the scale arm on our lever as a scale.
Conclusion and Future Work
Plant flow rate, the alum flow rate, orifice size, delta h, and the distance along the lever from the pivot point(dual scale) are related to one another and we utilized this relationship to develop both the dual scale and the orifice size at the same time. The mathcad file "2009 NCDC Lever Arm Calculations" links these different parameters and is designed to serve as a tool to enable the user to develop both the best orifice sizes and the dual scale by enabling the user to change the orifice sizes given other constant plant and lever arm parameters to meet the dosage needs of the plant as well as fully utilize the entire length of the scale of the lever arm(0.5m in length).
We utilized the matrix calculation ability of Mathcad to link the plant flow rate to the dual scale. We first link the plant flow to the target alum flow rate via the mass balance equation. We then utilized the orifice equation to link the alum float rate to the different delta h's. Utilizing a maximum angle deflection of 38 degrees we developed an array of points along the scale that corresponds to our array of different delta h's.
Results/Discussion
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Our next step is conduct experiments to find a solution to the clogging problem currently occurring with actual alum dosers in the fields of Honduras.
Bibliography
- CEE4540 Flow Control Measurement Notes at https://confluence.cornell.edu/display/cee4540/Syllabus
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