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Orifice

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Size and the Dual Scale

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Design for the Nonlinear Alum Doser

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Abstract:

During the fall semester of 2009, the Non-linear Chemical Alum Doser Team calculated the two orifice sizes and Nonlinear Chemical Dosing Team 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 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 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).

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^{Image Removed}

Deliverables

, orifice-based doser in order to be able to deliver both turbulent and laminar alum flow. Like its linear predecessor, this doser must automatically increase or decrease the alum solution to maintain a target dosage set by the operator as the plant flow changes. As an additional feature, the two different scales provide the operator with additional precision through a low dosage (5-25 mg/L) and a high (20-100 mg/L) alum dosage range. Refer to attached file Doser Diagrams and Dual Scale for editable files for diagram and dual scale.

In order to meet our objectives above, we first researched and identified the nonlinear relationship between plant flow rate and alum dosage and the movement of the lever arm. We then utilized this relationship to develop the lever arm design to include the dual scales and the dual orifices. Attached is the Mathcad File that contains the calculations for our dosing system. As shown on Figure 1, our current design consists of a 80 cm long lever arm with the pivot point in the center and two orifices of 2.2 mm and 1.1 mm diameter, 3/8" PVC tubing, and other associated hydraulic components listed in our component list.

There has also been an analysis of the drawbacks of the dual scale and the effect of surface tensionon the dosing schemes. Included in this analysis is the proposition for a submerged orifice and newly designed triple scale doser.

Summary of the Design Process:

In order to meet our design objectives mentioned above, we must link plant flow to alum flow coming out of our doser. We utilized Mathcad's vector calculation ability to help us in our calculations.
Our first step in developing this dosage system was the selection of the orifice to control the flow of alum. We increased the tubing size connecting the constant head tank to the orifice to 3/8" tubing which is wide and smooth enough to make the head loss from the tubing negligible compared to the head loss through each orifice, making the orifice the flow control component for the dosage system.

Head loss through orifices:

$$
h_{1Orifice}  = K_{DoseOrifice} {{V_{DoseTube}^2 } \over {2g}}
$$

Other Head Losses:

Major Head Losses:

$$
h_{Lmajor}  = f {L\over {D}}{{V^2} \over {2g}}
$$

Entrance Head Loss:

$$
h_{1Entrance}  = K_{Entrance} {{V^2 } \over {2g}}
$$

The analysis of the head losses in the system can be seen in Nonlinear Theory.
The orifice equation, shown below, demonstrates the nonlinear relationship between flow rate and the change in head loss.

\large
$$
Q = K_{vc} A_{or} \sqrt {2gh}
$$

Where

\large$$Q $$

= Flow Rate

\large$$h $$

= Head Loss

\large$$A_{or} $$

= Area of the Orifice

\large$$K_{vc} $$

= Orifice Constant

Head loss in the plant after the entrance tank occurs in the rapid mixer, the flocculation tank, and the launders. The flow of water through the AguaClara plant can be effectively represented as a series of flow expansions, a subset of minor losses. . The table below lists the major sources of head loss in the plant.

Table 1: Head Loss Through the Plant

The only source of head loss that doesn't have the relationship of head loss proportional to the square of the velocity is the weir at the exit of the plant that controls the plant water level. Because the majority of the head loss is due to minor losses, we can state that the minor loss equation dominates the relationship. Therefore, we can link the flow rate of the plant with the flow rate of alum required for the plant using the same square root relationship mentioned above. In other words, the rise and fall of the water height in the entrance tank caused by the change in flow rate, is nonlinearly proportional to the alum flow of our orifice based doser. Consequently, the lever arm must be long enough to rise and fall with the minimum and maximum water height in the entrance tank. This range is equal to the total head loss in the plant, which is 33.5 cm as shown in Table 1. Therefore, we designed an 0.8 m long lever arm that fits in the 1 m x 1 m entrance tank and that responds to the 33.5 cm water height change.

Refer to Orifice Size and the Dual Scale Design for the Nonlinear Alum Doser Part 2 for the rest of the research on orifice sizing and dual scale design.*Final hydraulic component list-2009 NCDC Component List
*Final orifice and dual scale calculations-2009 NCDC Lever Arm Calculations
*Hydraulic components for the lever arm prototype
*Dual scale engraved on the lever arm prototype