h1. Orifice Size and the Dual Scale Design for the Nonlinear Alum Doser
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{center:class=myclass} h5.Figure 1: Doser Overview {center}
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{center:class=myclass} h5.Figure 2: Close up of nonlinear scale {center}
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h3. Abstract:
During the fall semester of 2009, the Nonlinear Chemical Dosing Team developed the dual scale, 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.
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 |^Lever Arm Calculations 2009 NCDC TM.xmcd]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 equal lengths and two orifices of 3.175 mm and 1.587 mm diameter, 9.525 mm PVC tubing, and other associated hydraulic components listed in our [component list.|^NCDC Component List.xlsx]
There has also been an analysis of the drawbacks of the dual scale and the [effect of surface tension|effect of surface tension] on the dosing schemes. Included in this analysis is the proposition for a submerged orifice and newly designed triple scale doser.
h3. 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 9.525mm 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:
{latex}$$
h_{1Orifice} = K_{DoseOrifice} {{V_{DoseTube}^2 } \over {2g}}
$${latex}
Other Head Losses:
Major Head Losses:
{latex}$$
h_{Lmajor} = f {L\over {D}}{{V^2} \over {2g}}
$${latex}
Entrance Head Loss:
{latex}$$
h_{lEntrance)1Entrance} = K_{Entrance} {{V^2 } \over {2g}}
$${latex}
Since these headlosses vary with time, there will be a graph coming soon to compare the head losses.
The orifice equation, shown below, demonstrates the nonlinear relationship between flow rate and the change in head loss.
{latex}
\large
$$
Q = K_{vc} A_{or} \sqrt {2gh}
$$
{latex}
Where
{latex}\large$$Q $${latex}= Flow Rate
{latex}\large$$h $${latex}= Head Loss
{latex}\large$$A_{or} $${latex}= Area of the Orifice
{latex}\large$$K_{vc} $${latex}= Orifice Constant
The plant itself is also controlled by the orifice. Head loss in the plant after the entrance tank occurs in the rapid mixer, the flocculation tank, and the launders. Those components are all controlled by orifices. The table below lists the major sources of head loss in the plant.
h5. Table 1: Head Loss Through the Plant
|| Process || Head Loss ||
| Rapid Mix Tube | 10 cm |
| Flocculator | 13.5 cm |
| Launder | 5 cm |
| Weir | 5 cm |
| *Total* | *33.5 cm* |
The only source of head loss not controlled by an orifice is the weir. Because the majority of the head loss is due to the orifice, we can state that the orifice 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 equally balanced lever arm of 0.8 m that fits in our 1 m x 1 m entrance tank as well as respond to the 33.5 cm water height difference.
Refer to [Orifice Size and the Dual Scale Design for the Nonlinear Alum Doser Part 2|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.
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