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The current design for the rapid mix tube was developed to address the problems created by the initial design. A schematic of the new design is shown in Figure 3. This new rapid mix tube system consists of two separate 'stages,' a large-scale mixing process in the first portion of the system, and small-scale mixing process in the second portion. The tube protrudes up into the entrance tank to help regulate flow through the plant-flow through the plant will cease once the water level in the entrance tank reaches the top of the rapid mix tube, allowing the water already in the tank to be stored if there is low source flow or the plant needs to be cleaned.
Figure 3. Schematic of the current Rapid Mix Tube system.
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Water enters the top of the tube through the large-scale mixing orifice, where it is dosed with the aluminum sulfate and begins the rapid mix process. This orifice is in place to create large scale mixing in the first section of the tube. The design of this orifice size is based on the exit loss coefficient through the orifice, K. The target K value for this orifice is 2, which provides the best mixing in the first section of the tube for large-scale rapid mix. To calculate the necessary area and diameter of the large scale mixing orifice, the following equation was used:
Solving for A.in, which will be the area of the stream of water entering the tube through the orifice, we obtain:
In this equation, A.in is taken to be the area of contracted flow through the orifice, which is the area of the large-scale mixing orifice multiplied by the vena contracta coefficient, which accounts for the contraction of flow through an orifice. The equation the describes this is as follows:
Figure 4 illustrates the effect of the water contraction flowing through an orifice.
Figure 4. Diagram showing the area used for A.in in the Exit loss coefficient equation.
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After water flows into the rapid mix tube and through the top section of the pipe to achieve large-scale mixing, it reaches the small-scale mixing orifice. The area of the small-scale mixing orifice is designed to achieve a target head loss, providing a mechanism to measure the level of water in the plant to assist in the correct dosing of the plant's raw water source with aluminum sulfate. The equation used to calculate the area of the small-scale mixing orifice is as follows:
In this equation, Q signifies the flow rate of water through the plant, K.vc is the vena contracta coefficient as discussed above in the large-scale orifice design section, and Δh is the target head loss for which the plant is being designed; this design value can be varied based on the desired characteristics of each plant. K.vc is used here again because the flow of water through the small-scale mixing orifice is also a flow contraction, and the area of the water stream entering the pipe following is a fraction of the area of the orifice.
The area of the small scale orifice can be either cirucular or rectangular in shape, again depending upon the plant flow rate, desired energy dissipation rate, and desired head loss through the small-scale orifice. A diagram of some possbile orifice configurations is shown below in Figure 5. Each of these designs is preferred in different cases depending on the plant flow rate, pipe diameter, desired head loss, and desired energy dissipation rate. Tentatively, the Agalteca plant will feature a small-scale orifice featuring the multiple round orifices, which will best serve this plant in evenly mixing the aluminum sulfate dosed to the raw waste, as well as achieving the desired energy dissipation rate through the orifice. To calculate the dimensions of the round orifices that will occur in the small-scale mixing orifice, the following equation in used:
Here, ε is the value of the maximum energy dissipation rate for the plant, and the orifice is thus designed to achieve this value. Δh is the same target value for the head loss from the small-scale orifice design equation. This equation thus calculates the maximum minimum dimension of a rectangular orifice. This dimension can be adapted to the proposed Agalteca design with multiple small orifices, however, because of the presence of many small orifices in entire small-scale mixing orifice. The dimension calculated in this equation will then be used as the diameter of the multiple orifices that must be put into the small-scale mixing orifice. Figure 6 prvides a schematic of the rapid mix tube as well as the placement of the two orifices and a detail of the multiple-orifice small scale mixing orifice that will likely be used in the Agalteca plant.
Figure 6. Proposed schematic for the rapid mix tube showing orifice placements and design for the small and large scale mixing orifices.
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