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The equation for minor loss coefficients for a submerged orifice shown above is used to find the orifice diameter needed.
Figure 1: Design Layout of Rapid Mix System
Research has estimated that for a In the case of macro-mixing orifice, we should have a , we are setting the minor loss coefficient of 1to 1.3. Another design constraint from research is to have a 20-50 cm maximum head loss through both orifices with most of it going into the micro-mixing orifice. This This value is assumed to be adequate to allow for macro-mixing. The total head loss through the rapid mixer is set to 20 - 50 cm with most of the head loss belonging to the micro-mixer. This will be needed for the dose controller that will be integrated into the system. In the case of a macro-mixing orifice, each pipe diameter allows for one orifice sizeThe dose controller uses a flow measurement device which relates head loss to flowrate. From the equation for a submerged orifice, it can be seen with the design assumption of K = 1.3, each pipe size will allow for one macro-mixing orifice size.
A pipe size/macro-mixing combination can be used for a range of flow-rates. An increase in flow-rates will give the that macro-mixing orifice a significant head loss. In the algorithm, if there is significant head loss above a certain limitation (2 cm or above), then the piping is upgraded to the next size. To accomplish this, the pipe sizing algorithm is modified to select pipe sizes that will meet this constraint. Another assumption is that the head losses through the entire plant (both micro-mixer and macro-mixer as well as flocculator) would be used to measure flow This can actually result in the macro-mixing orifice having a higher head loss than the micro-mixing orifice. Due to this, this algorithm will be set to allow the user to determine the constraint, if any they would like to put on can select a constraint value for head loss(usually 2 to 10 cm) that will cap how high the macro-mixer mixing head . Having little or no constraints will allow for smaller pipe sizes. If we run this algorithm with no constraints with a 20 cm loss can be. This is done by selecting a larger pipe size and larger macro-mixing orifice. In figure 2, the results for head loss through the macro-mixer , we would obtain the following resultsare shown below. At high flow-rates, macro-mixing head loss becomes higher than micro-mixing head loss.
Figure 2: Rapid mix sizing algorithm for lower flow rates with 20 cm through micro-mixer and no constraints 
The results show that above that with each pipe size and macro-mixing size, we have high head losses through the macro-mixing orifice which will increase to levels greater than 20 cm and hence give most of the head loss through the micro-mixing orifice.
The algorithm can be summarized in these following steps:
1. Determine the inner pipe size given the flow-rates, maximum pressure drop (20 to 50 cm). total minor loss coefficients, and the available pipe sizes. The user also sets a constraint or limit for the macro-mixing orifice head loss.
2. Using the pipe size given, determine the orifice diameter of the macro-mixing orifice. This is determined using the equation for minor loss coefficients for submerged orifices
3. If the head loss through the macro-mixing orifice exceeds 2 cmthe user-set constraint, then move up to the next pipe available and recalculate the orifice size. This step is repeated until the head loss is 2 cm or less.less than the constraint value.
4. Use the assigned total head loss value (20-50 cm) and maximum flow rate to determine the minor loss coefficient needed for the micro-mixing orifice. Using the equation for minor loss coefficients for submerged orifices to determine the orifice diameter for the micro-mixing orifice.
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