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Where:
K.e.orifice: Minor loss Coefficient
K.vc: Vena Contracta Coefficient
d.pipe: Pipe Inner Diameter
d.orifice: Orifice Diameter
The equation for head loss is shown below:
Where:
h: Head Loss
K: Minor Loss Coefficient
V: Velocity of Fluid
G: Gravitational Constant
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 macro-mixing orifice, we should have a minor loss coefficient of 1.3. This is what we are using for our designAnother 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 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 size. An increase in flow-rates will give the 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. We want to keep the head loss through the rapid mixer at 20 - 50 cm maximum and prefer that most of this head loss can be given to the micro-mixing orifice. 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. Due to this, this algorithm will be set to allow the user to determine the constraint, if any they would like to put on the macro-mixer head. Having little or no constraints will allow for smaller pipe sizes.
The equation for head loss is shown below:
Where:
h: Head Loss
K: Minor Loss Coefficient
V: Velocity of Fluid
G: Gravitational Constant
If we run this algorithm with no constraints with a 20 cm head loss through the macro-mixer, we would obtain the following results.
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 orificeThe equation for minor loss coefficients for a submerged orifice shown above is used to find the orifice diameter needed.
The algorithm can be summarized in these following steps:
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Running this algorithm for flow-rates under 50 L/s gave the following results as shown below on Figure 23.
Figure 23: Rapid mix sizing algorithm for lower flow rates with 50 cm maximum head loss and 2 cm constraint on macro-mixer
We also did runs where the constraint was raised to 10 cm head loss through the maco-mixing orifice.
Figure 34: Rapid mix sizing algorithm for lower flow rates with 50 cm maximum head loss and 10 cm constraint on macro-mixer
With this lower constraint, we find much smaller pipe sizes used. The micro-mixing orifices are also larger. We can also change the results to see what happens when we want a 20 cm head loss through the rapid mixer with our 2 cm constraint through the macro-mixer.
Figure 45: Rapid mix sizing algorithm for lower flow rates with 20 cm maximum head loss and 2 cm constraint on macro-mixer
The results for the pipe sizing and and macro-mixer sizing are not changed but we have larger orifices.
The current work is now coding this onto the AutoCAD along with entrance tank.