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The FCM program calculates the diameter of the flow controller tube, the maximum allowable flow rate through the flow controller tube, and the head loss associated with the flow controller.
First the FCM program calculates the maximum alum flow based on in the inflow from the plant, the maximum concentration of alum allowable (per dose), and the concentration of alum in the stock tank. These values are found within the fluids functions and user inputs.
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Next, the maximum allowable flow rate through the valve must be calculated based on the maximum laminar flow through a reasonable length tube, the maximum head loss through the float valve (given in Design Assumputions, and available tube diameters. The allowable flow rate is based on eliminating the diameter from the Hagen-Poiseuille equation by using the maximum Reynolds number constraint. For higher flows multiple parallel tubes could be used. However the maximum flow rate that can be handled by the float valve needs to be considered.
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The allowable flow rate through the valve and the maximum alum flow are used to determine the number of flow control modules that are needed by dividing the alum flow rate by the allowable valve flow rate.
Next, the diameter of the tube is obtained by comparing the maximum and minimum diameters needed to meet certain constraints. The following equations outline those constraints.
The maximum diameter is calculated that will give the desired maximum head loss. Note that Nu.FcmAlum refers to the viscosity of alum, which is calculated by dividing the viscosity by the density of the alum.
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Note that the minimum length of the tube is equal to the maximum head loss to be at least as great as the maximum head loss with some additional length to be able to reach the ports.
The tube diameter is then selected based on the diameter required for laminar flow and the diameter required for head loss. The largest of the two is chosen. Note that the maximum diameter is not compared because this was already taken into account for the minimum diameters. From there the inner diameter of the FCM tube is found by comparing the minimum diameter to the available diameters.
Finally, the length of the tube is determined using the Hagen-Poiseulle equation and the diameter of the tube found in the previous step.
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The FCM program also calculates the viscosity of the alum based on given molecular weights, as well as data found by Gurevich, R.A.
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