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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.

Next, the This flow rate can then be used to determine the nominal diameter of the tube. First 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, 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.

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.

This diameter is then used to recalculate the maximum laminar flow given this tube diameter, substituting variables so the diameter is taken into consideration. This new flow rate is then used to determine the number of flow control modules needed by dividing the maximum alum flow rate (Q.FcmMax) by the new Q.FcmMaxLaminar. The maximum of the two numbers (based on the diameter and the flow rate) is used to find the maximum flow rate through each tube, since each module has one tube.

The minimum diameter is found based on the maximum Reynolds number for laminar flow (2100) and the maximum flow rate for the tube found above.

The Another minimum diameter is calculated based on the desired head loss at a maximum flow rate using the minimum tube length available. This calculation is derived from the Hagen-Poiseuille equation.

The tube diameter is then selected based on diameter required for laminar flow and the diameter required for head loss. The largest of the two is chosen.

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