**3. Optimal Number of PWCs for a Smooth Output of the PAT**

Based on Section 2.1, the decrease in the flow of the PAT is 38.4 L/s, for which, according to Equation (7), a total of five PWCs with a flow of 8 L/s each are required to smooth the flow at the inlet of the PAT. The PWC dimensions used for this purpose were the same as those shown in Table 1. Thus, the outlet nozzle of the PWC design becomes an additional inlet of the PAT, injecting the flow into the existing penstock, which is required for a particular stage of operation. Initially, the flow through the turbine was a design flow, and no change was required. As the flow decreases, the output also decreases. One water column is added by the system to acquire the design flow; if the new flow through the turbine meets the design flow, no further water column will be added by the system. However, considering a further deviation from the smooth output, another water column is added to the system to check whether the new scenario provides a smooth output. No changes are required if the new output is smooth. These five PWC were added to the system according to the flowchart shown in Figure 6.

**Figure 6.** Integration of the PWC to maintain the flow.

The integration of the five PWCs with the existing PAT penstock and the injection of an additional flow at the inlet were conducted in ANSYS, as shown in Figure 7.

**Figure 7.** Integration of the PWC with the existing penstock.

As the number of PWCs is increased according to the demand, the flow is maintained at approximately the designed value, as listed in Table 3.


**Table 3.** Flow profile of PAT before and after the addition of the PWCs.
