## 3 Results and Discussion
### Evaluate the Results of Numerical  
In this co-evaluation section, after checking (a) the optimal distance between the butterfly valve and the Howell-Bunger valve, as well as (b) the difference between the output results of the two distances of 8 m and 10 m, in order to save operating costs, then, the distance between the two valves was set at 8 m (equivalent to four times the diameter of the pipe). Besides, the desired distance with the butterfly valve was set and installed in one of the branches of the physical model. For the quantitative evaluation of the flow conditions in the distance between the butterfly valves and the Howell-Bunger valve, a dye injection flow visualization was added at a distance of 20 m from the howler valve (133.3 cm in the model). Figure 13 showed images of the flow situation in the area. In these images of Figure 13 it was concluded that the dye injection flow visualization at the inlet section of the intake valve can cover the entire section of the pipe and enter the Howell-Bunger valve uniformly and in a steady state. Laboratory results also confirm that, at low flow velocities, the fluid motion within a pipe is smooth and laminar, while at high velocity, the motion quickly becomes complex and turbulent. In some intermediate range of flow velocities, the flow is neither fully laminar nor fully turbulent, but rather a complicated combination of these two that varies over both space and time in a highly intermittent and unpredictable fashion.  
Figure 12: (**a**) The Sectional view of velocity magnitude contours for the longitudinal distance between two valves = 5D; (**b**) The Sectional view of turbulent energy contours for the longitudinal distance between two valves = 5D; and (**c**) Vorticity contours.  
In [PERSON]'s (2012) [37] study based on numerical simulation of butterfly valves, the required values for the velocity inlet boundary when using the k-e turbulence model, such as velocity vectors, turbulent kinetic energy, Reynolds Number, and turbulent dissipation rate, were extracted from the periodic simulations and considered for the inlet for the 2.5D-long upstream pipe. In the [PERSON] (2012) study, a distance of 2.5D times the diameter of the pipe has been confirmed to create conditions for the fully developed flow. Considering the existence of the Howell-Bunger valve and also the local expansion after the butterfly valve in the present study, it seems necessary to consider a distance of at least 5D times the diameter of the pipe.  
[PERSON] et al. (2022) [38] researched the DN50 butterfly valve and studied the flow situation of butterfly valves with different shafts. The resistance characteristics, flow state characteristics, Reynolds Number, and flow instability of butterfly valves with different structures were studied by experiments and numerical simulations. The results of the study showed that after 4D, the velocity in the valve is basically equal to the outlet velocity. The absence of velocity fluctuations shows that the developing flow becomes a fully developed flow, where flow characteristics no longer change with increased distance along the pipe. According to the location of the Howell-Bunger valve near the butterfly valve in the present study and the evaluation of the results presented in [PERSON] et al. (2022) studies, the minimum distance between the butterfly valve and the butterfly valve was confirmed to be 5D times the diameter of the pipe.  
Figure 13: The regimes of pipe flow are illustrated by experimental modelling and sketches modeled after those in [PERSON] (1883): (**a**) at low flow velocities, the fluid motion is laminar and dye injected at the pipe inlet produces a straight streamline; (**b**) the transitional regime occurs at intermediate flow velocities where the flow exhibits irregular, intermittent turbulence; and (**c**) at high flow velocities, swirling motions of injected dye reveal that the fluid becomes turbulent within a short distance of the pipe inlet.