I would like to share with you the method for calculating the flow restriction imposed by a valve on the fluid flow in a pipeline

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By adjusting the valve opening, the flow rate in the pipeline can be controlled. How is the relationship between this opening and the flow rate calculated? Valves are installed on the pipelines and operate as part of the entire piping system; the effect of changes in valve opening on the flow rate must be determined through hydraulic calculations of the whole system. In fact, there is local resistance when water flows through a valve. Let the local resistance coefficient of the valve be ζ, the cross-sectional area of the pipe through which water flows be F, and the density of water be ρ. When the fluid pressure before the valve is p1 and the fluid pressure after the valve is p2, with both p1 and p2 remaining constant, the flow rate through the valve is given by Q = (F/√ζ)√. The local resistance coefficient ζ changes as the valve opening degree changes; therefore, the flow rate also changes with the opening degree. This pattern of variation can only be determined through experiments. If the flow rate at full opening (100% opening) is Qmax, then the flow rate at an opening degree of X% is given by Q = f(X%) * Qmax, where the function is determined through experiments and is provided in the form of a curve for reference. In the simplest case, f(X%) is a straight line, meaning that the flow rate is proportional to the valve opening degree; in this case, the flow rate at a valve opening of 25% is Q = f(X%) * Qmax = 0.25Qmax