A Theoretical Derivation and Comparison Method for the Optimal Location for Energy Dissipation Boxes

In long-distance, high-elevation gravitational water supply systems, it is essential to incorporate energy dissipation to lower pipeline pressures. The energy dissipation box is a novel device for pressure reduction, extensively utilized in gravitational flow transition systems. Despite its appealing contribution, systematic selection methods still need to be used regarding its optimum location. Hence, this paper considers the sum-of-the-maximum hydrostatic pressure head (SMHPH) and derives an extreme location equation for the energy dissipation box (EDB) in the design stage, and then, it comprehensively accounts for the overcurrent capacity and proposes a theoretical comparison and selection method for the optimal location (OL) between the critical and extreme locations. A theoretical analysis with an engineering case study is conducted to compare the theoretical OL, and numerical simulations are carried out to compare the pressure protection effect of the same box cross-sectional area and initial water volume of the theoretical OL and other possible locations with different initial water depths. The results show that the location of the EDB in the design stage should comprehensively consider the overcurrent capacity and the SMHPH. On the basis of both conditions, the oscillation amplitudes of the pressure gradient beyond the box are significantly decreased as the OL approaches closer to the downstream pipe. If the initial water depth in the box is large, the EDB provides greater protection to the pressure head (PH) by decreasing the cross-sectional area and then maximizing the utilization of water depth in the box and decreasing the volume of the EDB.