A close analogy with archimedes’ principle: Understanding the relationship between flow resistance and tail vortex zone of square pier through experiments

The flow resistance on the pier has always been treated as a focus issue in fluid mechanics with great significance of application. Square, as an important cross-section form of pillar structure, has been applied widely in practice. To investigate the relationship of the formation mechanism of flow resistance on square pier and the trailing vortex zone of the pillar, in this study, the flow resistance of the square pier and the surrounding flow are firstly measured by pressure sensor and particle image velocimetry (PIV). Then, by analogy with the principle of Archimedes, the relationship between the characteristics of flow, the flow resistance and the trailing vortex zone of the square pier is analyzed in detail under different Reynolds numbers (2500≤ Re ≤20000). According to the experiments, the fitting relation between the time averaged relative volume of the tail vortex zone, the time averaged dimensionless flow resistance and the new time averaged dimensionless coefficient of flow resistance formula with varied Re has been found. It shows a good correlation with all of them and each one related well to Re by a quadratic relation. Both Linear and quadratic fitting of the flow resistance with the volume of trailing vortex zone fits relatively well. The linear fitting formula is recommended in practice of relative large flow.