Comparison and study of several methods for solving the hydraulic jump values in pumping well

Abstract

This paper was envisaged to provide deeper insights of the hydraulic jump value in pumping well in the loess aquifer. Herein, we discussed the research status and problems of the value, compared the differences between the analytical solution method and the empirical formula method. Subsequently, we proposed a fitting method with improvement and the tangent method to estimate the hydraulic jump value, and quantitatively analyzed the linear variation rule of the water level curve around the well. The results show that the value calculated by the traditional empirical formula was about one tenth of the theoretical value in constant flow and the water level around the well was found to be logarithmic in the range of N₁∼N₃. When the range was extended, the water level curve changed to a parabolic nature and power function in turn. The hydraulic jump value obtained by h-r extension of the modified water level curve fitting equation was improved greatly, and the average error was found to be less than 1 m. The stability of the hydraulic jump value using the tangent method was poor, and the estimated horizontal distance was larger than 3 m. The results show that the reliability of the improved curve fitting method was better, while the empirical formula method and the tangent method exhibited a larger error and poor stability. When the error correction was performed, the improved curve fitting method could be used to estimate the hydraulic jump value under the same conditions, and can replace the theoretical calculation value.