Uniform fertilization method based on differential pressure tank

Differential pressure tank is a widely used fertilization device in the application of fertilization in China and many other countries. However, the fertilizer concentration in the tank continuously decays with the inflow of water. The decay feature of fertilizer concentration can easily lead to excessive fertilization at the head and insufficient fertilization at the end of the irrigation system. An analytical solution was proposed in this paper to achieve uniform fertilization based on differential pressure tank with constant fertilizer concentration and flux. The relationship between the uniform fertilization analytical solution and the fertilizer continuity equation was obtained based on differential pressure tank. The analytical solution was expected to control the flux flowing into the differential pressure tank and the flux directly flowing into the irrigation system through the main pipe according to 4 parameters: Uniform fertilizer concentration, initial fertilizer concentration, the volume of differential pressure tank and the total fertilization flux of the main pipe. Based on the analytical solution, the fertilizer continuity equation and the incompressible continuity and momentum equations of water were used for describing the movement of mixture in the differential pressure tank. The numerical model for mixed water and fertilizer flow in the differential pressure tank was determined by experimental data. The fertilizer concentration simulated by numerical model was nearly uniform in the tank and the fertilizer concentration at tank outlet obtained by numerical model decayed with a negative exponential pattern as described by Feng’s theory. The numerical simulation results directly verified the accuracy of the basis of Feng’s theory. The differential equation was also the basis of the uniform fertilization. The mean absolute error between the differential equation and the experimental data was less than 0.041 when the boundary condition of traditional fertilization method was substituted into the differential equation, which indirectly proved the rationality of uniform fertilization method satisfying the boundary conditions of constant fertilizer concentration and flux. The analytical solution’s feasibility in the uniform fertilization process based on differential pressure tank was simulated by the numerical model of fertilizer solution in determining the uniform fertilizer concentration and the fertilization time. The fertilizer concentration at tank outlet simulated by the numerical model decayed almost linearly and agreed with the uniform fertilization analytical solution. The fertilizer concentration simulated by the numerical model at drip irrigation system inlet was almost uniform and in agreement with the analytical solution of uniform fertilization. The relative bias of fertilizer concentration between the analytical solution and computation calculated by the numerical model was less than 15%, which verified the feasibility of uniform fertilization method based on differential pressure tank. The results showed that the application of uniform fertilization method and the uniform fertilization method could basically achieve constant fertilizer concentration and flux based on differential pressure tank. According to the actual product, the relationship between valve opening and time could be obtained in order to realize the control of valve opening process by computer. Approximately 70% to 80% of fertilizer in the normal operation was within range of the excessive or insufficient amount, whereas the uniform fertilization method could effectively avoid the waste of excessive fertilization and the lack of insufficient fertilization. © 2020, Editorial Department of the Transactions of the Chinese Society of Agricultural Engineering. All right reserved.