Application of Numerical Newton-Raphson Method in Calculation of Emitter Water Discharge of Drip Irrigation System in “Mutis Cemerlang” Coffee Plantation

Abstract

Based on the slope class, the shape of the area and the elevation of dry land in Nusa Tenggara, agricultural land in Noepesu Village is suitable for planting coffee plants with an agroforestry scheme. To overcome the problem of limited water, drip irrigation system technology can be applied. The use of drip irrigation as an agricultural technology in Noepesu village has been carried out by many farmer groups. Still, the installation process does not consider the pipe specifications (pipe length and pipe diameter) and the condition of agricultural land. This causes the service life of drip irrigation to be not long. If this continues, of course, it will increase system installation costs. To optimize service life, a hydraulics analysis method is needed for drip irrigation pipe network systems that take into account pipe specifications and agricultural land conditions.The hydraulics analysis of the drip irrigation network system determines the emitter’s water flow rate. The emitter flow rate forms a nonlinear equation known as the closed pipe equation. In the process of solving these equations, numerical methods can be used, specifically the Newton-Raphson method. This study focuses on applying the Newton-Raphson method to calculate the amount of water discharge from each emitter of the drip irrigation network system on the farmland of the Mutis Cemerlang Farmer Group in Noepesu Village. The drip irrigation system is designed with 250 nodes, 275 pipes, 26 loops, and 86 outlets divided into two sides, with the left side containing 84 outlets with one emitter and the right side containing 102 outlets with two emitters. The amount of water discharge for each emitter is 0,0008 ml/second≤Q≤2,6 ml/second for the left side and 0,001 ml/second≤Q≤1,1 ml/second for the right side, as determined by simulation calculations utilizing the Newton-Raphson method and Matlab software. The simulation results show that the amount of water discharge at each emitter is ideal in the first iteration because it has a discharge correction value (∆Q)≈0.