The objective of this work was to use interpolation as an auxiliary tool in determining the performance of a Hydraulic Ram (CH), knowing approximately the amount of trees that can be irrigated, being able to adapt the CH to expand irrigation to more trees, in the case studied for the production of açaí by family farmers. In this context, the concept of irrigation was introduced, its importance and high cost, in addition to the importance of family farming for local communities, verifying the cost benefit for small producers. Then, a method of capturing water was presented for use in irrigation in conjunction with a mathematical formulation (mathematical model). After, the concepts of polynomial interpolation were presented, presenting Newton's interpolator polynomial which was defined by defining the Gregory-Newton polynomial, which is the one used in the work in question. Still as information, the Tauerá de Beja community is presented, in which the CH installation was carried out. When analyzing the results, it was possible to estimate through the Gregory-Newton interpolation, the CH yield in the heights used, making it possible to determine approximately how many açaí trees the CH could supply in irrigation, corroborating in
a perspective of potentiating the production of small producers that need an irrigation process taking into account cost / benefit.
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