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The jet flow problem concerning the discharge of a fluid (from an orifice in a container) into the atmosphere is studied herein in the framework of the Helmholtz-Kirchhoff model. The problem is reduced to the study of a system of nonlinear equations. Using Leray-Schauder's fixed point theorem we prove that the system of functional equations has at least one solution. Then we present a semi-inverse method which gives us the possibility to calculate numerically the unknown free lines fordoi:10.13111/2066-8201.2010.2.4.10 fatcat:mldgw7u72rcr5h6remn4bvu2bm