May Manal Bounif2022-02-282022-02-282022http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/28093In this thesis, we are interested to finding the analytical and the approximate solution to a two dimensional problem of a fluid flow under a gate, as well as a fluid flow over any obstacle, we consider that the fluid is incompressible and inviscid, and the effects of gravity are neglected. This problem is characterized by the nonlinear condition given by Bernoulli’s equation on the free surface as well as the unknown shape of this flow. When the surface tension effect is neglected, the exact solution can be obtained using the Hodograph method’s. But if we introduce the effect of surface tension, it becomes difficult to find the exact solution to this problem, so we resort to using an approximate method to find the approximate solution, and both methods based on the conformal transformations theory, these two methods demonstrate that there are easily implemented give very important simplifications to this type of problem. In the two cases the problem difficulty is reduced, and transformed it from a two-dimensional problem to a one-dimensional problem.Thesis