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A steady flow problem of a viscous incompressible fluid through an orifice is widely applicable to many physical phenomena and has been studied previously by many researchers. A problem of such type has been solved by applying LAD method given by Roache [Comp. Fluids 3 (1975) 179]. The resulting system of linear equations is solved by Adomian decomposition method [Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston, MA, 1994]. We study an analytic solution of a steady flow problem of a viscous incompressible fluid through an orifice by using the Adomian''s decomposition method. The numerical results show the effectiveness of the method for this type of equations, they show that the present approach is relatively easy and highly accurate. [Copyright &y& Elsevier]