The aim of this paper is to present a kinetic numerical scheme for the computations of transient pressurised flows in closed water pipes with variable sections. Firstly, we detail the derivation of the mathematical model in curvilinear coordinates under some hypothesis and we performe a formal asymptotic analysis. Then the obtained system is written as a conservative hyperbolic partial differential system of equations, and we recall how to obtain the corresponding kinetic formulation based on an upwinding of the source term due to the ``pseudo topography'' performed in a close manner described by Perthame and al.