A set of equations governing an isothermal compressible fluid how is resolved numerically for two practical cases. The first case concerns the fast fluid flow in short gas pipelines where the equations, written in conservative form, are resolved by a predictor-corrector scheme for the interior mesh points: an improved Lax-Friedricks scheme as a predictor and a leapfrog scheme as a corrector. Characteristics and upwind methods are used for the boundary conditions. The second case is concerned with massic slow fluid flow in relatively long gas pipelines. The equations, written in non conservative form, are resolved by a simple explicit finite difference scheme. The boundary conditions are considered by using the characteristic form of the equations including an inertial multiplier (Yow model) and resolved by a Newton-Raphson method. The obtained results agree with those of other methods. These numerical experiments permit the user to gain more computational time and simplicity in comparison with methods.