We use ideas related to involutive completion of a system of partial differential equations (PDEs) to formulate computational problems of fluid mechanics. As for the solution of differential algebraic equations, the approach requires solution of extra equations for derivative consequences. The extra calculation cost is negligible whereas the discrete form becomes much simpler to handle. We show that in this way we can quite easily improve the performance of existing solvers. Another interest in this article is the derivation of special solutions of the Navier-Stokes system under incompressibility constraint in cylindrical domains.