ABSTRACT
130Regular perturbation expansions are used to analyze the fluid dynamics of unsteady, inviscid, slender, thin, incompressible (constant density), axisymmetric, upward and downward, annular liquid jets subjected to nonhomogeneous, conservative body forces. In this chapter, one-dimensional models for inviscid, incompressible, axisymmetric, annular liquid jets falling under gravity will be obtained by means of methods of regular perturbations for slender or long jets, integral formulations, Taylor’s series expansions, weighted residuals, and variational principles. Then, the hydraulic model will be asymptotically presented Boussinesq for slender and thin annular liquid jets. These models are based on Taylor’s series expansions, method of weighted residuals, and the Kantorovich-Galerkin technique so will be resulted in third-order ordinary differential equations. For these purposes, the control-volume formulation can be utilized for assumption to be uniform throughout the annular jet.
