10. Boundary Conditions for Fluid Mechanics

With this chapter, we complete the formulation of fluid mechanical model systems by considering the requisite boundary conditions for the governing partial differential equations developed in the last one. The no-penetration and no-slip fluid mechanical boundary conditions at rigid surfaces are catalogued for various configurations and the kinematic boundary condition at material surfaces is deduced from the relative normal speed of such a moving interface. The concept of a surface of discontinuity is introduced and careful application of the balance laws to that surface is shown to yield jump-type boundary conditions satisfied by the dependent variables across them. Then these are applied to the two-dimensional propagation of a shock front through an inviscid fluid to deduce the Rankine Hugoniot jump conditions for that situation. The problems deal with those specific jump-type conditions to be imposed for a variety of other continuum processes containing such surfaces when modeled in this manner, which involves its curvature and surface tension.