The conservation equations for fluids were derived in the previous chapter. Because of viscosity, the velocity boundary condition on a solid–fluid interface in common applications is no-slip. Velocity slip occurs during gas flow when the gas molecular mean free path is not negligible in comparison with the characteristic dimension of the flow passage. It is discussed in Chapter 13.

The complete solution of viscous flow conservation equations for an entire flow field, it seems, is in principle needed in order to calculate what actually takes place on the surface of an object in contact with a fluid. The complete solution of the entire flow field is impractical, however, and is fortunately unnecessary. The breakthrough simplification that made the analysis of the flow field at the vicinity of surfaces practical was introduced by Ludwig Prandtl in 1904. He suggested that any object that moves while submerged in a low-viscosity fluid will be surrounded by a thin boundary layer. The impact of the no-slip boundary condition at the surface of the object will extend only through this thin layer of fluid, and beyond it the fluid acts essentially as an inviscid fluid. In other words, outside the boundary layer the flow field does not feel the viscous effect caused by the presence of the object. It feels only the blockage caused by the presence of the object, as a result of which the streamlines in the flow field become curved around the object.