Boundary layers, Prandtl’s and others

John Anderson’s article on Ludwig Prandtl’s boundary layer is both interesting and informative. More recently, beginning in 1961, the boundary layer concept has been applied to flow about a type of surface called “continuous.” ¹ A characteristic of flows over continuous surfaces is that, for any given period, any two solid surface elements exhibit different drag-time histories, as contrasted with finite-surface flows, in which all surface elements exhibit equal drag-time histories. As a result the formation and termination of the boundary layer are not identified with any part of the surface, but are determined by the system’s boundaries.

Flows over continuous surfaces constitute a new class of boundary-layer problem. Although the differential equations governing flow around the continuous and finite surfaces are the same, the boundary conditions are different, which results in substantially different solutions for the two types of surfaces. Continuous surfaces are primarily encountered in industrial processes—for example, in fiber spinning, ² sheet casting, ³ and film coating ⁴ —where the production of such surfaces is technically feasible and economically desirable.