Analogy between Laval Nozzle and One-Dimensional Compressible Flow under Centrifugal Force

A supersonic flow is achieved by a convergent-divergent Laval nozzle. A subsonic-supersonic transition is also possible in a one-dimensional isentropic flow through a uniform rotating pipe of constant cross-sectional area with a bend by the centrifugal effect. A uniform pipe with a bend lies in a meridional plane and rotates around an axis and the centrifugal force on the pipe flow has the same effect as that of an area change in a Laval nozzle. The governing equations similar to those of a Laval nozzle are derived for the one-dimensional isentropic flow in a rotating uniform pipe with a bend of constant cross sectional area, and the shock relations are also obtained.