The passage of a swirling liquid through a convergent-divergent nozzle is accompanied by the formation of a retarded layer on the nozzle wall. On the assumption that this layer is thin, the motion in the main stream may be taken as frictionless; and the pressure and velocity distributions in it, when the flow is derived from a high-pressure reservoir, can be obtained by an application of eritical flow theory. As usual, it is necessary to suppose that the angle of the conical nozzle is small so that radial velocities can be disregarded. The streaming velocity is found to be uniform over each cross-section, and it is equal at the throat to the velocity of a ‘long’ wave moving on the surface of the air core. With the aid of the results mentioned above, the boundary-layer equations are worked out by an extension of the method used by Taylor in his study of swirling flow without streaming, and a solution is obtained with the use of the Pohlhausen approximation. A numerical case is examined in detail, and the boundary layer is compared with those caused by swirl with no streaming and by streaming with no swirl. The effects of surface-tension over the air core are considered and are shown to be negligible in the numerical example.
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Binnie et al. (1950) studied this question.