§ 76. Source and Sink, Superposed Translation.—We might (with certain reservations) regard such a combination of source and sink as a tube (Fig. 41) through which fluid is being pumped, the fluid entering the tube at B and emerging again at A. If we suppose such a tube to move longitudinally through the fluid in the same direction as that in which the fluid flows in its interior, or, that which is in reality the same, if we suppose the tube fixed whilst the fluid as a whole has a velocity of translation in the opposite direction, the system of flow undergoes considerable modification.
Fig. 42 gives the solution of such a case for a two-dimensional field. The source and sink system of Fig. 40 being superposed on a motion of translation, it is found that two distinct systems of flow result, internal and external respectively to a surface of oval form ; the internal system consists of a source and sink in a region bounded externally, and the external system gives the stream lines proper to an oval cylinder in motion through the fluid; it is evident that we may suppose such a body substituted for the internal system. The form of this oval represents the shape of a body that will give rise to the same external system of flow as the simple source and sink, and according as the flux of the motion of translation is greater or less in relation to that of the source and sink, the oval will be more or less elongated, the limiting conditions approximating to a line joining the foci on the one hand and to a circle on the other. The form of this oval is not an ellipse, being fuller towards the extremities, especially in cases where the ratio of major to minor axis is considerable.
§ 77. Rankine's Water Lines.—These curves and the whole external series have been closely studied by Rankine, the method of plotting here given being that employed by him. Rankine has pointed out the general resemblance of these curves to ships, water lines, and has given them the name “Oogenous Neoids.”
In a paper read before the Royal Society (November, 1863)
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