Abstract
By modifying the bipolar transformation used by Lagally, we have obtained the complex velocity potential for the irrotational motion of an inco- mpressib'.e perfect fluid in the outer region of two parallel circular cylinders when the constants of circulation round them are given and the flaw at infinity is uniform. Ill the next place, by the aid of the Blasius' formula, we have calculated the resultant pressures on the cylinders and obtained tie expressions of the forces. In the course of the analysis, we have arrived at an interesting result that the well-known theorem of Kotta and Joukowski holds also for the vectorial sum of the forces acting on then, Moreover we have proved the conclusion mathematically that the forces on the cylinders are equal in inagnitude and opposite in sense when either of the uniform flow or the circulatory one is present. The same holds also when the algebraic sum of the circulation constants vanishes even if the uniform flow is superposed. In case when the distance of the cylinders is large compared with their radii, approximate expressions of the f, rtes have been given. Further it is ascertained that when they are apart enough, the shove expressions reduce to those when one cylinder alone is placed in an unlimited stream, as is expccted from the first. Finally we have, as examples, worked out the forces numerically for a few cases, and consideration is also male on some possible applications of this problem
