Гидродинамика

SOLUTION OF A PROBLEM IN HYDROSTATICS The problem solved by Prof. Joukowsky is as follows: a liquid mass of density p fills an unlimiited space enclosed between two parallel planes separated from each other by a very great d i s ­ tance Л: a finite solid body of density , having the form of a straight cylinder with an arbitrary base, is immersed in this layer so that the plane of the base is parallel to the planes bounding the layer; to determine the depth to which the cylinder will be immersed in the liquid and the change in the free surface of the liquid layer, taking into consideration the force of mutual 'attraction between the particles of liquid and the cylinder. At a very great distance from the cylinder the free surface of the liquid will be horizontal; continue this surface up t o the point of intersection with the cylinder (Fig. 1) and call a the height of the portion of the cylinder above the surface, and h the height of the portion of the cylinder below the surface. In the potential of all masses considered and of all forces acting on the cylinder we suppose that b = a and that the f r ee surface of the liquid is the д:(/-р1апе; in this case, the potential of the cylinder will not be included in the conditions of its equili ­ brium, and the difference Ь—a is given-by formula (7). To determine the shape of the free surface we have to make an approximate calculation of the potential of the cylinder. The curve along which the surface of the liquid cuts the л-z-plane depends on the form of the cylinder, but, given the very great distance of .x from the cylinder, its shape does not depend on that form and is given in terms of the area s by equation (9).