Exercises on buoyancy on a truncated conical surface developed in different ways

The file contains different ways of solving exercise P2.13 of the Hydraulics book by Mossa and Petrillo (CEA, Milan, 2013). It can be seen how the exercise can be solved both with case 1 (control volume with real fluid inside) and with case 2 (with volume with fictitious control fluid). It should be noted that in the latter case two modalities are presented. One of these is that the truncated cone is closed with a cylinder which is another curved surface. In the particular case of this exercise, this is possible because the cylinder can be imagined as consisting of infinite rectangular surfaces with base ds and height equal to any of the generatics of the cylinder. For each rectangle of infinitesimal thickness, to which a -pi greca1 belongs, there is a diametrically opposite rectangle to which a -pi greca1 equal in module and opposite in direction belongs.
Contribution by Arianna Basile (Environmental Hydraulics, Academic Year 2022-2023).