Equilibrium of a horizontal elastic tube holding heavy liquid

Abstract

The work studies the equilibrium of a light-wall tube made of hyperelastic material that rests on a smooth rigid horizontal plane and loaded from inside by the pressure of heavy liquid. The gravity is directed downwards. The weight of the tube is neglected in comparison with the weight of the liquid. The membrane theory is used. The equilibrium equations for an infinitely long cylindrical membrane are reduced to the system of ordinary differential equations. The solution of the problem about the equilibrium of a cylindrical membrane with constant-thickness circular cross-section is analyzed. In this case, principal stretch ratios are constant, consequently tensions are constant, too. The solution of this problem is found in Euler's coordinates. The shape of a strained cross-section is defined. Dependences of the contact zone with the surface, maximum height and tension of the membrane on the liquid pressure and density are investigated.