Closed-form expression of the similarity solutions for an air-filled, heavy membrane tube section on an incline

In this study, an air-filled, heavy membrane tube section resting on an incline is considered. The shape of the tube section is determined by the equilibrium of its weight and the transmural pressure. All quantities are normalized to obtain similarity solutions. A system of nonlinear ordinary differential equations with undetermined boundary conditions is solved analytically. The closed-form solutions are expressed in terms of the non-dimensional pressure for a given inclination angle. Using the results of this study, one can estimate the shape and characteristic values of a tube section without the burden of numerical calculations.

► Analytic solutions in closed form for an air-filled, heavy membrane tube section on an incline are derived.
► The solutions are similarity solutions that are applicable to any tube section size.
► The validity of the analytic solutions is confirmed by comparing the results with those from previous studies.