Ponding on an inflated tube and the membrane trough

The ponding on an inflated membrane tube is studied. Membrane tubes have the advantage of zero leakage and ease of transportation and set-up. A novel related problem is the membrane trough which can be used to contain water and does not need anchoring. These problems depend on two non-dimensional parameters which characterize membrane tension and pressure. Perturbation solutions to second order are found for shallow ponding, and compare well with those of exact numerical integration. Tables for the pertinent parameters are constructed and cross section geometries are found. This research illustrates the interaction of membrane structure, pressure load, and hydrostatics.