A cylinder is aligned along zz' and both ends are closed, one with a rigid plate which has a smaller tube and valve attached. If the other end is covered with an elastic material and the edges are thin enough so that at time t, if the pressure is lowered in the cylinder by evacuating air, the sheet breaks and begins to travel toward z' calculate the image at time t' if the elastic constant is k. Assume the image has a radius of one unit of distance and the frictional force between edges is linear. Derive a general form for a sheet with a differential thickness of material including sheets with thick but infinitesimally small radii, with a puncture at the center p which draws air from z to z' through a small channel one molecule of air wide; assume a small amount of energy is lost for each molecule transported into the near vacuum, which is recovered as heat in the material. Each molecule carries vibrational and rotational momentum into the void at constant T, or ambient background. Do I need a triple, like a single and a duple here? If S the elastic surface isn't punctured it will deform linearly which depends on the material's geometry, how isotropic for the initial uniform case, so can use a straightforward deformation since diffusion is constant and so is friction, the sheet will be trying to restore its shape. Then the pressure is the deformation operator and the image is a sheet curved or expanded into 3 from 2 dimensions, all the curvature is written by the forces experienced be cause of kP, if dT is also internally conserved, the temperature of the cylindrical system should stay ambient over sufficient periods for the defomation, since evacuation can be brought to the point of separation of the circular sheet from the edges, which is the 'launch', a volume measure, that's where the algebra is Can the generalization be viewed as a kind of signal loss per molecule for the punctured sheet? Anyone have pointers here, please? I've read something about a fluid in a long flattened tube and pressure images and want to know more. The image is a volume product or form, isn't it?