Abstract: A container for fluids is disclosed in which the container is comprised of two flexible sheets joined so as to form a fluid reservoir. Leading from the reservoir is an exit flow channel to permit the expulsion of the fluid contents when pressure is applied to the container. When the applied pressure falls below a predetermined critical value, the exit flow channel will automatically self-seal, thus preventing further fluid flow, leakage, or spoilage. This self-sealing is achieved so long as the exit channel exhibits characteristics of width and length which are proportional to certain dimensionless parameters which are, in turn, proportional to several specific parameters which are dependent on the fluid, material of the container, and the desired context in which the container is intended for use. Thus, self-sealing can be achieved by an exit flow channel which is independent of its path (i.e., the course it follows), thus permitting great flexibility in container and exit flow channel design.