The membrane cover has fold lines therein intersecting the walls of the reservoir at intersection points. A geometric chord or secant joins two intersection points, and defines, with a portion of the walls of the reservoir, a static segment in the membrane cover. The membrane cover in the static segment is tensioned along lines of force that are parallel to or that make acute angles, with the aforesaid chord or secant. The membrane cover in the static segment remains substantially planar and stationary, thus static, despite the rising and lowering of the remaining portion of the cover in response to variations in the level of the content of the reservoir. A hatchway is mounted in the static segment of the cover. In another aspect of the invention, the hatchway has an airtight compartment extending between the membrane cover and a point below the level of the material inside the reservoir.