Final answer:
Yes, the level of fluid corresponds to the pressure at the bottom of a container because the fluid pressure at any depth is determined by the height of the fluid column above that point, leading to equal pressure at equal depths.
Step-by-step explanation:
The level of fluid in a container does correspond to the pressure at the bottom of the container. According to fundamental principles of fluid mechanics, in a container where a fluid can freely move in various parts, such as connected tubes or sections of different shapes and sizes, the liquid reaches the same height in every part. This occurs because the pressure at the bottom of each part must become equal; if it were not, the fluid would continue to flow until the pressures were equalized.
The pressure at the bottom is determined by the fluid's depth from the surface, not the shape of the container. The pressure at any given depth is equal to the atmospheric pressure plus the pressure exerted by the weight of the fluid above that point. In a manometer open to the atmosphere on both sides, the fluid levels equalize due to the atmospheric pressure being the same on both sides, regardless of tube diameters. This concept is largely based on Pascal's principle, which states that when pressure is applied to a confined fluid, the change in pressure is transmitted equally throughout the fluid.