Final answer:
In a water-filled tube, the pressure is lower at the top and higher at the bottom due to hydrostatic pressure, which increases with depth. The bottom pressure is the sum of atmospheric pressure, the water's pressure, and any additional applied pressure. This demonstrates the principles of hydrostatics and Pascal's law.
Step-by-step explanation:
In a tube filled with water, the pressure is lower at the top and higher at the bottom. This is due to the water depth and the hydrostatic pressure that the water exerts. The hydrostatic pressure is a result of the weight of the water above a certain point and increases with depth. According to Pascal's principle, any change in pressure, such as from an added mass, is transmitted equally throughout the fluid. Therefore, the pressure at the bottom of the tube is the sum of the atmospheric pressure, the pressure due to the water column, and any additional applied pressure, such as that from a mass (Mg/A).
As illustrated in Figure 11.14 of an open-tube manometer, the pressure exerted by the fluid must be equal at the same depth on both sides to prevent the flow of liquid from the deeper side. Similarly, when there is a positive gauge pressure on one side, it supports a column of fluid of height 'h', which represents the gauge pressure as Pg = hpg, where 'p' is the density of the liquid and 'g' is the acceleration due to gravity.
In conclusion, the pressure at the bottom includes the atmospheric pressure plus the hydrostatic pressure due to the liquid column above it, and any additional applied pressure, such as from mass or gauge pressure. The rigidity of the container, like a jar with peanuts, prevents atmospheric pressure from being transmitted to its contents.