Final answer:
The rate of change of water depth in a spherical tank is related to the flow rate at the hole, which can be affected by the gravitational force, height of the water, and area of the hole. For Earth's oceans, hydrostatic equilibrium means that as a scuba diver descends, pressure increases, indicating that at greater depths, water experiences significant compression.
Step-by-step explanation:
The rate of change of the depth of water in a container correlates with the leak's flow rate, which can be determined through principles of fluid mechanics. For the case of a spherical tank, the exact rate will depend on the shape of the vessel, the initial water level, the inflow rate (if any), and the outflow through the hole. However, the given information suggests a scenario similar to Torricelli's Law, where a hole beneath a fluid involves a flow rate that is a function of the gravitational acceleration, the height (difference in elevation between the liquid surface and the hole), and the cross-sectional area of the hole.
Concerning hydrostatic equilibrium, this term denotes the balance between gravitational forces and pressure gradient forces within Earth's oceans. As a scuba diver descends, due to the weight of the overlying water, the pressure exerted on the diver increases with depth, meaning the pressure at 200 feet would be significantly higher than at the surface, posing various physiological challenges and requiring specialized equipment to manage the increasing pressure.
The compressibility of water at great depths is another significant aspect, as water's volume decreases under extreme pressure. This concept is critical in understanding the behavior of bodies like oceans subjected to high pressures, particularly for engineering applications.