In general, hydrostatic valves relieve or manage pool water pressure, manage drainage of cerebrospinal fluid, and are used on oceanic oil rigs to manage the vast pressures that involve pumping volatile oil under conditions of high pressure great atmospheric depth.
The science of hydrostatics concerns the pressures of fluids that are under pressure and at equilibrium or rest. This is a very complex issue when the fluids are already at great pressures deep underwater, then are being pumped out of their normal containment space. When the fluids are complex fluids with volatile gaseous components, the science of hydrostatics becomes more complicated.
Add in the "mud" that is used to keep the vast pressures under control and we have an incredibly complex and dynamic system.
What is being managed is resistance to flow or sudden changes in flow when the presence of gas or other conditions cause sudden changes in pressure in a hydrostatic system. Pumps pump the oil, but certain conditions cause the pump to overwork because something is making the flow more difficult. This places more burden on the pump. Imbalances can happen between the oil going in and the oil coming out of the pump, creating imbalances in the pressure of the oil.
When there is too much pressure, a sensor will detect that and stop the pump. But there is still enormous pressure that must be maintained. A simple relief valve can divert the liquid to a tank that will holds the fluid but allow all of the fluid in the system to return to steady pressure. This actually creates problems if overused, as the process can overwork the pump and can create the wrong pressure at the right time.
Hydrostatic systems have a way to route the fluid through complex systems of pipes, tanks and valves and through hydrostatic relief valves to various ports on the pump, allowing the pump to restart more easily when the pressure returns to acceptable levels..
Simply put, hydrostatic relief valves are the part of a whole complex hydrostatic hydraulic system that maintains a tolerable oil pressure throughout the system as the oil is pumped from the earth. When the motor or the fluid in a dynamic and hydrostatic oil drilling system has created too much pressure, then the hydrostatic valves work better than simple relief valves to reroute the excess to other parts of the hydrostatic system, bypassing the pump so that pressure can either be returned to a better state.
There have been many cases where these systems have failed, and drilling oil from a mile beneath the surface of the ocean is an invitation to surprise. With no real knowledge of the composition of the gasses and volatility of oil fields, pumping under hydrostatic conditions leads to completely unanticipated, unexpected and massive changes in pressure. At the same time, this is done under conditions of atmospheric pressure and freezing cold that are, themselves, not that well understood.
In these situations, hydrostatic theory that works in principle has proven to be flawed in practice when we add in the complexities of operating these systems at great depth.
Hydrostatic III: Overload!