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We usually deal with incompressible fluids like water. When such fluid is not moving and it is at rest, it is in a stable equilibrium (in terms of all the forces that are applied to it). Whatever we need to know about such state comes in the area of hydrostatic. When we deal with such a fluid in motion, then all the stuff related to it comes in the area of fluid dynamics.
for example, hydrostatic pressure is the pressure of the fluid at rest. In such condition, there is no shear or frictional stress as opposed to in fluid dynamics.
Manometer (open manometer and differential manometer) is an equipment to measure the pressure of fluid (based on the height of the fluid above any point of measurement).
Hydrostatic paradox is another concept that comes in the hydrostatic area of fluid mechanics. It states that the pressure at any point in a hydrostatic consition, depends only on the height of the fluid above that point to the surface. That is the length of the container, weight of the water above it, etc. does not matter, it only depends on how deep it is!!
Pascal's Law (or principle) says that in a hydrostatic condition, the pressure at any point in the fluid is the same in every direction.
Barometer works similar to manometer but uses the pressure concept to measure the pressure of atmosphere! The next subject is the force that fluid applies on the submerged surfaces (horizontal, vertical and inclined). This nice pdf file I found from Dr. Inamdar's page from University of Delaware, has much detailed explanations and examples on this matter.
That's about hydrostatic, so what if the fluid flows?! All the above s not gonna be of much help solving for the FE problems. That goes into the fluid dynamics, which is the next subject.
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