Fluid Static Definitions, Pressure at a point, Variation of Pressure in a static fluid

Fluid Statics When the fluid velocity is zero, called the hydrostatic condition.
Definition of Pressure
Pressure is defined as the ratio of normal force to area at a point. For example, Fig. 3.2 shows fluid inside an object such as air inside a soccer ball. The molecules of the fluid interact with the walls to produces a pressure distribution. At each point on the walls, this pressure distribution creates a resultant force F normal that acts on an infinitesimal unit of area A as shown. Pressure is the ratio of normal force magnitude to unit area A at a point:


Figure Pressure acting on the walls of a sphere
The reason that pressure is defined using a derivative is that pressure often varies from point to point. For example, pressure acting on the windshield of a moving car will vary at different locations on the windshield.
Pressure is a scalar quantity; that is, it has magnitude only. Pressure is not a force; rather it is a scalar that produces a resultant force by its action on an area. The resultant force is normal to the area and acts in a direction toward the surface (compressive).
The pressure variation is due only to the weight of the fluid. Consider a small wedge of fluid at rest of size ?x, ?z, ?s and depth b into the paper.