### Fluid Pressure

Pressure at any point of a fluid. :-

Pressure is the amount of force acting per unit area. The symbol of pressure is p or P

Mathematically:

$p = \frac{F}{A}\ \mbox{or}\ p = \frac{dF_n}{dA}$
where:
$p$ is the pressure,
$F$ is the normal force,
$A$ is the area of the surface on contact.
Pressure is a scalar quantity. It relates the vector surface element (a vector normal to the surface) with the normal force acting on it. The pressure is the scalar proportionality constant that relates the two normal vectors:
$d\mathbf{F}_n=-p\,d\mathbf{A} = -p\,\mathbf{n}\,dA$

Uniform Pressure :-
The pressure on a Plane area is uniform when the thrust on any portion of it is proportional to the area of that portion, and the pressure is measured by the thrust on a unit area.

Mean Pressure :-
The mean pressure on a plane area is the uniform pressure on it which will give the same resultant thrust as the actual one.

Pressure at a Point :-
The Pressure at any point of an area is the limit of the mean pressure on an indefinitely small area enclosing the point.