Pascal's Law of Hydrostatics

Pascal's Law

The normal stresses at any point in a fluid element at rest are directed towards the point from all directions and they are of the equal magnitude.

Fig 3.2     State of normal stress at a point in a fluid body at rest

Derivation:
The inclined plane area is related to the fluid elements (refer to Fig 3.1) as follows

	(3.4)
	(3.5)
	(3.6)

Substituting above values in equation 3.1- 3.3 we get

(3.7)

Conclusion:

The state of normal stress at any point in a fluid element at rest is same and directed towards the point from all directions. These stresses are denoted by a scalar quantity p defined as the hydrostatic or thermodynamic pressure.
Using "+" sign for the tensile stress the above equation can be written in terms of pressure as

(3.8)