Pascal's law states that the pressure at any point in a liquid at rest is the same in all directions. This is proven using a wedge-shaped fluid element where the forces acting on each face - Px, Py, and Pz - are shown to be equal based on the pressures px, py, and pz acting over the same area. Applications of Pascal's law include hydraulic presses, jacks, lifts, and pressure measurement instruments.

1. Pascal’s Law
Of
Pressure At A Point
prepared by:-
Dhiren P Patel

2. STATE:“ The Intensity Of Pressure At Any Point In A Liquid At Rest, Is The Same In All Directions.”
PROOF:Consider An Arbitrary Fluid Element Of Wedge Shape ABC In A Fluid Mass At Rest As Shown
In Fig. (A). The Width Of Element Perpendicular To The Plane Of Paper Is Unity.
Let, Px = pressure acting on a face AB
Py = pressure acting on a face AC
Pz = pressure acting on a face BC
Px = force on a face AB
Py = force on a face AC
Pz = force on a face BC
Figure - A

3. The forces acting on the element are:(1) Normal force to the surface due to fluid pressure
(2)Force due to weight of fluid mass in vertical direction
Px = px
area of face AB = px
(dy
1)
Py = py
area of face AC = py
(dx
1)
Pz = pz
area of face BC = pz
(ds
1)
Weight of element = mass of element
= ρ volume g
=
= W = ρ (dy× dy) g
g

6. From equation – 1 & 2
Px = Py = Pz
Hence, at any point in a fluid rest the pressure is exerted equally in all
directions.
APPLICATIONS:hydraulic press
hydraulic jack
hydraulic lift
in measuring instruments (i.e. manometer, pressure gauge)

11. Thank you