Pascal’s Law Of

Pressure At A Point prepared by:-

Dhiren P Patel

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

STATE:-

“ The Intensity Of Pressure At Any Point In A Liquid At Rest, Is The Same In All Directions.”

Figure - A

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 × g

= ρ × volume × g

=

= W = ρ (dy× dy) g

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)

Thank you