Share

Get Access to:

- Ask & get answers from experts & other users
- Play Quiz and test your skills
- Free Download eBooks, Notes, Templates, etc.
- Study Materials
- Latest Articles

Lost your password? Please enter your email address. You will receive a link and will create a new password via email.

Please briefly explain why you feel this question should be reported.

Please briefly explain why you feel this answer should be reported.

Please briefly explain why you feel this user should be reported.

Pascal’s Law : It states that intensity of pressure for a fluid at rest is equal in all directions. This is proved as :

The fluid element is of very small dimensions i.e. dx, dy, ds.

Consider a arbitrary fluid element of the wedge shape in a fluid mass at rest. Let the width of the element perpendicular to the plane of paper is unity and

px, py , pz are the pressure intensity acting on the face AB, AC, BC respectively.

Then the forces acting on the element are :

i. Pressure forces normal to the surfaces ,

ii. Weight of element in the vertical direction ,

The forces on the faces are :

Forces on the face AB = px × Area of face AB = px × dy × 1

Forces on the face AC = py × area of face AC = py × dx × 1

Forces on the face BC = pz × area of face BC = pz × ds × 1

Weight of element = ( Mass of element ) × g = ( Volume × rho ) × g

= [ ( AB × AC ) / 2 × 1 ] × rho × g

where, rho = density of fluid

Resolving the forces in x – direction, we have

px × dy × 1 – pz.ds × 1 cos ( thita ) = 0

px × dy × 1 – pz × dy × 1 = 0

px = pz ……(i)

{ ds cos ( thita ) = AB = dy }

Similarly, Resolving the forces in y – direction, we get

py × dx × 1 – pz × ds × 1 cos ( 90 ° – thita ) – ( dx × dy ) / 2 × 1 × rho × g = 0

py × dx – pz ds sin ( thita ) – ( dx . dy ) / 2 × rho × g = 0

But [ ds . Sin ( thita ) ] = dx and also the element is very small and hence the weight is negligible.

Therefore, py.dx – pz × dx = 0

py = pz ……(ii)

From (i) and (ii) ; we have

px = py = pz

This equation shows that the pressure at any point in x, y and z directions is equal.