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Transmission of Pressure in Liquids: Pascal’s Law

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Pascal’s Law
According to Pascal’s Law, the pressure applied to an enclosed liquid is transmitted undiminished to every portion of the liquid and the walls of the containing vessel.
The hydraulic system works on Pascal’s law. When a force is exerted on an area, the ratio will be the same at all cross¬sections.

`"F"_1/a_1 = "F"_2/a_2`

For example:-

  • Consider a vessel filled with water which is uniform throughout as there is only one type of fluid which is water.

  • Consider a vessel that has oil and water then it is not uniform. As it has two different fluids.

Fluid should be confined meaning fluid is present within a region in space. It is not allowed to spread.

For example 1:-

  • A balloon filled with water and when we press it hard against the wall.

  • We will see the shape of the balloon changes. This is because if we apply force on the balloon, pressure is exerted on the water.

  • Water is uniform fluid and it is confined within this balloon and is not allowed to spread.

  • On applying pressure it is transmitted in all other directions.

For example 2:-

  • Consider a vessel of circular shape filled with water which has 4 openings and in the entire openings, 4 pistons are attached.

  • Apply force on the first piston; this piston will move inward and all other pistons will move outwards.

  • This happens because when this piston moves inwards the pressure is exerted on the water. Water transmits this pressure in all directions.

  • The other pistons, except A, move at the same speed which shows water has exerted pressure in all the directions.

conclusion:-

  1. For a uniform fluid in equilibrium, the pressure is the same at all points in a horizontal plane. This means there is no net force acting on the fluid the pressure is the same at all the points.

  2. A fluid moves due to the differences in pressure. That means fluid will always move from a point that is at a higher pressure to the point which is at a lower pressure.

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