Pressure in Fluids:-

• Normal force exerted by fluid per unit area.
• This means force is acting perpendicular to the surface of contact.
• Consider a body submerged in the water, force is exerted by the water perpendicular to the surface of the body.
  • If there is no force applied perpendicularly but in the parallel direction then there will be motion along the horizontal direction.
  • Since fluid is at rest and body is submerged in the fluid. Therefore there cannot be motion along the horizontal direction.
  • Therefore we always say the force is applied perpendicularly.
• Pressure is a scalar quantity. Because the force here is not a vector quantity but it is the component of force normal to the area.
• Dimensional Formula [ML^-1T^-2]
• I Unit: N/m² or Pascal(Pa).
• Atmosphere unit (atm) is defined as pressure exerted by the atmosphere at sea level.It is a common unit of pressure.
• 1atm=1.013×10⁵ Pa

Pascal’s Law

• Pascal’s law states that if the pressure is applied to uniform fluids that are confined,the fluids will then transmit the same pressure in all directions at the same rate.
• Pascal’s law holds good only for uniform fluids.
• 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 which has oil and water then it is not uniform.As it have two different fluids.

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

Conclusion:-

1. For a uniform fluid in equilibrium, pressure is same at all points in a horizontal plane. This means there is no net force acting on the fluid the pressure is same at all the points.
2. A fluid moves due to the differences in pressure. That means fluid will always move from a point which is at a higher pressure to the point which is at a lower pressure.

Example: – Blowing of Wind. Wind is nothing but moving air. Air is a fluid so the air moves from the region of higher pressure to the region of lower pressure.