Important points for Entrance

Liquid pressure is always perpendicular to surface area under consideration.

•              Pressure acts equally in all possible directions.

•              Liquid pressure depends on depth (h) of point below free surface, density  of liquid and acceleration due to gravity (g) at the place.

•              Liquid pressure is independent of amount of liquid, shape of vessel and area of consideration. So a given liquid is filled in vessels of different shapes to same heights then pressure at the base of each vessels will be same.

•              Pressure will be same at all points in a liquid lying at the same level. Therefore the height of liquid level at rest is equal in all vessels of different shapes and sizes when they are in communication but amount of liquid will be different depending on their sizes. This is called Hydrostatic paradox

•              Any increased external pressure applied to a fluid enclosed in a vessel, is equally transmitted to every position of the fluid and to the wall of the vessel. This is called pascal's law.

•              For a given mass of ideal gas at constant temperature, its pressure is inversely proportional to its volume. This is called Boyle's law

 

 

The dimensions for pressure is [ML–1 T–2] and its SI unit is Nm–2 or pascal. Other practical units for pressure are atmosphere, bar, torr. But pressure is frequently measured in terms of height of mercury column as mm of Hg, cm of Hg for the sake of simplicity. A pressure of 1 mm of Hg means a pressure equal to the pressure exerted at the base of  a tube containing mercury column upto height 1 mm. So, if pressure is equal height h (in meter) of Hg, then pressure in Nm–2 is given by

                Pressure = height of Hg column×density of Hg×g.

 

When a floating body is slightly tilted from its equilibrium position, the center of buoyancy gets shifted to new position B'. The vertical line passing through new center of buoyancy and previous vertical line intersects at a point M which is called metacenter

•              If the metacenter is above the centre of gravity then the couple formed by its weight and upthrust tends to bring the body back to its original position. Hence the restoring couple restores the previous stable equilibrium position when meta center is above c.g. But if metacenter is below c.g. then couple set up due to weight and upthrust, tends to tilt the body away from its previous position and body gets toppled. The floating body is in unstable equilibrium.