Pressure
A liquid exerts pressure.To show it,consider a vessel containing a liquid.If it has a small hole near the bottom,the liquid will flow out of it.If the motion of the liquid is stopped by pressing a finger against the hole,the finger will experience an outward force due to the liquid contained in the vessek.Therefore,it can be concluded that the liquid exerts pressure on the walls and base of the containing vessel
Thrust.The total force exerted by a liquid on any surface in contact with it ,is called thrust of liquid
Pressure.The thrust exerted by a liquid (at rest) per unit area of the surface in contact with the liquid is called pressure
If F is the thrust exerted by a liquid on a surface of area A,then pressure is given by
\(
\boxed{p = \frac{F}
{A}}
\)
The unit of pressure is dyn cm-2 in cgs system and Nm-2 in SI.
A pressure of 1Nm-2 is also called1 pascal (Pa)
1Pa (or 1Nm-2)=10 dyn cm-2
The dimensional formula of pressure is \(
[ML^{ - 1} T^{ - 2} ]
\)
When a liquid is in equilibrium,forces acting on the liquid must act perpendicular to its surface .It can be easily proved as below:
Pressure in a liquid increases with depth.If a vessel contains a liquid,the pressure on the top surface=P0(atmospheric preesure),the pressure at depth h below the top
surface is P=P0+\(
h\rho g
\).Here
\(
h\rho g
\)is gauge pressure,P is absolute pressure.Pressure difference between two points in a liquid seperated by a distance y in vertical direction is \(\rho\) g y
(Here \(\rho\) is density of the liquid)
Pressure in a liquid at two points will be the same is they lie at the same horizontal level
Pressure at a point in a liquid depends on the vertical depth and density of liquid only but it is independent of shape of the vessel containing the liquid
8.The pressure difference between static pressure and atmospheric pressure is known as gauge pressure
P-P0=\(h\rho g\)
PRACTICAL APPLICATIONS OF THE KNOWLEDGE OF PRESSURE
1.paper-pins and nails are made to have pointed ends.Because of their pointed end,pins and nails have very small area .When force is applied over the head of apin or a nail,it will exert a large pressure \(
\left[ { = \frac{{force}}
{{area}}} \right]
\) on the surface and hence will easily penetrate into the surface
2.It is painful to walk on a road covered with pebbles having sharp edges.The weight of our bodyis supported on the pebbles under our feet.In turn ,the pebbles give equal reaction to the feet.As the pebbles have very small area at their sharp edges,the pressure exerted by them on the feet is very large and they prove painful
3.Railway tracks are laid on large sized wooden/concrete sleepers.In the absence of wooden sleepers,the weight of the train acts on the ground through rails and as such pressure would be so large that the rails may get depressed.When wooden sleepers are provided below the rails,the weight acts on greater area and hence pressure is reduced quite appreciably.Due to this,the rails do not get depressed