Mechanics of Solids and Fluids


   
 
Pressure
There are many situations in which effects of a force are better described in terms of force per unit area i.e. pressure.
 
 
Example
 
Pins and nails have pointed ends so that, when a pin is pressed, high pressure is applied on the surface with lesser force, as area is small.
 
Tractors with wide wheels can move over soft ground because their weight (force of gravity) is spread over a large area and so that the tractors do not sink.
 
Bags and suitcases are provided with broad handles so that a small pressure is exerted on the hands.
 
Railway tracks are laid on large concrete sleepers so that the pressure on the ground is reduced, which would otherwise, yield to weight of trains.
 
S.I unit of pressure is or Pascal (Pa) and its dimensional formula is [ML-1T-2 ]
 
Pressure exerted by a liquid column
 
 
Consider a liquid of density 'r' contained in a cylinder of cross-sectional area 'A'. Let 'h' be the height of the liquid column. The weight of liquid will exert a downward thrust on the bottom surface of the vessel. The weight of liquid inside the vessel = volume x density x g = Ahrg
 
Thrust or force of liquid on the area = weight of liquid = Ahrg
 
 
Pressure exerted by a liquid column = hrg
 
The above expression tells us why dams are broader at the bottom. The liquid pressure increases with breadth.
 
With a broader base, the pressure on the walls of the dam are reduced.
 
 
     
   
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