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Fluid Mechanic's

 STATIC PRESSURE OF LIQUIDS, HYDRAULIC PRESSURE, ABSOLUTE AND GAUGE PRESSURE

 Introduction

  • Fluid has property that it exerts force on all the sides, top and bottom. Pressure exerted by fluid is given as force per unit area which is as follows:

         Pressure= Force Applied /Area Exposed

  • SI unit of pressure is newton per square metre (N/m2). This is also known as pascal (Pa). 
  • The values of standard atmospheric pressure are as follows:
  •   760 mm of mercury column
  •  10.3 m of water column
  •  101.3 kN/m2
  •  101.3 kPa 
  •  1 bar

Hydrostatic Law:

  • Pressure in a continuously distributed uniform static fluid varies only with vertical distance and is independent of the shape of the container.
  • The pressure is the same at all points on a given horizontal plane in the fluid. 
  • The pressure increases with depth in the fluid.

Pressure head of liquid:

  • Consider a fluid of density ρ, having fluid element of area ∆A at a depth distance h from the top surface of liquid (Fig)


Fig.  Forces acting on fluid element of height ∆h

Height of fluid element = ∆h

Pressure at top of fluid element = p

Force on the top of fluid element = p ∆A

Weight of fluid element = ∆A. ∆h. ρ g

  • Upward force acting at bottom of the fluid element =   ̶
  • Under equilibrium conditions (downward force = upward force),

   

     

    

   

  • Pressure variation in any static fluid is described by the above basic pressure height relationship. 
  • This equation describes hydrostatic law and indicates that rate of increase of pressure in a vertical downward direction is equal to the weight density (also known as specific weight) of fluid at that point.

         Integrating,

                      

                           P =

    Here h is known as the pressure head and its unit is in metres (m).

Liquid Paradox

  • The pressure in a liquid is not a function of shape or size of the container.
  • Pressure is only the function of density and height or depth h inside the liquid at which pressure has to be calculated.









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