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Fluid Mechanics

 Gauge Pressure and Absolute Pressure:

Gauge Pressure:

  • It is convenient to measure pressure in terms of taking atmospheric pressure as reference datum. 
  • Pressure measured above atmospheric pressure is known as gauge pressure. 
  • The atmospheric pressure on the scale is marked as zero.

Absolute Pressure:

  • Since, atmospheric pressure changes with atmospheric condition, a perfect vacuum is taken as an absolute standard of pressure. 
  • Pressure measured above perfect vacuum are called absolute pressure. The figure  explains the concept of gauge and absolute pressure. 
  • Absolute pressure = atmospheric pressure + gauge pressure
  • Pabs = Patm + Pgauge


                                  Fig. 1 Concept of gauge and absolute pressure

Pascal's Law:

  • It states that the intensity of pressure at any point in a liquid at rest is same in all direction.
  • We consider a fluid element of dimensions as shown in the figure Ps is the pressure exerted on the inclined surface, δ is the linear dimension of the surfaces x, y and z.


Fig. 2 Fluid element


Equation for horizontal forces:

          Px.δy.δz = PsSinϴ.δz.δs

          Px.δy.δz = δz.δs.Ps.

          Px = Ps  ---------------(i)

 Equation for vertical forces:

          Py.δx.δz = Ps.Cosθ.δs.δz + .δy.δx.δz.ρg

            Py.δx.δz = Ps.δs.δz + .δy.δx.δz.ρg

 

                                                

  Can be neglected as δ is very small

          Py = Ps  --------------- (ii)

  From equation (i) and (ii) we have,

          Px = Py = Ps 



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