Measurement of Pressure

Measurement of Pressure

Introduction : In previous topic we have studied about pressure and Pascals law. Now it is necessary to measure this physical quantity pressure in order to express it's application in real world. The instrument use to measure pressure are  called as pressure meters. In this topic we will focus on various instrument use to measure pressure.

Pressure meter
Image by crystal kwok on unsplash

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Mercury Barometer

It is an instrument use to measure atmospheric pressure. This instrument was first discovered by  torricelli.

Mercury Barometer

In the given figure, consider a barometer instrument completely filled with mercury and kept upside down inside a small container containing mercury. 

Steps : A tube of 1m long and diameter about 1cm fully filled with mercury is kept upside down into a container containing mercury. It is observed that the mercury level falls in the tube  and a vacuum is created between the upper surface of mercury and closed end of the glass tube. ie (P = 0)

Consider three point P , Q , R   at same horizontal level. We know that pressure at point P and R is atmospheric pressure P₀. Mathematically we can write 

P_P = P_Q = P_R = P₀ ---(1)

Absolute pressure at point Q is given by ,

P_Q = P + ρgh

P_Q = 0 + ρgh

P_Q = ρgh ---(2)

from (1) and (2)

 P₀  = ρgh

Torricelli found that the height at point Q from upper surface of the liquid was 76cm .

Putting all the value (h = 76cm =76x10^-2 m, ρ = 13600kg/m³, g=10m/s²)in equation A, we get

 P₀  = 13600 x 10 x 76x10^-2

 P₀  = 13600 x 10 x 76x10^-2

 P₀  = 1033600 x10^-1

 P₀  = 103360 Pascal

 P₀  = 1.03360 x 10⁵ Pascal ----(B)

Equation (B) gives value of atmospheric pressure

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Manometer

U-tube Manometer

It is an instrument use to measure pressure inside a closed container containing gas. 

From the above diagram, it is clear that the setup consist of a U shaped tube containing some liquid. One end of the pipe is open to atmosphere and other end is connected to a container containing gas. Point B is at height h from open surface of the liquid and at same horizontal level as point A. Let P be the pressure of the gas, P_A is the pressure at point A and P_B is the pressure at point B. 

The pressure at point A is equal to the pressure of the gas. Thus we can write

P = P_A ----(1) 

As point A and point B is on the same horizontal level, we can write

P_A  =  P_B ----(2) 

But  absolute pressure at point B is given by

P_B  =  P₀  + ρgh ----(3) 

from (2) and (3)

P_A  =  P₀  + ρgh ----(4)

from (1) and (4)

P  =  P₀  + ρgh  ----(5)

Equation (5) gives value of pressure in a closed container containing gas.

_{│<<< Pascal's Law││ Surface Tension>>>│}

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 Related Topic :  Mechanical Properties of fluid      Pressure due to liquid column     Absolute and gauge pressure  Hydrostatic Paradox       Pascal's Law        Measurement of pressure         Surface Tension Surface Energy         Angle of contact          Capillary Action            Motion in a fluid                    Critical velocity and Reynold's Number                      Viscosity                 Stokes' Law            Terminal velocity                 Equation of continuity                  Bernoulli Equation          Speed of Efflux    Ventury Tube

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