Mechanics of Fluids and Pressure - Part VI

Units of pressure
As discussed above, height of a Hg column is a standard way of measuring pressure. At sea level, and at standard gravitational force, the air pressure is defined as one atmosphere.

1 atmosphere = 760 mm of Hg.

There are other units of measuring pressure also. They are Newtons/m², Pascal, bars and torr, pounds per square inch (psi), etc.

1 atm = 14.7 psi

1atm = 101,325 N/m²

1atm = 1.01325 bar

1 torr = 1 mm of Hg

Aneroid Barometer
Hg barometer is not very portable and poses many problems while reading pressure accurately from the column. Another barometer, made out of corrugated metal sheets is generally used. This has no liquid and hence is called the aneroid barometer. A chamber holding the corrugated metal sheet is partially evacuated. Depending on the air pressure this chamber either expands or contracts. This minute movement is amplified and can be seen on a dial.  The dial is calibrated to measure the atmospheric pressure directly.  

There are several advantages of an aneroid barometer :

• It is rugged and portable

• It can also be used to measure altitudes since air pressure drops by about 10 mm for every 20 m
  height from the mean sea level.

5. Measurement of density of unknown liquids  
The principle of height of liquid column being proportional to the pressure in the liquid, can be easily applied for determining density of unknown liquids.  

Take a U-tube mounted on a calibrated stand. Place Hg in the U-tube. The height of the Hg in the two arms of the U-tube will come to one level.  Note down the level.

Pour the liquid whose density has to be measured in one arm of the U-tube. The Hg level in this tube will get depressed.

Pour water in the second arm of the U-tube till the heights of the Hg in both the arms read the same as before.

Let h₁ = the height of the water column
And h₂ = the height of the liquid column

The atmospheric pressure exerted on the surfaces of water and the liquid column is the same. Let this be denoted by P_o.

The pressure at the liquid ñ mercury interface = P_o.+ h₂ x _liquid  x g

The pressure at the water ñ mercury interface = P_o.+ h₁ x _water  x g

Since the Hg in both the limbs stand at the same horizontal level, the pressure at that level is the same.
Thus

P_o.+ h₂ x _liquid  x g   = P_o.+ h₁ x _water  x g

                      h_1
liquid  =     æææ         x _water
                      h₂

Thus density of a liquid can be found by measuring the ratios of the heights of the water and liquid column and multiplying this by the density of water (1gm/cm³ or 10³ kg/m³). There are various simple apparatuses available for measuring densities of liquids, using the above principle. One such is a Hareís apparatus.

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