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Absolute Pressure

Barometric pressure refers to the air pressure existing at any point within the Earth's atmosphere. This pressure can be measured as an absolute pressure (with reference to absolute vacuum or can be referenced to some other value or scale. The meteorology and avionics industries traditionally measure the absolute pressure and then reference it to a sea level pressure value. This complicated process is used in generating maps of weather systems. An absolute zero pressure reading in a container indicates absolute vacuum, meaning there is no more air left in the container. In practice, achieving absolute zero pressure is not possible, meaning at least a little air will remain in the container.

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Definition

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Pressure is defined as a force per unit area. Pressures are exerted by gases, vapors and liquids. It is necessary to establish an absolute pressure scale which is independent of the changes in atmospheric pressure. A pressure of absolute zero can exist only in complete vacuum. Any pressure measured above the absolute zero of pressure is termed an 'absolute pressure'. 
Mathematically:

1) Absolute Pressure = Atmospheric pressure + Gauge pressure

    Pabs = Patm + Pgauge

2)
Vacuum Pressure = Atmospheric pressure - Absolute pressure 

Vacuum is defined as the absence of pressure. A perfect vacuum is obtained when absolute pressure is zero, at this instant molecular momentum is zero.

Guage Pressure

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If there are no molecules/atoms (complete vacuum), then the pressure will be zero. Also, if there is no molecular movement (absolute zero temperature) then the pressure will be zero. Pressure above this zero condition are referred to as absolute pressures. As the atmosphere is all around, in engineering it is often the pressure present in addition to atmospheric pressure that is of interest, and this gives rise to the concept of gauge pressure. Most instruments for measuring pressure are so constructed that they indicate gauge pressure (i.e., the pressure relative to atmospheric pressure). Gauge pressure is related to atmospheric pressure thus:
Gauge pressure = Absolute Pressure - Atmospheric Pressure

Atmospheric Pressure

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Atmospheric pressure is defined as the force exerted by the area of a particular surface. We can measure the atmospheric pressure using a barometer. It is consisting of a long glass tube with full of mercury inverted over a mercury pool. 
Atmospheric pressure PA is mathematically expressed as;
$P_{A}$ = $\rho _{Hg}$gh
Where $\rho _{Hg}$ = 13.6 gcm-3 is the density of mercury 

g = 9.8 ms-2 is the acceleration due to gravity. 

The average value of h at sea level = 76.0 cm

Relative Pressure

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Relative pressure is nothing but the atmospheric pressure, which is corrected according to the sea level conditions. 

Difference between Gauge Pressure & Absolute Pressure

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Differences between Gauge and absolute pressure are listed below:

Absolute Pressure   Gauge Pressure
 Reference point is absolute vacuum  Reference point is atmospheric pressure
 Indicated by an affix 'a', such as kPa (a)  Indicated by an affix 'g', such as kPa (g)
 Value at mean sea level is 101.3 kPa (a)  Value at mean sea level is 0 kPa (g)
 Always has a positive value  Value below atmospheric pressure is negative and indicates a vacuum condition
 Equals (gauge pressure + atmospheric pressure)  Equals (absolute pressure - atmospheric pressure)
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