Lecture Notes on Barometer and Pressure Measurement

Barometer

• Definition: A scientific instrument used to measure atmospheric pressure.
• Common Type: Mercury barometer, where mercury is the liquid used.
• Setup:
  • Fill a glass tube with mercury, ensuring no air is trapped.
  • The tube is inverted into a container of mercury, creating a vacuum at the top.
• Pressure Relationship:
  • At any two points (A and B) in the liquid, pressure at A equals pressure at B.
  • If point B is deeper (point C), pressure increases due to the liquid above.

Pressure Calculation

• Pressure Formula: For liquids, pressure can be expressed as:

  • ( P = h \cdot \rho \cdot g )
    • Where:
      • ( P ) = Pressure
      • ( h ) = height of the liquid column
      • ( \rho ) = density of the liquid
      • ( g ) = acceleration due to gravity

• Specific Case for Mercury:

  • Atmospheric pressure is given as 1 atm.
  • Density of mercury = 13.6 g/cm³.
  • Height of mercury column can be calculated from atmospheric pressure.
  • Result: 760 mm (or 76 cm) of Hg corresponds to 1 atm.

Comparison with Other Liquids

• Water Column Height:
  • If water is used instead of mercury, the height needed to balance 1 atm is significantly greater (around 10 meters).
  • Reason for using mercury: Higher density allows for a manageable column height.

Pascal's Law

• Overview: Pressure changes in a fluid at rest are transmitted equally in all directions.
• Key Points:
  1. Pressure at a point is the same in all directions.
  2. Pressure is the same at all points on a horizontal level.
  3. Pressure increases with depth in a fluid.

Manometer

• Definition: An instrument used to measure gas pressure in a container.
• Pressure at point A (gas pressure) relates to pressure at point B (atmospheric pressure + height of liquid).
• Relationship:
  • ( P_x + h \cdot \rho , g = P_{atm} )
• If the gas pressure is lower than atmospheric pressure, it indicates a decrease in pressure.

Conclusion

• Understanding the principles of barometers and manometers is crucial for measuring pressure accurately in various scientific contexts.
• The relationship between liquid height and pressure is foundational for practical applications in fluid mechanics.