Lesson 2b: Introduction to Pressure

Key Concepts

• Pressure Definition: Pressure is a scalar defined at a point in a fluid, similar to temperature. It is a normal stress with dimensions of force per unit area.
• Units of Pressure: Common units include atmospheres, pascals, kilopascals (kPa), bar, and psi.

Pressure Types

• Absolute Pressure: Denoted as ( P ) or ( P_{abs} ), used in equations where pressure stands alone (e.g., ideal gas law).
  • Equation: ( P_{abs} = P_{gauge} + P_{atmosphere} )
• Gage Pressure: Pressure above local atmospheric pressure.
  • Equation: ( P_{gauge} = P_{abs} - P_{atmosphere} )
• Vacuum Pressure: Pressure below atmospheric pressure.
  • Equation: ( P_{vac} = -P_{gauge} )
  • Used only when positive, i.e., ( P_{vac} > 0 ).

Example Problem: Tire Pressure

• Given: Gage pressure and local atmospheric pressure.
• Calculate: Absolute pressure inside the tire in various units:
  • kPa: 340.9 kPa
  • Atmospheres: 3.365 atm
  • Bars: 3.409 bar
  • PSI: 49.45 psi (or psi a for absolute)

Example Problem: Vacuum Chamber

• Given: Vacuum pressure and local atmospheric pressure.
• Calculate: Gage and absolute pressures:
  • Gage Pressure: ( P_{gauge} = -P_{vac} )
  • Absolute Pressure: ( P_{abs} = P_{atmosphere} - P_{vac} )
  • Results: 1.35 kPa (absolute)

Additional Concepts

• Pressure as Scalar: Acts along the inward normal at every surface point, even in an imaginary fluid.
• Pressure in Fluid: Increases in the direction of gravity.
• Column Height (Head): Equivalent column height of a liquid is used to express pressure:
  • Example: 760 mm Hg = 1 atmosphere.

Equivalent Column Height

• Concept: Pressure can be expressed as an equivalent column height of liquid (head).
• Equation: ( P_{below} = P_{above} + \rho g \times \text{height} )
• Example Calculation: Convert absolute pressure to equivalent column height of water and mercury:
  • Water: 34.83 meters
  • Mercury: 2.556 meters

Takeaways

• Pressure always acts inward normal on any object, real or imaginary.
• Head is used to express pressure using the equivalent column height of a fluid.
• Understanding pressure as a stress explains the relationship between pressure and stress in everyday language.

Conclusion

• This lesson provided a foundation on pressure types, units, and measurement methods.
• Future lessons will explore the derivation of pressure equations and additional applications.