Lecture Notes on Pressure in Physics

Definition of Pressure

• Pressure is defined as force divided by area.
• Standard unit of pressure: Pascals (Pa)
  • 1 Pascal = 1 Newton per square meter.
  • 1 kilopascal (kPa) = 1000 Pascals.
  • 1 atmospheric pressure (atm) = 101.3 kilopascals.
• Relationship: Pressure is directly proportional to force and inversely proportional to area.

Pressure Concepts

• Increasing Area with Same Force:
  • Larger area reduces pressure.
  • Example: 100 Newtons of force on 1 m² = 100 Pa; same force on 4 m² = 25 Pa.
• Increasing Force:
  • Increases pressure.
• Key Understanding: Increase in area decreases pressure, increase in force increases pressure.

Example Problems

Problem 1: Pressure by a Rectangular Block

• Given:
  • Block mass: 15 kg
  • Block dimensions: 70 cm × 40 cm
• Solution:
  • Convert dimensions to meters: 0.7 m × 0.4 m
  • Force (Weight) = mass × gravitational acceleration = 15 × 9.8 = 147 N
  • Area = 0.7 m × 0.4 m = 0.28 m²
  • Pressure = Force / Area = 147 N / 0.28 m² = 525 Pa

Problem 2: Pressure by Water in a Container

• Given:
  • Container dimensions: 4 m × 5 m × 6 m
  • Density of water = 1000 kg/m³
• Solution:
  • Pressure due to weight of water: Density × gravitational acceleration × height
  • Height = 6 m
  • Pressure = 1000 × 9.8 × 6 = 58,800 Pa

Problem 3: Pressure in a Cylindrical Container

• Given:
  • Specific gravity of fluid = 1.7
  • Depth = 15 m
• Solution:
  • Density of fluid = Specific gravity × density of water = 1.7 × 1000 kg/m³ = 1700 kg/m³
  • Pressure = Density × gravity × depth = 1700 × 9.8 × 15 = 249,900 Pa
  • Pressure in kPa = 249.9 kPa

Important Formulas

• Pressure (P) = Force (F) / Area (A)
• Pressure due to fluid: [ P = \rho g h ]
  • ( \rho ): density of the fluid
  • ( g ): gravitational acceleration (9.8 m/s²)
  • ( h ): height or depth of the fluid
• Density from Specific Gravity: Density = Specific Gravity × Density of Water

Key Takeaways

• Understanding the relationship between pressure, force, and area is crucial.
• Converting units (e.g., cm to m, Pa to kPa) is an essential step in solving problems.
• The pressure due to fluids is dependent on the fluid's density and the depth of the fluid in a container.