Lecture: Understanding Pressure

Key Concepts

• Pressure Definition: Pressure is defined as force divided by area.
• Units of Pressure:
  • The standard unit in physics is Pascals (Pa).
  • 1 Pascal = 1 Newton per square meter.
  • 1 kilopascal (kPa) = 1,000 Pascals.
  • Atmospheric pressure (atm) = 101.3 kPa.

Relationship Between Force, Area, and Pressure

• Formula: Pressure = Force / Area
• Effect of Area and Force on Pressure:
  • Increasing the area with the same force reduces pressure.
  • Increasing the force on the same area increases pressure.
• Example Calculation:
  • Force: 100 Newtons over 1 square meter = 100 Pascals.
  • Area doubled to 4 square meters with 100 Newtons = 25 Pascals.
• Conclusion: Pressure is directly proportional to force and inversely proportional to area.

Example Problem 1: Rectangular Block on a Table

• Given: A block of 15 kg with dimensions 70 cm x 40 cm.
• Calculation Steps:
  • Convert dimensions to meters: 0.7 m x 0.4 m.
  • Calculate force: Weight = mass x gravitational acceleration = 15 kg x 9.8 m/s² = 147 N.
  • Calculate area: 0.7 m x 0.4 m = 0.28 m².
  • Calculate pressure: 147 N / 0.28 m² = 525 Pascals.

Example Problem 2: Water in a Rectangular Container

• Given: Container dimensions 4 m x 5 m x 6 m, filled with water.
• Water Density: 1,000 kg/m³.
• Calculation:
  • Pressure = Density x Gravitational Acceleration x Height.
  • Height = 6 m.
  • Pressure = 1,000 kg/m³ x 9.8 m/s² x 6 m = 58,800 Pascals.

Example Problem 3: Fluid in a Cylindrical Container

• Given: Fluid with specific gravity 1.7, at a depth of 50 meters.
• Specific Gravity: Density relative to water.
• Density Calculation:
  • Density of fluid = Specific Gravity x Density of water.
  • Density = 1.7 x 1,000 kg/m³ = 1,700 kg/m³.
• Pressure Calculation:
  • Pressure = Density x Gravitational Acceleration x Depth.
  • Pressure = 1,700 kg/m³ x 9.8 m/s² x 15 m = 249,900 Pascals.
  • Convert to kPa: 249.9 kPa.

Important Equations

• Pressure: P = F / A
• Fluid Pressure at Depth: P = Density x Gravity x Height

Additional Notes

• Remember the conversion of units, especially when switching between cm and m.
• Specific gravity is crucial for calculating density of unknown fluids.