Pressure: Fundamental Principles and Applications in Fluids and Gases

Defining Pressure

Pressure () quantifies force distribution over a surface area:

Where:

• : Normal force component (N)
• : Contact area (m²)
• 1 Pa = 1 N/m²

Fluid Pressure

Hydrostatic Pressure

Where:

• : Atmospheric pressure (101.3 kPa)
• : Fluid density (kg/m³)
• : Gravitational acceleration (9.81 m/s²)
• : Depth (m)

Pascal’s Principle

Pressure transmission enables hydraulic force multiplication:

Gas Pressure

Ideal Gas Law

Constants:

• 
• STP: 273.15 K, 101.325 kPa

Practical Applications

Engineering Systems

• Hydraulic lifts: Achieve 100:1 force amplification
• Scuba diving: Pressure increases ~101 kPa per 10m depth

Meteorology

• Barometric pressure: 98-104 kPa typical range
• Weather fronts: ~5 kPa pressure differences

Worked Example

Water Pressure at 5m Depth:

Note: Total pressure = 49.05 kPa + 101.3 kPa = 150.35 kPa

Common Errors

1. Using gauge pressure instead of absolute pressure
2. Neglecting temperature in gas law calculations
3. Confusing density units (kg/m³ vs g/cm³)

Practice Problems

1. A hydraulic press has pistons with 10:1 area ratio. What input force lifts a 500 kg mass?
2. Calculate the moles of oxygen in a 0.02 m³ tank at 300 kPa and 293 K.
3. Explain why submarines have maximum operating depths.

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