Definition of Pressure
Basic Concept
Pressure (P): force (F) applied perpendicular to surface area (A). Expressed as P = F/A. Scalar quantity. Direction normal to surface.
Physical Interpretation
Represents intensity of force distribution. Higher pressure = greater force concentration. Critical for fluid statics and dynamics.
Pressure in Thermodynamics
State variable. Independent variable in equations of state. Indicates molecular collision intensity in gases/liquids.
"Pressure is the fundamental link between microscopic molecular motion and macroscopic fluid behavior." -- Richard P. Feynman
Units and Measurement
SI Units
Pascal (Pa): 1 Pa = 1 N/m². Derived unit. Standard for scientific use.
Common Units
Atmosphere (atm): 101325 Pa. Bar: 100000 Pa. Torr: 133.322 Pa. psi (pounds per square inch): Imperial unit.
Unit Conversion
Conversion essential for cross-disciplinary applications. Use exact factors for accuracy.
| Unit | Equivalent |
|---|---|
| 1 atm | 101325 Pa = 1.01325 bar = 760 Torr = 14.696 psi |
| 1 bar | 100000 Pa = 0.987 atm |
Pressure in Fluids
Hydrostatic Pressure
Pressure due to fluid weight at depth h: P = P₀ + ρgh. P₀: reference pressure at surface. ρ: fluid density. g: gravity acceleration.
Pascal’s Principle
Pressure applied to confined fluid transmits undiminished in all directions. Basis for hydraulics.
Pressure Gradient
Variation of pressure with position. Drives fluid flow in pipes, atmosphere, oceans.
Gas Laws and Pressure
Ideal Gas Law
Relation: PV = nRT. P: pressure, V: volume, n: moles, R: gas constant, T: temperature. Assumes ideal behavior.
Boyle’s Law
At constant temperature, P inversely proportional to V: P₁V₁ = P₂V₂.
Charles’s and Gay-Lussac’s Laws
Pressure proportional to temperature at constant volume: P/T = constant.
Thermodynamic Pressure
Definition
Pressure defined as partial derivative of internal energy with respect to volume at constant entropy: P = −(∂U/∂V)ₛ.
Relation to Molecular Motion
Pressure arises from molecular collisions per unit area. Statistical mechanics link.
Non-equilibrium Considerations
Pressure may vary locally in non-equilibrium systems. Requires advanced models.
Atmospheric Pressure
Definition and Variability
Pressure exerted by air column above measurement point. Varies with altitude, weather.
Barometric Pressure
Measured by barometers. Indicator of weather changes.
Standard Atmosphere
Defined as 101325 Pa. Used as reference in engineering and science.
Pressure Measurement Techniques
Manometers
Measure pressure difference using column height of liquid. Simple, accurate for low pressures.
Bourdon Gauges
Mechanical deformation of curved tube proportional to pressure. Used in industrial applications.
Electronic Sensors
Piezoelectric, capacitive sensors convert pressure to electrical signals. High precision, fast response.
Applications of Pressure
Hydraulics
Force multiplication via fluid pressure. Used in brakes, lifts, machinery.
Thermodynamics Cycles
Pressure control essential in engines, refrigeration cycles, turbines.
Biomedical
Blood pressure monitoring critical for health assessment.
Pressure in Phase Transitions
Phase Diagrams
Pressure-temperature plots define phases: solid, liquid, gas boundaries.
Clapeyron Equation
Relates pressure and temperature changes during phase change: dP/dT = ΔH / TΔV.
Critical Pressure
Pressure above which distinct liquid and gas phases do not exist.
Pressure and Energy
Work Done by Pressure
Work W = ∫PdV during volume change. Key in thermodynamic processes.
Pressure-Volume Energy
Pressure energy stored in compressed gases and fluids.
Enthalpy
H = U + PV. Enthalpy includes internal energy and energy due to pressure-volume work.
Pressure in Engineering
Design Considerations
Structural integrity based on maximum expected pressure. Safety factors applied.
Pressure Vessels
Contain fluids at high pressure. Design codes regulate thickness, materials.
Fluid Mechanics
Pressure distribution critical for pump, pipe, and aircraft design.
References
- Çengel, Y. A., & Boles, M. A. Thermodynamics: An Engineering Approach. McGraw-Hill, 8th ed., 2015, pp. 45-78.
- Reif, F. Fundamentals of Statistical and Thermal Physics. McGraw-Hill, 1965, pp. 120-150.
- Van Wylen, G. J., & Sonntag, R. E. Fundamentals of Classical Thermodynamics. Wiley, 3rd ed., 1985, pp. 60-90.
- Moran, M. J., & Shapiro, H. N. Fundamentals of Engineering Thermodynamics. Wiley, 7th ed., 2010, pp. 100-130.
- White, F. M. Fluid Mechanics. McGraw-Hill, 7th ed., 2011, pp. 200-240.