Pressure measurement is crucial in physics and engineering. From barometers tracking weather to manometers gauging fluid systems, these tools help us understand and control the forces at play in gases and liquids.

Absolute pressure measures total force, while gauge pressure compares to atmospheric levels. Various devices like mercury barometers, U-tube manometers, and Bourdon gauges offer different ways to quantify pressure in diverse applications.

Pressure Measurement

Gauge vs absolute pressure

• Pressure is the force per unit area exerted by a fluid on a surface expressed mathematically as $P = \frac{F}{A}$
• Absolute pressure $P_{abs}$ is the total pressure measured relative to a perfect vacuum used in thermodynamic calculations and when considering the behavior of gases
• Gauge pressure $P_{gauge}$ is the pressure measured relative to the surrounding atmospheric pressure commonly used in engineering applications (tire pressure, pressure in pipes)
• Relationship between absolute and gauge pressure: $P_{abs} = P_{gauge} + P_{atm}$ where $P_{atm}$ is the atmospheric pressure

Methods of pressure measurement

• Barometers measure atmospheric pressure
  • Mercury barometers use the height of a mercury column to indicate pressure
  • Aneroid barometers use the deflection of a sealed, flexible chamber to measure pressure changes
  • Limitations include sensitivity to temperature changes and require calibration
• Manometers measure pressure differences between two points in a fluid
  • U-tube manometers use the height difference of a liquid column to indicate pressure difference
  • Inclined manometers use a sloped tube to increase sensitivity for small pressure differences
  • Limitations include requiring a reference pressure and can be affected by fluid density changes
• Pressure gauges measure pressure relative to a reference (usually atmospheric pressure)
  • Bourdon tube gauges use the deformation of a curved tube to indicate pressure
  • Diaphragm gauges use the deflection of a flexible membrane to measure pressure
  • Limitations include being affected by temperature changes and may require frequent calibration

Open-tube barometers for atmosphere

• Open-tube barometers (mercury barometers) consist of a glass tube filled with a liquid (mercury) inverted in a reservoir
• The height of the liquid column in the tube is proportional to the atmospheric pressure
  • At sea level, standard atmospheric pressure (1 atm) equals the pressure exerted by a 760 mm mercury column
• As atmospheric pressure changes, the height of the liquid column in the barometer adjusts accordingly
• The height of the liquid column can be measured using a scale, allowing for the determination of atmospheric pressure
• Open-tube barometers are used in weather stations, laboratories, and other applications requiring accurate atmospheric pressure measurements

Manometers for fluid pressure

• Manometers measure the pressure difference between two points in a fluid system
• U-tube manometers consist of a U-shaped tube filled with a manometric fluid (usually a liquid)
  1. The pressure difference is determined by the height difference of the liquid columns in the two legs of the U-tube
  2. The pressure difference is given by $\Delta P = \rho gh$, where $\rho$ is the density of the manometric fluid, $g$ is the acceleration due to gravity, and $h$ is the height difference between the liquid levels
• Inclined manometers use a sloped tube to increase the sensitivity for measuring small pressure differences
  1. The pressure difference is determined by the horizontal distance the liquid travels along the inclined tube
  2. The pressure difference is given by $\Delta P = \rho g l \sin \theta$, where $l$ is the horizontal distance traveled by the liquid, and $\theta$ is the angle of inclination of the tube
• Manometers are used in various applications (measuring pressure drops across filters, determining flow rates, monitoring pressure in closed systems)

Fluid statics and pressure applications

• Hydrostatic equilibrium occurs when a fluid is at rest and the pressure at any point is determined by the weight of the fluid above it
• Pressure head is the height of a fluid column that would produce a given pressure, often used in hydraulic systems
• Compressibility affects how pressure changes with depth in a fluid, with incompressible fluids having a linear pressure increase
• Hydraulic systems use the principles of fluid statics to transmit force and multiply mechanical advantage in various applications