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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.

measures total force, while 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

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

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 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 ΔP=ρgh\Delta P = \rho gh, where ρ\rho is the density of the manometric fluid, gg is the acceleration due to gravity, and hh 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 ΔP=ρglsin⁡θ\Delta P = \rho g l \sin \theta, where ll is the horizontal distance traveled by the liquid, and θ\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

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

Key Terms to Review (32)

Absolute pressure: Absolute pressure is the total pressure exerted on a system, including atmospheric pressure. It is measured relative to a perfect vacuum (zero pressure).
Absolute Pressure: Absolute pressure is the total pressure acting on a surface, including both the atmospheric pressure and any additional pressure applied to the system. It is the sum of the gauge pressure and the atmospheric pressure at a given location.
Aneroid Barometer: An aneroid barometer is a type of barometer that measures atmospheric pressure without the use of liquid. It utilizes a flexible, sealed metal capsule that expands and contracts in response to changes in air pressure, allowing for a direct reading of the pressure value.
Atmospheric pressure: Atmospheric pressure is the force per unit area exerted by the weight of the atmosphere above a surface. It is measured using a barometer and typically expressed in units like Pascals (Pa) or atmospheres (atm).
Atmospheric Pressure: Atmospheric pressure is the force exerted by the weight of the air molecules in the Earth's atmosphere on a given surface. It is a fundamental concept in the study of fluids and is crucial in understanding various physical phenomena related to pressure and its measurement.
Barometer: A barometer is an instrument that measures atmospheric pressure. It is commonly used in meteorology and fluid mechanics to determine altitude and forecast weather.
Barometer: A barometer is an instrument used to measure atmospheric pressure, which is the force exerted by the weight of the air above a given surface area. It is a crucial tool in the study of meteorology and weather forecasting.
Bourdon tube gauge: A Bourdon tube gauge is a mechanical device used to measure pressure, consisting of a curved tube that straightens when pressure is applied. This movement is translated into a dial reading, allowing for accurate monitoring of pressure in various systems. Bourdon tube gauges are widely utilized in industrial applications due to their durability and reliability.
Compressibility: Compressibility is a measure of the relative volume change of a fluid or solid as a response to a pressure change. It quantifies how much the material can be compressed when subjected to external forces.
Compressibility: Compressibility is a measure of how much a material or substance can be reduced in volume by the application of pressure. It is a fundamental property that describes the ability of a material to be compressed or deformed under an applied force.
Diaphragm Gauge: A diaphragm gauge is a type of pressure-measuring instrument that uses a flexible diaphragm to detect changes in pressure. It is commonly used to measure both positive and negative pressures in various applications, such as in the automotive, HVAC, and industrial sectors.
Fluid Statics: Fluid statics is the study of fluids at rest and the pressures they exert. It encompasses the principles and concepts that govern the behavior of fluids, such as liquids and gases, when they are not in motion, focusing on the properties and effects of pressure within these stationary systems.
Gauge pressure: Gauge pressure is the pressure relative to atmospheric pressure. It is the difference between absolute pressure and atmospheric pressure.
Gauge Pressure: Gauge pressure is the pressure of a fluid or gas measured with respect to the surrounding atmospheric pressure. It represents the pressure in excess of the ambient or atmospheric pressure, rather than the total or absolute pressure acting on a system.
Hydraulic Systems: Hydraulic systems are mechanical systems that use pressurized fluid, typically oil or water, to transmit power and perform work. These systems rely on the principles of fluid dynamics to convert energy into controlled, precise movements and forces.
Hydrostatic Equilibrium: Hydrostatic equilibrium refers to the state of balance where the pressure exerted by a fluid on its surroundings is equal in all directions. This concept is particularly relevant when studying the measurement of pressure, as it underlies many of the principles and techniques used to determine pressure in static fluid systems.
Inclined Manometer: An inclined manometer is a device used to measure the pressure of a fluid by observing the difference in height between two columns of the fluid. It consists of a U-shaped tube that is tilted at an angle, with one end connected to the pressure source and the other end open to the atmosphere.
Manometer: A manometer is a device used to measure the pressure of a fluid or gas. It operates by detecting the difference in height between two columns of a fluid, typically a liquid, to determine the pressure of the system being measured.
Mercury Barometer: A mercury barometer is a device used to measure atmospheric pressure. It consists of a glass tube filled with mercury that is inverted and immersed in a mercury reservoir. The height of the mercury column in the tube is directly proportional to the pressure of the surrounding air, providing a reliable way to measure changes in atmospheric pressure.
Open-tube Barometer: An open-tube barometer is a device used to measure atmospheric pressure. It consists of a glass tube that is open at one end and filled with mercury, which is inverted and placed in a container of mercury. The height of the mercury column in the tube is directly proportional to the atmospheric pressure, providing a way to measure and monitor changes in air pressure.
Pabs = Pgauge + Patm: Pabs, or absolute pressure, is the sum of the gauge pressure (Pgauge) and the atmospheric pressure (Patm). This relationship is fundamental in understanding how pressure is measured and its various components.
Pascal: A pascal (Pa) is the SI unit of pressure, defined as one newton per square meter. It is used to quantify internal pressure, stress, Young's modulus, and tensile strength.
Pascal: Pascal is a unit of pressure, named after the French mathematician and physicist Blaise Pascal. It is a fundamental concept in physics that is closely related to the study of stress, strain, elasticity, fluids, and hydraulics.
Pressure: Pressure is a measure of the force applied per unit area, representing the amount of force exerted on a surface or object. This concept is fundamental in understanding various physical phenomena and principles, including mass and weight, hydraulic systems, fluid dynamics, sound propagation, and shock waves.
Pressure (P = F/A): Pressure is the force exerted per unit area on a surface. It is defined by the equation P = F/A, where P is the pressure, F is the force applied, and A is the area over which the force is applied. This concept is fundamental in understanding the behavior of fluids and solids under various forces and is essential in fields such as physics, engineering, and materials science.
Pressure Gauge: A pressure gauge is a device used to measure the pressure of a fluid or gas within a system. It is an essential tool for monitoring and controlling the pressure in various applications, such as in plumbing, HVAC systems, and industrial processes.
Pressure Head: Pressure head, also known as static head, refers to the height of a column of fluid that exerts a specific pressure. It is a measure of the potential energy of a fluid due to its position relative to a reference point, typically the surface of the fluid or a specific point in the system.
Torr,: A torr is a unit of pressure defined as 1/760th of an atmosphere. It is named after Evangelista Torricelli, an Italian physicist known for his work in fluid mechanics.
Torricelli: Evangelista Torricelli was an Italian physicist and mathematician who is best known for inventing the barometer. His work laid the foundation for the study of atmospheric pressure.
U-tube Manometer: A U-tube manometer is a device used to measure the pressure difference between two points in a fluid system. It consists of a U-shaped glass or plastic tube filled with a liquid, typically water or mercury, which is connected to the two points where the pressure is to be measured.
ΔP = ρgh: The change in pressure (ΔP) is directly proportional to the density of the fluid (ρ), the acceleration due to gravity (g), and the height of the fluid column (h). This relationship is known as the hydrostatic pressure equation and is a fundamental concept in the study of fluid mechanics.
ΔP = ρgl sin θ: The equation ΔP = ρgl sin θ represents the change in pressure (ΔP) within a fluid column due to the force of gravity acting on the fluid. This relationship is fundamental in understanding how pressure varies with depth and is a key concept in the topic of measuring pressure.
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14.3 Pascal's Principle and Hydraulics