Glossary

14.1 Fluids, Density, and Pressure

3 min read•june 24, 2024

are all around us, from the air we breathe to the water we drink. Understanding their properties is key to grasping how they behave in different situations. This topic dives into the , , , and fluid dynamics.

We'll explore how molecules in fluids interact, why some fluids are compressible while others aren't, and how pressure affects fluid behavior. We'll also look at real-world applications like hydraulic systems and airplane wings, connecting theory to everyday life.

Phases of Matter and Fluid Properties

Phases of matter in fluids

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  • has a rigid and fixed shape because its atoms or molecules are closely packed and have limited motion
  • has a definite volume but no fixed shape since its atoms or molecules have more freedom to move than in
  • has no definite shape or volume as its atoms or molecules move randomly with large distances between them

Molecular structure and fluid behavior

  • Fluids ( and ) flow and deform under applied forces because their molecules have weaker intermolecular forces compared to solids, allowing them to move past one another
  • Liquids have stronger intermolecular forces than gases, making them more difficult to compress and giving them a definite volume, while gases expand to fill their container
  • in liquids results from these intermolecular forces, causing the liquid surface to behave like an elastic membrane

Compressible vs incompressible fluids

  • (gases, such as air) have a density that changes significantly with pressure
  • (liquids, such as water, and dense gases) have a density that remains nearly constant with changes in pressure

Density and Pressure

Density and its SI units

  • Density (ρ\rho) is the mass per unit volume of a substance, calculated using the formula ρ=mV\rho = \frac{m}{V}
  • SI units for density are kilograms per cubic meter (kg/m3kg/m^3)

Density comparisons in fluids

  • Water has a density of 1000 kg/m3kg/m^3
  • Air at sea level has a density of 1.225 kg/m3kg/m^3
  • Oil has a density ranging from 800-900 kg/m3kg/m^3
  • Mercury has a density of 13,600 kg/m3kg/m^3

Pressure and its SI units

  • Pressure (PP) is the force per unit area applied perpendicular to a surface, calculated using the formula P=FAP = \frac{F}{A}
  • SI units for pressure are pascals (PaPa) or newtons per square meter (N/m2N/m^2)
  • at sea level is 101,325 PaPa (1 atm)
  • is the pressure relative to
  • is the sum of and atmospheric pressure
  • is the pressure exerted by a fluid at rest due to its weight

Pressure, force, and area relationship

  • Pressure is directly proportional to force and inversely proportional to area
    • Increasing force on a constant area increases pressure
    • Increasing area with a constant force decreases pressure
  • Applications include hydraulic lifts that use a small force over a small area to generate a large force over a large area, and sharp objects exerting more pressure than blunt objects for the same force due to their smaller area

Problem-solving with fluid pressure

  1. Use the pressure formula (P=FAP = \frac{F}{A}) to calculate pressure, force, or area when given the other two quantities
  2. Consider the effects of atmospheric pressure and gauge pressure when solving problems
  3. Apply the concept of pressure to real-world situations (hydraulic systems, tire inflation, underwater depth)

Fluid Dynamics

Bernoulli's Principle

  • Describes the relationship between fluid pressure, velocity, and height in a flowing fluid
  • As fluid velocity increases, pressure decreases, and vice versa
  • Explains lift in airplane wings and the curved flight of spinning balls

Viscosity and Fluid Flow

  • is a measure of a fluid's resistance to flow
  • Higher viscosity fluids (like honey) flow more slowly than lower viscosity fluids (like water)
  • Affects fluid behavior in pipes, blood flow in vessels, and lubrication in engines

Buoyancy

  • The upward force exerted by a fluid on an immersed object
  • Explains why objects float or sink in fluids
  • Related to the volume of fluid displaced by the object and the densities of the object and fluid

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.
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.
Bernoulli's Principle: Bernoulli's principle is a fundamental concept in fluid dynamics that describes the relationship between the pressure, speed, and elevation in a flowing fluid. It states that as the speed of a fluid increases, the pressure within the fluid decreases, and vice versa.
Buoyancy: Buoyancy is the upward force exerted by a fluid on an object immersed in it, which counteracts the object's weight and allows it to float. This principle is fundamental to understanding the behavior of objects in various contexts, including mass and weight, drag force and terminal speed, and fluids, density, and pressure.
Coefficient of viscosity: The coefficient of viscosity is a measure of a fluid's resistance to flow. It quantifies the internal friction within the fluid.
Compressible fluids: Compressible fluids are fluids whose density can change significantly when subjected to pressure variations. Unlike incompressible fluids, which maintain a constant density regardless of pressure changes, compressible fluids exhibit varying densities depending on the applied pressure and temperature. This property makes them essential in understanding various phenomena in fluid dynamics, particularly in scenarios involving high-speed flows and thermodynamic processes.
Density: Density is a fundamental physical property that describes the mass per unit volume of a substance. It is a measure of how much matter is packed into a given space and is a crucial concept in understanding the behavior of fluids, solids, and gases across various physics topics.
Fluids: Fluids are substances that can flow and take the shape of their container, including liquids and gases. They lack a fixed shape but have a definite volume in the case of liquids.
Gas: A gas is one of the four fundamental states of matter, characterized by its ability to expand and fill any container, having no fixed shape or volume, and being highly compressible. Gases are essential in the study of fluids, density, and pressure, as they exhibit unique properties that distinguish them from solids and liquids.
Gases: Gases are one of the states of matter characterized by low density and high compressibility, with molecules in rapid random motion. They have no fixed shape or volume, expanding to fill their containers.
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.
Heterogeneous substance: A heterogeneous substance is a material composed of different components that are not uniformly distributed. In fluid mechanics, it refers to fluids or mixtures where the composition varies at different points.
Homogeneous substance: A homogeneous substance has a uniform composition and properties throughout its entire volume. This means that any sample taken from the substance will have the same characteristics as any other sample.
Hydrostatic Pressure: Hydrostatic pressure is the pressure exerted by a fluid, such as water or air, due to the force of gravity acting on the weight of the fluid. It is a fundamental concept in the study of fluids, density, and buoyancy.
Incompressible Fluids: Incompressible fluids are fluids that do not experience any significant change in volume when subjected to changes in pressure. This means that the density of an incompressible fluid remains essentially constant, regardless of the pressure applied to it.
Linear mass density: Linear mass density is the measure of mass per unit length of a one-dimensional object, such as a string or rod. It is typically denoted by the symbol $\lambda$ and expressed in units of kg/m.
Liquid: A liquid is a state of matter that has a definite volume but no fixed shape, taking the shape of the container it is in. Liquids are characterized by their ability to flow and their high density compared to gases.
Liquids: Liquids are a state of matter characterized by a fixed volume but no fixed shape, allowing them to flow and conform to the shape of their container. They exhibit properties such as incompressibility and viscosity.
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.
Phases of matter: Phases of matter describe the distinct forms that different states of matter take on. The primary phases include solid, liquid, and gas, each with unique properties and behaviors under various conditions.
Plasma: Plasma is an ionized gas composed of ions, electrons, and neutral particles. It exhibits unique properties such as electrical conductivity and responsiveness to magnetic fields.
Pressure: Pressure is the force exerted per unit area. It is typically measured in Pascals (Pa) or atmospheres (atm).
Solid: A solid is one of the three fundamental states of matter, characterized by structural rigidity and resistance to changes in shape or volume. Solids have a definite shape and volume, and their particles are closely packed together with limited freedom of movement.
Solids: Solids are a state of matter characterized by structural rigidity and resistance to changes in shape or volume. In solids, particles are closely packed together, usually in a regular pattern.
Specific gravity: Specific gravity is the ratio of the density of a substance to the density of a reference substance, typically water. It is a dimensionless quantity that indicates whether a material will sink or float in water.
Static fluid: A static fluid is a fluid that is not in motion, meaning there are no flow velocities. It remains at rest or in a state of equilibrium under the influence of external forces like gravity.
Surface Tension: Surface tension is a property of liquids that arises from the cohesive forces between the molecules at the surface of the liquid, which allows the surface to behave like an elastic sheet. This property is crucial in understanding the behavior of fluids, their density, and the pressure exerted by them.
Viscosity: Viscosity is a measure of a fluid's resistance to flow. It describes the internal friction within a fluid, which determines how easily the fluid can move and deform under an applied force.
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