Glossary

2.1 Physical Properties of Fluids

3 min read•july 19, 2024

Fluid properties are the building blocks of fluid mechanics. , , and help us understand how fluids behave under different conditions. These properties are crucial for solving real-world engineering problems.

Ideal fluids simplify analysis, but real fluids are more complex. , a key property, affects flow behavior and energy dissipation. and also impact fluid properties, influencing density and viscosity in both liquids and gases.

Fluid Properties

Density and specific properties

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  • Density (ρ\rho) represents the mass per unit volume of a fluid
    • Formula: ρ=mV\rho = \frac{m}{V}
    • Units: kgm3\frac{kg}{m^3} (SI), slugft3\frac{slug}{ft^3} (English)
    • Examples: Water at 4°C has a density of 1000 kgm3\frac{kg}{m^3}, air at standard conditions has a density of 1.225 kgm3\frac{kg}{m^3}
  • Specific weight (γ\gamma) represents the weight per unit volume of a fluid
    • Formula: γ=ρg\gamma = \rho g
    • Units: Nm3\frac{N}{m^3} (SI), lbft3\frac{lb}{ft^3} (English)
    • Relationship with density: γ=ρg\gamma = \rho g, where gg is the acceleration due to gravity
    • Examples: Water at 4°C has a specific weight of 9810 Nm3\frac{N}{m^3}, mercury has a specific weight of 133,100 Nm3\frac{N}{m^3}
  • Specific gravity (SG) represents the ratio of a substance's density to the density of a reference substance (usually water at 4°C)
    • Formula: SG=ρsubstanceρreferenceSG = \frac{\rho_{substance}}{\rho_{reference}}
    • Dimensionless quantity
    • Examples: The specific gravity of oil is typically around 0.8, while the specific gravity of glycerin is about 1.26

Ideal vs real fluids

  • Ideal fluids have simplified properties that make them easier to analyze
    • Incompressible (constant density) regardless of pressure changes
    • Inviscid (no viscosity) meaning they have no resistance to shear stress
    • No thermal conductivity, so heat transfer within the fluid is not considered
    • Examples: Potential flow around an airfoil, inviscid flow through a nozzle
  • Real fluids have properties that more closely represent actual fluids encountered in engineering applications
    • Compressible (density changes with pressure) especially relevant for gases
    • Viscous (has viscosity) which causes resistance to flow and energy dissipation
    • Has thermal conductivity, allowing heat transfer within the fluid
    • Examples: Air flow over an aircraft wing, water flow through a pipe, oil lubricating a bearing

Viscosity in fluid mechanics

  • Viscosity (μ\mu) measures a fluid's resistance to deformation under shear stress
    • Dynamic (absolute) viscosity represents the ratio of shear stress to velocity gradient
      • Formula: τ=μdudy\tau = \mu \frac{du}{dy}
      • Units: Pa⋅sPa \cdot s (SI), lb⋅sft2\frac{lb \cdot s}{ft^2} (English)
      • Examples: Water at 20°C has a of 1.002 mPa·s, while honey at room temperature has a dynamic viscosity of about 10,000 mPa·s
    • (ν\nu) represents the ratio of dynamic viscosity to density
      • Formula: ν=μρ\nu = \frac{\mu}{\rho}
      • Units: m2s\frac{m^2}{s} (SI), ft2s\frac{ft^2}{s} (English)
      • Example: The kinematic viscosity of air at standard conditions is about 1.46 × 10⁻⁵ m2s\frac{m^2}{s}
  • Viscosity plays a crucial role in various aspects of fluid mechanics
    • Affects boundary layer formation near solid surfaces
    • Influences flow regime (laminar vs. turbulent) through the
    • Determines pressure drop in pipes and ducts ()
    • Impacts heat transfer in fluids ()

Temperature and pressure effects

  • Temperature effects on fluid properties
    • Density
      1. Liquids: Density decreases with increasing temperature due to thermal expansion
      2. Gases: Density decreases with increasing temperature according to the ideal gas law (ρ=PRT\rho = \frac{P}{RT})
    • Viscosity
      1. Liquids: Viscosity decreases with increasing temperature as molecular cohesion weakens
      2. Gases: Viscosity increases with increasing temperature due to increased molecular agitation
  • Pressure effects on fluid properties
    • Density
      1. Liquids: Slight increase in density with increasing pressure due to their nearly incompressible nature
      2. Gases: Density increases with increasing pressure according to the ideal gas law (ρ=PRT\rho = \frac{P}{RT})
    • Viscosity
      1. Liquids: Negligible effect on viscosity since liquid molecules are already closely packed
      2. Gases: Viscosity is independent of pressure for most engineering applications

Key Terms to Review (26)

Bernoulli's Equation: Bernoulli's Equation is a principle in fluid mechanics that describes the relationship between pressure, velocity, and elevation in a moving fluid. This equation connects the physical properties of fluids with the behavior of fluids under various pressure conditions, showing how energy is conserved within a streamline flow.
Capillarity: Capillarity is the ability of a liquid to flow in narrow spaces without the assistance of external forces, such as gravity. This phenomenon occurs due to the interplay of cohesive forces between the liquid molecules and adhesive forces between the liquid and surrounding solid surfaces. It is essential for understanding how fluids behave in small spaces and influences many natural processes, such as water movement in soil and plant transpiration.
Continuity equation: The continuity equation is a fundamental principle in fluid mechanics that expresses the conservation of mass within a fluid flow. It states that the mass flow rate of a fluid must remain constant from one cross-section of a pipe or channel to another, provided there are no mass additions or losses. This concept connects with various aspects of fluid behavior and dynamics, playing a crucial role in understanding how fluids move and behave under different conditions.
Density: Density is the mass per unit volume of a substance, typically expressed in units like kg/m³. It plays a crucial role in determining how fluids behave under various conditions, influencing buoyancy, pressure distribution, and flow characteristics.
Dynamic Viscosity: Dynamic viscosity is a measure of a fluid's resistance to flow or deformation under applied stress. It quantifies how thick or thin a fluid is, influencing how it moves and behaves in various situations. Dynamic viscosity plays a crucial role in understanding the physical properties of fluids, as it directly affects factors like flow rates, pressure drops, and energy losses in fluid systems.
Hagen-Poiseuille Equation: The Hagen-Poiseuille equation describes the flow of incompressible and Newtonian fluids through a cylindrical pipe, providing a quantitative relationship between flow rate, pressure difference, fluid viscosity, and pipe dimensions. This equation is essential in understanding how physical properties of fluids and the nature of flow influence the behavior of liquids in various engineering applications.
Hydrostatic Pressure: Hydrostatic pressure is the pressure exerted by a fluid at rest due to the force of gravity acting on it. This pressure increases with depth in a fluid, and it is directly proportional to the density of the fluid and the height of the fluid column above the point of measurement. Understanding hydrostatic pressure is essential for analyzing how fluids behave in various physical and thermodynamic contexts, as well as for pressure measurement and buoyancy calculations.
Ideal fluid: An ideal fluid is a theoretical concept in fluid mechanics representing a fluid that is incompressible and has no viscosity. This means that it does not resist shear stress and flows without any internal friction, allowing for simplified analyses of fluid motion. The ideal fluid model helps in understanding various fluid behaviors and lays the foundation for more complex fluid dynamics involving real fluids.
Incompressible Fluid: An incompressible fluid is a fluid whose density remains constant regardless of the pressure applied to it. This concept is essential in understanding fluid behavior, as it simplifies the analysis of fluid motion and the forces acting on it, particularly in incompressible flow situations where changes in pressure have negligible effects on fluid density.
Kg/m³: The unit kg/m³, or kilograms per cubic meter, is a measure of density, which indicates how much mass is contained in a given volume of a substance. Density plays a critical role in understanding how fluids behave under various conditions, affecting buoyancy, pressure, and flow characteristics. This measurement is vital in fluid mechanics for characterizing different fluids, whether they are gases or liquids, and influences calculations related to force, stability, and motion.
Kinematic Viscosity: Kinematic viscosity is a measure of a fluid's internal resistance to flow, specifically defined as the ratio of dynamic viscosity to fluid density. It plays a crucial role in understanding how fluids behave under various flow conditions and is key to characterizing the physical properties of fluids. Kinematic viscosity is typically expressed in units of square meters per second (m²/s) or centistokes (cSt), which helps quantify how easily a fluid flows when subjected to gravitational forces.
Laminar Flow: Laminar flow is a fluid motion characterized by smooth, parallel layers of fluid that move in an orderly fashion, with minimal mixing between the layers. This type of flow typically occurs at low velocities and is influenced by the fluid's viscosity and density, which play a crucial role in determining the flow behavior.
N/m³: The term n/m³ represents a unit of measurement that indicates the concentration of a substance, commonly used to express density in fluid mechanics. This unit is essential for understanding the physical properties of fluids, as it quantifies how much mass (in kilograms or grams) is contained within a given volume (in cubic meters). Understanding n/m³ is crucial in various applications, including calculating buoyancy, pressure, and flow rates in fluids.
Pascal: Pascal is the SI unit of pressure, defined as one newton per square meter. It quantifies the force applied per unit area and is crucial for understanding how fluids behave under various conditions. This measurement is essential in analyzing physical properties of fluids, how pressure is distributed within them, and the losses encountered in pipe systems, as well as in taking accurate pressure and temperature measurements.
Pascal's Law: Pascal's Law states that when pressure is applied to a confined fluid at rest, the pressure change is transmitted undiminished in all directions throughout the fluid. This fundamental principle highlights how pressure behaves in fluids, influencing various applications such as hydraulic systems and understanding force distribution.
Pascal's Principle: Pascal's Principle states that a change in pressure applied to an enclosed fluid is transmitted undiminished throughout the fluid in all directions. This principle explains how pressure works in fluids and highlights the importance of pressure as a physical property, demonstrating that when force is applied to a confined fluid, it results in equal pressure changes throughout that fluid.
Prandtl Number: The Prandtl Number is a dimensionless quantity that characterizes the relative thickness of the momentum and thermal boundary layers in a fluid flow. It is defined as the ratio of kinematic viscosity to thermal diffusivity and helps in understanding the heat transfer and fluid flow behavior in various systems. A high Prandtl number indicates that momentum diffuses much slower than thermal energy, which is crucial for analyzing heat transfer processes in fluids.
Pressure: Pressure is defined as the force exerted per unit area on a surface, commonly measured in Pascals (Pa). It plays a crucial role in understanding how fluids behave under different conditions, influencing everything from fluid movement to energy transfer in thermodynamic processes.
Real Fluid: A real fluid is any fluid that exhibits viscosity, meaning it resists flow and has internal friction when layers move past one another. Unlike ideal fluids, which are hypothetical and do not resist motion, real fluids account for practical considerations like turbulence and energy loss in flow, making them essential for understanding the behavior of fluids in real-world applications.
Reynolds Number: Reynolds number is a dimensionless quantity used to predict flow patterns in different fluid flow situations. It helps in understanding whether the flow is laminar or turbulent, which is essential in various applications like pipe flow, aerodynamics, and hydrodynamics.
Specific Gravity: Specific gravity is a dimensionless quantity that compares the density of a fluid to the density of a reference substance, typically water at 4°C. This ratio helps in understanding how heavy a fluid is relative to water, which is crucial for various applications in fluid mechanics, such as buoyancy and stability calculations. Knowing the specific gravity can also assist in determining whether a fluid will float or sink when placed in another fluid.
Specific Weight: Specific weight is defined as the weight of a fluid per unit volume, typically expressed in units like pounds per cubic foot (lb/ft³) or newtons per cubic meter (N/m³). This property is critical in understanding how fluids behave under gravitational forces, influencing concepts such as buoyancy and hydrostatic pressure. It helps to differentiate fluids in terms of their density and weight, providing insight into their behavior when subjected to external forces.
Surface Tension: Surface tension is the property of a liquid that causes its surface to behave like a stretched elastic membrane. This phenomenon occurs due to the cohesive forces between liquid molecules, which are stronger at the surface where molecules are in contact with air or another medium. Surface tension is critical in various physical behaviors of fluids, such as droplet formation and capillary action, influencing how fluids interact with solids and gases.
Temperature: Temperature is a measure of the average kinetic energy of the particles in a substance, reflecting how hot or cold that substance is. It plays a crucial role in determining the physical and thermodynamic properties of fluids, influencing behaviors like viscosity and density. Understanding temperature is vital for analyzing how fluids react under different thermal conditions and how energy transfers within these systems.
Turbulent flow: Turbulent flow is a type of fluid motion characterized by chaotic changes in pressure and velocity, leading to the formation of eddies and vortices. This flow regime significantly impacts various fluid mechanics principles, such as energy dissipation, momentum transfer, and the behavior of fluid particles within a system.
Viscosity: Viscosity is a measure of a fluid's resistance to deformation and flow, essentially describing how thick or sticky a fluid is. This property plays a crucial role in understanding fluid behavior under different conditions and directly affects various phenomena, such as flow rates, pressure distribution, and energy loss in fluid systems.
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