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Intro to Chemical Engineering
Table of Contents
Unit 5 Overview: Fluid Mechanics
5.1 Fluid properties and classification
5.2 Fluid statics
5.3 Bernoulli's equation and applications
5.4 Momentum balance and flow measurement
5.5 Pipe flow and pressure drop
5.6 Pumps and compressors

Fluid mechanics is all about how liquids and gases behave. We'll look at their key properties like density and viscosity, and how they respond to forces. This stuff is super important for designing things like pipes and reactors.

We'll also explore the differences between Newtonian and non-Newtonian fluids, and how temperature and pressure affect fluid behavior. Understanding these concepts is crucial for solving real-world engineering problems.

Fluids, Liquids, and Gases

Defining and Differentiating Fluids, Liquids, and Gases

  • Fluids continuously deform under an applied shear stress and include both liquids and gases
    • Fluids have the ability to flow and take the shape of their container (water, air)
  • Liquids are a type of fluid that have a definite volume but no fixed shape
    • Liquids are nearly incompressible and have a free surface at the interface with a gas (water, oil)
  • Gases are a type of fluid that have neither a definite volume nor shape
    • Gases are highly compressible and will expand to fill their container (air, helium)
  • The key differences between liquids and gases are their compressibility and the presence of a free surface
    • Liquids are much less compressible than gases and have a distinct interface with gases
    • Gases do not have a free surface and are easily compressed

Properties and Behavior of Fluids

  • Fluids can be characterized by their ability to flow and deform under stress
    • Fluids will continue to deform as long as the stress is applied, unlike solids which resist deformation
  • The behavior of fluids is governed by their properties such as density, viscosity, and compressibility
    • These properties determine how fluids respond to forces and how they flow through pipes and channels
  • Fluids can be classified as either Newtonian or non-Newtonian based on their viscosity characteristics
    • Newtonian fluids have a constant viscosity, while non-Newtonian fluids have a viscosity that varies with shear rate
  • The properties and behavior of fluids are crucial for understanding and designing fluid systems in chemical engineering
    • Examples include pipeline transport, heat exchangers, and chemical reactors

Density, Viscosity, and Compressibility of Fluids

Density

  • Density is the mass per unit volume of a fluid, typically expressed in units of kg/m³
    • Density is a measure of the compactness of a fluid and varies with temperature and pressure
    • The density of water at standard conditions (20°C, 1 atm) is approximately 1000 kg/m³
  • Density is an important property for determining the buoyancy and hydrostatic pressure of fluids
    • Objects with a density less than the fluid will float, while objects with a higher density will sink
    • The hydrostatic pressure at a given depth depends on the density of the fluid and the depth below the surface

Viscosity

  • Viscosity is a measure of a fluid's resistance to flow or shear deformation
    • Viscosity arises from the internal friction between fluid layers as they move past each other
  • Dynamic viscosity (μ) is the ratio of shear stress to shear rate and has units of Pa·s
    • Dynamic viscosity represents the fluid's inherent resistance to flow
    • The dynamic viscosity of water at 20°C is approximately 1.002 mPa·s
  • Kinematic viscosity (ν) is the ratio of dynamic viscosity to density and has units of m²/s
    • Kinematic viscosity relates the fluid's resistance to flow with its density
    • The kinematic viscosity of water at 20°C is approximately 1.004 × 10⁻⁶ m²/s
  • Viscosity is important for determining pressure drops in pipes, flow rates, and heat transfer characteristics

Compressibility

  • Compressibility is a measure of the relative volume change of a fluid in response to a change in pressure
    • Compressibility is typically expressed as the bulk modulus, which is the ratio of the change in pressure to the fractional change in volume
  • Liquids are generally considered incompressible because they require large changes in pressure to cause a small change in volume
    • The bulk modulus of water is approximately 2.2 GPa, indicating its low compressibility
  • Gases are highly compressible, and their volume can change significantly with changes in pressure
    • The compressibility of gases is described by the ideal gas law, which relates pressure, volume, and temperature
  • Compressibility is important for understanding the behavior of fluids under high-pressure conditions and in compressible flow applications

Newtonian vs Non-Newtonian Fluids

Newtonian Fluids

  • Newtonian fluids have a constant viscosity that is independent of the applied shear rate
    • The shear stress is directly proportional to the shear rate, and the proportionality constant is the dynamic viscosity
    • Examples of Newtonian fluids include water, air, and most simple fluids like organic solvents and dilute solutions
  • Newtonian fluids follow Newton's law of viscosity, which states that shear stress (τ) is proportional to shear rate (γ̇): τ=μγ˙τ = μγ̇
    • The constant of proportionality, μ, is the dynamic viscosity of the fluid
  • The flow behavior of Newtonian fluids is well-understood and can be easily modeled using the Navier-Stokes equations
    • This makes Newtonian fluids easier to work with in many engineering applications

Non-Newtonian Fluids

  • Non-Newtonian fluids have a viscosity that varies with the applied shear rate
    • The relationship between shear stress and shear rate is not linear, and the apparent viscosity changes with the shear rate
  • There are several types of non-Newtonian fluids, each with distinct flow characteristics:
    • Shear-thinning (pseudoplastic) fluids exhibit a decrease in apparent viscosity with increasing shear rate (blood, paint, polymer solutions)
    • Shear-thickening (dilatant) fluids exhibit an increase in apparent viscosity with increasing shear rate (cornstarch suspensions, some colloidal solutions)
    • Bingham plastic fluids require a yield stress to be exceeded before they begin to flow, after which they behave as Newtonian fluids (toothpaste, mayonnaise, some slurries)
  • Non-Newtonian fluid behavior is more complex and requires specialized models to describe their flow characteristics
    • Examples of non-Newtonian fluid models include the power-law model, the Herschel-Bulkley model, and the Casson model
  • The classification of a fluid as Newtonian or non-Newtonian is important for understanding its flow behavior and selecting appropriate models for fluid flow calculations
    • Incorrectly assuming Newtonian behavior for a non-Newtonian fluid can lead to significant errors in pressure drop, flow rate, and other design parameters

Temperature and Pressure Effects on Fluids

Temperature Effects

  • Temperature affects the density, viscosity, and compressibility of fluids
  • Density:
    • As temperature increases, the density of most fluids decreases due to thermal expansion
    • This effect is more pronounced in gases than in liquids, as gases have more space between molecules to expand
    • For example, the density of water decreases from 1000 kg/m³ at 4°C to 958 kg/m³ at 100°C
  • Viscosity:
    • Viscosity generally decreases with increasing temperature for both liquids and gases
    • Higher temperatures increase the average kinetic energy of the molecules, reducing the intermolecular forces and making the fluid less resistant to flow
    • For instance, the dynamic viscosity of water decreases from 1.787 mPa·s at 0°C to 0.282 mPa·s at 100°C
  • Compressibility:
    • The compressibility of liquids increases slightly with increasing temperature, while the compressibility of gases decreases with increasing temperature
    • This is because increased temperature causes the molecules in a liquid to move further apart, making it easier to compress, while in gases, higher temperatures lead to increased molecular motion and resistance to compression

Pressure Effects

  • Pressure also influences fluid properties, particularly density and compressibility
  • Density:
    • Increasing pressure causes an increase in the density of fluids, particularly gases
    • Liquids are much less compressible than gases, so their density is less affected by pressure changes
    • For example, the density of air at standard atmospheric pressure (101.325 kPa) and 20°C is approximately 1.204 kg/m³, but it increases to 11.21 kg/m³ at a pressure of 1000 kPa
  • Viscosity:
    • The viscosity of liquids generally increases with increasing pressure, while the viscosity of gases is relatively insensitive to pressure changes
    • This is because higher pressures force the molecules in a liquid closer together, increasing the resistance to flow
  • Compressibility:
    • The compressibility of fluids decreases with increasing pressure, as the molecules are forced closer together, making it more difficult to compress the fluid further
    • This effect is more significant in gases than in liquids due to the greater compressibility of gases
    • For instance, the bulk modulus of water increases from 2.2 GPa at atmospheric pressure to 2.6 GPa at a pressure of 100 MPa

Understanding the effects of temperature and pressure on fluid properties is crucial for accurate modeling and design of fluid systems, as well as for predicting fluid behavior under various operating conditions. Engineers must account for these effects when designing equipment such as heat exchangers, pumps, and compressors to ensure optimal performance and safety.

Key Terms to Review (20)

Density: Density is defined as the mass of a substance per unit volume, typically expressed in units like grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³). It plays a crucial role in understanding fluid properties, helping to classify fluids based on their behavior and interaction under various conditions. Density is fundamental when applying Bernoulli's equation, as it influences pressure variations within fluid flow. It is also critical in analyzing pressure drops in pipe flow, where different densities affect friction losses and flow rates. Additionally, units and dimensions of density are essential for conversions and calculations in engineering contexts.
Viscosity: Viscosity is a measure of a fluid's resistance to flow, essentially describing how thick or sticky a liquid is. It plays a crucial role in characterizing fluid behavior under various conditions, influencing how fluids move through pipes, how they behave in different flow regimes, and how they transfer momentum and heat.
Newtonian fluid: A Newtonian fluid is a type of fluid that maintains a constant viscosity regardless of the shear rate applied to it. This means that the relationship between shear stress and shear rate is linear, which is a characteristic behavior of many common fluids like water and air. Understanding Newtonian fluids is crucial for analyzing their flow behavior in various engineering applications, as they provide a baseline for comparison with non-Newtonian fluids.
Non-newtonian fluid: A non-newtonian fluid is a type of fluid whose viscosity changes under stress or strain, meaning its flow behavior cannot be described by a single constant viscosity. This characteristic makes them distinct from Newtonian fluids, where the viscosity remains constant regardless of the applied force. Non-newtonian fluids can exhibit a range of behaviors such as shear-thinning, shear-thickening, or even displaying time-dependent viscosity, which makes their behavior interesting and complex in various applications.
Compressible fluid: A compressible fluid is a fluid whose density can change significantly when subjected to changes in pressure or temperature. This behavior is particularly noticeable in gases, where variations in pressure can lead to substantial density fluctuations, unlike incompressible fluids, where density remains constant regardless of pressure changes.
Pascal's Law: Pascal's Law states that when pressure is applied to a confined fluid, that pressure change is transmitted equally in all directions throughout the fluid. This principle is foundational for understanding fluid statics and fluid mechanics, as it explains how forces are distributed within fluids at rest. The law has practical applications in various engineering fields, including hydraulics, where it helps in the design of hydraulic systems that rely on fluid pressure to transmit force.
Hydrostatic Pressure: Hydrostatic pressure is the pressure exerted by a fluid at equilibrium due to the force of gravity. This pressure increases with depth in a fluid and is a critical concept in understanding how fluids behave when they are at rest, as well as how their properties change with varying densities and heights.
Continuity Equation: The continuity equation is a mathematical expression that represents the conservation of mass in a flowing fluid. It states that the mass flow rate of a fluid must remain constant from one cross-section of a flow system to another, ensuring that mass is neither created nor destroyed as it moves through a system. This principle is foundational for understanding various processes involving fluids, allowing engineers to analyze and design systems effectively.
Pressure: Pressure is defined as the force exerted per unit area on a surface. It plays a critical role in various physical and chemical processes, influencing fluid behavior, reactions, and system operations in engineering. Understanding pressure is essential for converting units, classifying fluids, applying principles like Bernoulli's equation, and designing reactors and simulations.
Compressibility: Compressibility is a measure of how much a substance can be compressed under pressure, indicating the change in volume in response to an applied force. In fluids, this property is essential for understanding behaviors in various applications, such as flow dynamics and equipment performance. It helps engineers assess how gases and liquids will behave in systems involving changes in pressure and temperature.
Navier-Stokes Equations: The Navier-Stokes equations are a set of nonlinear partial differential equations that describe the motion of fluid substances. They capture the relationship between the velocity, pressure, density, and viscosity of a fluid, and are fundamental in understanding how fluids behave under various conditions. These equations are crucial for analyzing fluid properties, classifying fluids based on their flow behavior, and modeling convective mass transfer processes in different engineering applications.
Shear Stress: Shear stress is defined as the force per unit area acting parallel to the surface of a material, which causes layers of the material to slide past one another. This concept is crucial for understanding how fluids behave under different conditions, as it influences flow characteristics and resistance within a fluid system. Shear stress plays a significant role in classifying fluid types and understanding their properties, as well as in momentum balance calculations that measure how fluids move and interact with surfaces.
Turbulent flow: Turbulent flow is a type of fluid motion characterized by chaotic changes in pressure and flow velocity. It typically occurs at high velocities or in situations with obstacles, resulting in eddies and vortices that disrupt the smooth layering of fluid particles. This phenomenon is crucial for understanding various physical processes like heat transfer, momentum balance, and energy losses in pipelines.
Fluid transport: Fluid transport refers to the movement of liquids and gases from one location to another, driven by various forces such as pressure, gravity, and momentum. Understanding fluid transport is crucial because it involves the study of fluid dynamics, which helps in predicting how fluids behave in different conditions, impacting processes like mixing, separation, and reaction in chemical engineering.
Pumping systems: Pumping systems are mechanical devices designed to move fluids from one location to another, often overcoming obstacles such as elevation changes or friction losses in pipes. They are essential in various industrial processes and applications, where the efficient transfer of liquids is crucial for maintaining flow rates and pressure levels. Understanding pumping systems involves grasping the behavior of fluids under different conditions and the effects of pipe flow and pressure drop on system performance.
Dynamic viscosity: Dynamic viscosity is a measure of a fluid's internal resistance to flow, reflecting how thick or sticky a fluid is. It quantifies the force needed to move one layer of fluid over another and is crucial for understanding how fluids behave under different conditions, which helps in classifying fluids into categories like Newtonian and non-Newtonian types.
Kinematic Viscosity: Kinematic viscosity is a measure of a fluid's internal resistance to flow under the influence of gravity. It describes how easily a fluid flows when no external forces, other than gravity, are acting on it, allowing for a clearer understanding of fluid behavior in various applications. This property is crucial for classifying fluids and understanding their dynamics in engineering processes, as it directly affects flow rates and the design of equipment like pumps and pipelines.
Incompressible Fluid: An incompressible fluid is a type of fluid whose density remains constant regardless of the pressure applied to it. This means that the volume of the fluid does not change significantly under pressure, making it an idealization often used in fluid mechanics to simplify analysis. Incompressible fluids are typically liquids, and their behavior is governed by the principles of hydrostatics and hydrodynamics.
Laminar Flow: Laminar flow is a type of fluid motion characterized by smooth, orderly layers or streamlines that move parallel to each other, minimizing turbulence and allowing for predictable behavior. This flow regime is crucial in various applications, as it influences how fluids interact with surfaces and how heat is transferred within the system.
Bernoulli's Principle: Bernoulli's Principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or potential energy. This principle highlights the relationship between velocity, pressure, and elevation in fluid dynamics, demonstrating how these properties interact in different fluid flow situations. Understanding Bernoulli's Principle is crucial when examining fluid properties and their classification, as well as applying Bernoulli's equation to real-world scenarios.