🦫Intro to Chemical Engineering Unit 5 – Fluid Mechanics
Fluid mechanics is a fundamental area of study in chemical engineering, focusing on the behavior and properties of fluids at rest and in motion. This unit covers key concepts like density, viscosity, and pressure, as well as fluid statics, dynamics, and conservation laws.
The study of fluid mechanics is crucial for understanding and designing various chemical engineering processes and equipment. From pumps and heat exchangers to reactors and separation processes, fluid mechanics principles are applied to optimize flow, heat transfer, and mass transfer in industrial systems.
Fluids encompass both liquids and gases that continuously deform under applied shear stress
Density (ρ) represents the mass per unit volume of a fluid, typically expressed in units of kg/m3
Viscosity (μ) measures a fluid's resistance to flow or deformation, with units of Pa⋅s or N⋅s/m2
Pressure (P) is the force per unit area exerted by a fluid, measured in Pa or N/m2
Absolute pressure considers the total pressure, including atmospheric pressure
Gauge pressure measures the pressure relative to atmospheric pressure
Compressibility describes how a fluid's density changes with pressure, with gases being more compressible than liquids
Surface tension (σ) arises from intermolecular forces at the interface between two fluids or a fluid and a solid, expressed in N/m
Capillary action occurs when surface tension and adhesive forces cause a fluid to rise in a narrow tube or porous material
Fluid Properties and Behavior
Fluids exhibit unique properties that distinguish them from solids, such as the ability to flow and take the shape of their container
Shear stress in fluids is proportional to the velocity gradient, with the proportionality constant being the fluid's viscosity
Newtonian fluids have a constant viscosity independent of shear rate (water, air), while non-Newtonian fluids have viscosity that varies with shear rate (blood, polymers)
Shear-thinning fluids decrease in viscosity with increasing shear rate (pseudoplastic)
Shear-thickening fluids increase in viscosity with increasing shear rate (dilatant)
Viscosity is affected by temperature, with liquids becoming less viscous and gases more viscous as temperature increases
Fluids can be classified as ideal (inviscid and incompressible) or real (viscous and compressible) for simplifying analysis
Bulk modulus (K) quantifies a fluid's resistance to compression, defined as the ratio of pressure change to volumetric strain
Fluid Statics and Pressure
Hydrostatic pressure is the pressure exerted by a fluid at rest due to its weight, increasing with depth
Hydrostatic pressure formula: P=ρgh, where ρ is density, g is gravitational acceleration, and h is depth
Pascal's law states that pressure applied to a confined fluid is transmitted undiminished in all directions
Archimedes' principle explains buoyancy, stating that an object immersed in a fluid experiences an upward force equal to the weight of the displaced fluid
Manometers measure pressure differences using a U-shaped tube filled with a liquid (mercury, water)
Barometers measure atmospheric pressure using a column of mercury or other liquid
Pressure head is the equivalent height of a fluid column that would produce a given pressure: h=P/(ρg)
Gauge pressure and absolute pressure are related by: Pabsolute=Pgauge+Patmospheric
Fluid Dynamics and Flow Types
Fluid dynamics studies the motion and forces in fluids, considering velocity, pressure, and other properties
Streamlines are curves tangent to the velocity vector at each point in a flow field, representing the path of fluid particles
Laminar flow occurs when fluid moves in parallel layers without mixing, characterized by low Reynolds numbers (Re<2300)
Velocity profile in laminar flow is parabolic, with maximum velocity at the center and zero at the walls
Turbulent flow is characterized by chaotic motion and mixing, with high Reynolds numbers (Re>4000)
Velocity profile in turbulent flow is flatter, with more uniform velocity across the cross-section
Transitional flow exists between laminar and turbulent regimes (2300<Re<4000), exhibiting characteristics of both
Compressible flow involves significant changes in fluid density, typically occurring at high velocities (Mach number > 0.3)
Incompressible flow assumes constant fluid density, valid for most liquids and low-speed gas flows
Steady flow has fluid properties (velocity, pressure) that do not change with time at a given point, while unsteady flow has time-varying properties
Conservation Laws in Fluid Mechanics
Conservation of mass (continuity equation) states that mass is neither created nor destroyed in a system
For steady, incompressible flow: ρ1A1v1=ρ2A2v2, where ρ is density, A is cross-sectional area, and v is velocity
Conservation of momentum (Newton's 2nd law) relates the net force on a fluid element to its rate of change of momentum
Momentum equation: ∑F=dtd(mv), where F is force, m is mass, and v is velocity
Conservation of energy (1st law of thermodynamics) states that energy is conserved in a system, accounting for work and heat transfer
Energy equation: 2v12+gz1+ρP1=2v22+gz2+ρP2+hL, where v is velocity, g is gravitational acceleration, z is elevation, P is pressure, ρ is density, and hL represents head losses
Bernoulli's equation is a simplified form of the energy equation for steady, incompressible, inviscid flow along a streamline
Bernoulli's equation: 2v2+gz+ρP=constant
Head loss (hL) accounts for energy dissipation due to friction and other irreversibilities in real fluid flows
Major losses occur along pipe lengths due to wall friction
Minor losses occur at fittings, valves, and other flow disturbances
Fluid Flow in Pipes and Channels
Pipe flow is characterized by fluid moving through a closed conduit, driven by a pressure difference
Laminar pipe flow has a parabolic velocity profile, with maximum velocity at the center and zero at the walls
Hagen-Poiseuille equation describes laminar flow in a circular pipe: Q=8μLπR4ΔP, where Q is flow rate, R is pipe radius, ΔP is pressure drop, μ is viscosity, and L is pipe length
Turbulent pipe flow has a flatter velocity profile, with more uniform velocity across the cross-section
Friction factor (f) relates pressure drop to flow rate in turbulent flow: ΔP=fDL2ρv2, where D is pipe diameter and v is average velocity
Moody diagram is a graphical tool for determining the friction factor based on Reynolds number and relative pipe roughness
Equivalent pipe length is used to account for minor losses by expressing them as an equivalent length of straight pipe
Open-channel flow occurs when a fluid flows with a free surface, such as in rivers or partially filled pipes
Manning's equation estimates the average velocity in open-channel flow: v=n1Rh2/3S1/2, where n is Manning's roughness coefficient, Rh is hydraulic radius, and S is channel slope
Dimensional Analysis and Similitude
Dimensional analysis is a technique for simplifying complex problems by considering the fundamental dimensions of variables (mass, length, time)
Buckingham Pi theorem states that a physically meaningful equation involving n variables can be reduced to an equation with n−k dimensionless groups, where k is the number of independent dimensions
Dimensionless numbers are ratios of forces or other quantities that characterize fluid behavior, enabling scaling and comparison of different systems
Reynolds number (Re) represents the ratio of inertial to viscous forces: Re=μρvD, where ρ is density, v is velocity, D is characteristic length, and μ is viscosity
Froude number (Fr) represents the ratio of inertial to gravitational forces: Fr=gDv, where g is gravitational acceleration
Similitude is the concept of achieving similar behavior between a model and a prototype by maintaining geometric, kinematic, and dynamic similarity
Kinematic similarity requires similar velocity and acceleration fields
Dynamic similarity requires similar force ratios (equal dimensionless numbers)
Applications in Chemical Engineering
Fluid mechanics principles are essential for designing and analyzing various chemical engineering processes and equipment
Pumps and compressors are used to transport fluids and increase their pressure, with selection based on flow rate, pressure rise, and fluid properties
Centrifugal pumps are common for high flow rates and moderate pressure rises
Positive displacement pumps (gear, diaphragm) are used for high pressures and viscous fluids
Heat exchangers transfer heat between fluids, with design considerations including flow arrangement (parallel, counter), surface area, and pressure drop
Shell-and-tube exchangers are widely used, with one fluid flowing through tubes and the other through the surrounding shell
Plate heat exchangers offer high surface area and ease of cleaning for viscous or fouling fluids
Reactors involve fluid flow and mixing to facilitate chemical reactions, with design factors such as residence time, mass transfer, and heat management
Continuous stirred-tank reactors (CSTRs) provide good mixing and temperature control for liquid-phase reactions
Plug flow reactors (PFRs) are used for gas-phase reactions or when minimal mixing is desired
Separation processes, such as distillation, absorption, and extraction, rely on fluid mechanics principles for design and optimization
Packed columns use a packing material to increase surface area for mass transfer between phases
Tray columns employ a series of perforated plates to promote mixing and separation
Fluidization is used in processes such as catalytic cracking and drying, where a fluid is passed upward through a bed of solid particles, suspending them in a fluid-like state
Minimum fluidization velocity is the fluid velocity required to initiate fluidization
Fluidized beds offer high heat and mass transfer rates due to the large surface area and mixing of particles