Intro to Chemical Engineering

🦫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.

Key Concepts and Definitions

  • Fluids encompass both liquids and gases that continuously deform under applied shear stress
  • Density (ρ)(\rho) represents the mass per unit volume of a fluid, typically expressed in units of kg/m3kg/m^3
  • Viscosity (μ)(\mu) measures a fluid's resistance to flow or deformation, with units of PasPa \cdot s or Ns/m2N \cdot s/m^2
  • Pressure (P)(P) is the force per unit area exerted by a fluid, measured in PaPa or N/m2N/m^2
    • 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)(\sigma) arises from intermolecular forces at the interface between two fluids or a fluid and a solid, expressed in N/mN/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)(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=ρghP = \rho g h, where ρ\rho is density, gg is gravitational acceleration, and hh 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)h = P / (\rho g)
  • Gauge pressure and absolute pressure are related by: Pabsolute=Pgauge+PatmosphericP_{absolute} = P_{gauge} + P_{atmospheric}

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)(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)(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)(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\rho_1 A_1 v_1 = \rho_2 A_2 v_2, where ρ\rho is density, AA is cross-sectional area, and vv 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=ddt(mv)\sum F = \frac{d}{dt} (mv), where FF is force, mm is mass, and vv 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: v122+gz1+P1ρ=v222+gz2+P2ρ+hL\frac{v_1^2}{2} + gz_1 + \frac{P_1}{\rho} = \frac{v_2^2}{2} + gz_2 + \frac{P_2}{\rho} + h_L, where vv is velocity, gg is gravitational acceleration, zz is elevation, PP is pressure, ρ\rho is density, and hLh_L 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: v22+gz+Pρ=constant\frac{v^2}{2} + gz + \frac{P}{\rho} = constant
  • Head loss (hL)(h_L) 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=πR4ΔP8μLQ = \frac{\pi R^4 \Delta P}{8 \mu L}, where QQ is flow rate, RR is pipe radius, ΔP\Delta P is pressure drop, μ\mu is viscosity, and LL is pipe length
  • Turbulent pipe flow has a flatter velocity profile, with more uniform velocity across the cross-section
    • Friction factor (f)(f) relates pressure drop to flow rate in turbulent flow: ΔP=fLDρv22\Delta P = f \frac{L}{D} \frac{\rho v^2}{2}, where DD is pipe diameter and vv 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=1nRh2/3S1/2v = \frac{1}{n} R_h^{2/3} S^{1/2}, where nn is Manning's roughness coefficient, RhR_h is hydraulic radius, and SS 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 nn variables can be reduced to an equation with nkn-k dimensionless groups, where kk 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)(Re) represents the ratio of inertial to viscous forces: Re=ρvDμRe = \frac{\rho v D}{\mu}, where ρ\rho is density, vv is velocity, DD is characteristic length, and μ\mu is viscosity
    • Froude number (Fr)(Fr) represents the ratio of inertial to gravitational forces: Fr=vgDFr = \frac{v}{\sqrt{gD}}, where gg is gravitational acceleration
  • Similitude is the concept of achieving similar behavior between a model and a prototype by maintaining geometric, kinematic, and dynamic similarity
    • Geometric similarity requires proportional dimensions
    • 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


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© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.