Transport Phenomena Concepts

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Transport Phenomena

• Also called the transport process.
• These are irreversible processes that involve the exchange or transfer of momentum, heat, and mass.

Order Tensors and Scalars

• 0th order tensors/scalars possess only magnitude, such as temperature, pressure, and concentration.
• 1st order tensors/vectors possess magnitude and direction, such as velocity, momentum, and force.
• 2nd order tensors/dyads require magnitude and two directions or indices to specify their value, such as momentum flux and shear stress.

Conservation Equations

• Describe how quantity is conserved.

Constitutive Equations

• These describe how quantity responds to an external stimuli (such as applied field or force).
• Also known as phenomenological rate or transport laws.

Momentum Transfer or Fluid Dynamics

• Involves the transfer of momentum.

Heat Transfer

• Involves the transfer of energy.

Molecular Transport

• Depends on of the motion of individual molecules.

Turbulent Transport

• Results from the large groups or clusters of molecules

Fluxus or Fluere

• Latin word meaning "to flow."

Dimensional Analysis

• It is a procedure of grouping variables into meaningful dimensionless groups
• Reduces the number of parameters involved in the experimental investigation of physical phenomena.

Concepts from History

• 1822: An analytical theory of heat was developed.

Metrology

• The science of measurement.

Direct/Rayleigh Method

• Expresses a functional relationship of some variables in the form of exponential equations.

Indirect/Buckingham Theorem

• Used for experimental physical phenomena investigations
• Involves more variables than the primary dimensional quantities
• It is not possible to find a unique relation between the variables.

Fluid

• A substance that deforms continuously (flows) under an applied shear stress has been classified to a substance called Fluid.

Stress

• It is a physical quantity that expresses the internal forces that adjacent particles of a continuous material exert on each other.

Fluid Mechanics

• Branch of classical mechanics that deals with the study of the mechanical and flow properties of fluids.
• Involves the laws of force and motion to fluids and the response of fluids to forces exerted upon them.

Fluid Statics (Hydrostatics)

• Study of fluids at rest

Fluid Dynamics

• Study of the effect of forces on fluid motion.

Pressure

• The amount of force exerted on a unit area.

Types of Pressure

• Absolute pressure is zero-referenced against a perfect vacuum where no molecules are in space.
• Gauge pressure is measured relative to the local atmosphere, usually against ambient air pressure.
• Atmospheric pressure (or barometric pressure) is the pressure within the Earth's atmosphere.
• Closely approximated by the hydrostatic pressure caused by the weight of air above the reference point.

Pascal's Law

• Known as Pascal's principle or the principle of transmission of fluid pressure.

Manometers

• These are devices used to measure pressure
• Derived from the Greek words "manos" (thin/rare) and "metron" (measure).
• Glass tube bent into a U-shape, filled with a liquid (usually mercury) that settles at the bottom curved region

Manometer Types

• Open-end manometers measure relative or gauge pressure.
• Sealed-end manometers measure absolute pressure.
• Inclined manometers are used to easily measure smaller pressure differentials, increasing sensitivity.
• Scale can be extended by decreasing the angle of the inclined leg.
• Double-well manometers involve two different fluids, used to measure small pressure differences.

Continuous Gravity Decanter

• Used for continuous separation of two immiscible liquids of differing densities.

Centrifugal Decanter

• Used to separate liquids with small density differences
• Gravity's force is too weak to separate these liquids.

Fields

• Quantity defined as a function of position and time throughout a region.

Lagrangian Description

• Focuses on fluid particles as they move, describes flow by recording the detailed histories of each fluid particle.

Eulerian Form

• Fluid particles are observed at every point in space, described by a field, and a probe is fixed in space.

Streamlines

• Lines drawn in a flow field that is tangent to the direction of the flow at a given instance.

Streaklines

• Line produced in a flow when all particles moving through a fixed point are marked in way.

Pathlines

• Relate to the flow over a certain fluid
• Similar to recording the path of the fluid element.

Viscosity

• Measures of a fluid’s resistance to flow under stress/ the resistance a fluid offers to another fluid

Reynolds Number

• Defined as the ratio of inertial force to viscous force.

Types of Flow Based on Dimensions

• One-dimensional flow: The velocity vector depends on one space variable.
• Two-dimensional flow: The velocity vector depends on only two space coordinates.
• Three-dimensional flow: The velocity vector depends on three space coordinates.

Developed Flows

• Velocity profile does not vary with respect to the space coordinate in the direction of flows.

Uniform Flow

• Velocity and other fluid properties are constant over the area.

Inviscid Flow

• Viscous effects are insignificant and can be neglected.

External vs. Internal Flow

• External flows exist exterior to bodies and internal flows/duct flow are completely bounded by solid surfaces.
• Flows around streamlined bodies like airfoils or hydrofoils are examples of external flow.

Viscous Flow

• Flow in which affects of viscosity are significant and cannot be ignored.

Laminar Flow

• Flow without no significant mixing of neighboring fluid is called: Laminar Flow.

Turbulent Flow

• Fluid motions vary irregularly
• Quantities like velocity and pressure show random variations with space and time coordinates

Incompressible Flow

• Density of each fluid particle remains relatively constant

Compressible Flow

• Flow influenced by density variations and compressibility effects.

Mach Number

• Defined as the ratio of flow velocity past a boundary to the local speed of sound.

Nature of Fluids

• Purely viscous fluids don't possess solid-like elastic behavior and doesn't reverse deformation after shear stress removal.
• Viscoelastic fluids exhibit elastic recovery from deformations during flow.

Fluid Dynamics

• Pseudoplastic/Shear thinning fluids decrease in apparent viscosity with increasing deformation rate.
• Dilatant/Shear thickening fluids increases the apparent viscosity with increasing deformation rate
• Bingham plastic/ideal plastics fluids behave like a solid until a minimum stress is exceeded, and then exhibits a linear relation between stress and the rate of deformation.

Conservation of Mass

• Mass in the universe is constant.

Flow Measurement

• Mass flow rate is the the amount of mass flowing through a cross section per unit time.
• Volume flow rate is the volume of fluid flowing through a cross section per unit time.
• The Bernoulli equation states that the sum of kinetic, potential, and flow (pressure) energies of a fluid particle is constant along a streamline during steady flow.

Pitot Probes (and Pitot-Static Probes)

• Widely used for flow rate measurement.
• Pitot Probe: Tube with a pressure tap at the stagnation point that measures stagnation pressure.
• Pitot-Static Probe: Has both stagnation pressure tap and static pressure taps that measures both stagnation and static pressures.
• Pitot Tubes: Used to measure the local velocity at a given point in the flow stream and not the average velocity in the pipe or conduit.`

Orifice Meter

• A standard sharp-edged orifice is an accurately machined plate between two flanges with a hole cut concentrically.

Venturi Meter

• Invented by Clemens Herschel and named after Giovanni Venturi.

Rotameters

• Considered a variable-area flowmeter, also called a float meter.

Pumps

• General term for any fluid machine that adds energy to a fluid, commonly called energy-absorbing devices.

Turbines

• Energy producing devices that Extract energy from the fluid and transfer this energy to some mechanical energy output.

Energy

• Transferred to and extracted from the fluid in pumps and turbines respectively, usually via a rotating shaft.

Turbomachine

• Term used for pumps and turbines where energy is supplied or extracted by rotating shaft.

Fluid Machine

• Used for pumps which use the up and down reciprocating motion of a plunger or piston replacing the rotating shaft.

Dynamic Machines

• Rotating blades supply/extract energy to/from fluid without a closed volume.

Brake Horsepower

• The external power supplied to the pump.

Fans

• Low-speed machines that generate very low pressures (~0.04 atm)
• Used when large gas volumes are moved, for example, air into open spaces/ducts.

Blowers

• Develop a maximum pressure of about 2 atm
• High speed rotary devices

Similarity Conditions

• Dynamic Similarity is achieved when all forces in the model flow scale by a constant factor to corresponding forces in the prototype flow.
• Geometric Similarity describes the the model must be the same shape as the prototype but may be scaled by some constant scale factor.
• Kinematic Similarity velocity at those points and in the model flow must be proportional by a constant factor

Suction and Discharge

• Suction Head: Exists when the source of supply is above the center line of the pump.
• Static Suction Head: Vertical distance from the center line of the pump to the level of the liquid
• Static Discharge Head and distance from the pumps center line to the discharge on the surface of the liquid in the discharge tank
• Total Static head
• Vertical distance or feet from the free level the source of supply down to the frees level of liquid being pumped.
• Suction Lift: Exists when the source of supply is below the center line of the pump
• Static Suction Lift: Vertical distance from center line to free level of the liquid.

Explanation of transport processes. Includes discussion of fluxes, tensors, molecular and turbulent transport. Also covers dimensional analysis, continuum mechanics and fluid mechanics.