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Fluid Mechanics and Energy Transport BIEN 301 Lecture 2 Introduction to Fluids, Flow Fields, and Dimensional Analysis

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Fluid Mechanics and Energy Transport BIEN 301 Lecture 2 Introduction to Fluids, Flow Fields, and Dimensional Analysis Juan M. Lopez, E.I.T. Research Consultant – PowerPoint PPT presentation

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Title: Fluid Mechanics and Energy Transport BIEN 301 Lecture 2 Introduction to Fluids, Flow Fields, and Dimensional Analysis


1
Fluid Mechanics and Energy TransportBIEN
301Lecture 2 Introduction to Fluids, Flow
Fields, and Dimensional Analysis
  • Juan M. Lopez, E.I.T.
  • Research Consultant
  • LeTourneau University
  • Adjunct Lecturer
  • Louisiana Tech University

2
History of Fluid Mechanics
  • White 1.14 shows us how Fluid Mechanics has
    evolved in a helical fashion, returning to its
    roots, with improvements each time.
  • Pre-historic and early history aqueducts and
    waterworks Empirically Designed and Built
  • Archimedes (200s B.C.) and Buoyancy / Vector
    addition Theoretical work with Experimental
    roots
  • 200s B.C. to Renaissance ship and canal building
    Empirical advances, no great amount of
    experimental work
  • Leonardo da Vinci first formulated the
    one-dimensional conservation of mass equation
    Theoretical stemming from empirical observations.

3
History of Fluid Mechanics
  • Mariotte (1600s) built the first wind tunnel
    Testing theoretical ideas with experimental work.
  • Isaac Newton (1600s-1700s) generated the
    mathematics which allowed fluid momentum to be
    studied.
  • Bernoulli, DAlembert, Euler, Lagrange, Laplace,
    all developed their work in frictionless fluids,
    and showed the need for a formulation that would
    do away with the paradox of an object with no
    drag immersed in a moving stream, a natural
    result of frictionless fluid assumptions
    Theoretical advances mostly.
  • These theoretical results were unsatisfactory to
    engineers, so as a natural backlash, hydraulics
    was developed as an almost purely experimental
    form by Pitot, Borda, Poiseuille, etc.

4
History of Fluid Mechanics
  • Late 1800s, finally there was a trend towards
    the unification between experimental hydraulics
    and theoretical hydrodynamics by the likes of
    Froude, Raylegh, and Reynolds. All of these
    gentlemen have dimensionless groups named after
    them due to the importance of their work.
  • Navier and Stokes began to more fully explore
    viscous flow in the mid to late 1800s, setting
    the stage for Prandtl.
  • In the early 1900s, Prandtl developed boundary
    layer theory, one of the most important advances
    in fluid mechanics, identified by White as the
    single most important tool in modern flow
    analysis.

5
History of Fluid Mechanics
  • The past tied to the present
  • These past examples of development in fluid
    mechanics remain important due to the individual
    contributions each advance has made to our
    current understanding.
  • In fact, we continue to study many of these
    individual ideas as simplified examples of fluid
    behavior.
  • Fluid mechanics encompasses almost every field of
    physical systems, and a basic understanding of
    the mathematics, terminology, and usage will
    greatly benefit you in any engineering field.

6
What is a Fluid?
  • Matter that is unable to resist shear by a static
    deflection. (White, 1.2)
  • Fluid will deflect under shear unless opposed by
    some external force. The rate of strain to stress
    is dependent on the viscosity of the fluid.

7
What is a Fluid?
  • This lack of resistance to shear explains why
    fluid take the shape of their containers, or
    spill when there is no body to contain them.

8
What is a Fluid?
  • Mechanical Description Mohrs Circle

9
What is a Fluid?
  • As with everything, we make some assumptions in
    our definition-
  • Continuum (White 1.3)
  • Infinitely Divisible All divisions have same
    properties in homogeneous fluid
  • For real systems, there are uncertainties brought
    about by volumes that are too small or too large.
  • Physical properties are defined and have finite
    values throughout the continuum
  • Thermal properties are defined and have finite
    values throughout the continuum

10
Dimensions vs. Units
  • We must inherently have a way to describe the
    systems we are studying. We describe these
    systems with Dimensions and quantify these
    dimensions with Units.
  • Four primary Dimensions in our study of Fluid
    Mechanics
  • Mass, M
  • Length, L
  • Time, T
  • Temperature, T

11
Dimensions vs. Units
  • It is imperative that you learn consistency in
    your dimensional analysis. Fluid mechanics lends
    itself to some extremely awkward units,
    especially in the British system.
  • For this course, we will primarily stick with the
    International System (SI), but we will refresh
    our memories from time to time on how to interact
    with the British Gravitational (BG) units.
  • The use of tables is an inherent task in
    engineering work. Become familiar with the tables
    such as White, Table 1.1, 1.2, and Appendix
    Tables A.1-A.6, and how to properly use them.

12
Dimensions vs. Units
  • Using the tables, perform the following
    conversion

13
Dimensions vs. Units
14
Dimensional Consistency
  • Dimensional Homogeneity (White 1.4)
  • Theoretical Equations dimensionally homogeneous

15
Dimensional Consistency
  • However, much work in fluid mechanics has been
    empirical, and this can lead to problematic
    situations.

16
Uncertainty
  • Once we have established a way to describe these
    systems, we must also account for the uncertainty
    in our experimentation. (White 1.11)
  • Instruments and all physical measurements have
    some form of uncertainty.
  • Accounting for all the measurements is important
  • Adding them all is simply not realistic
  • A simplified Root Mean Square (RMS) approach is
    recommended.

17
Uncertainty
  • RMS Formulation

18
Uncertainty
  • RMS Example

19
Basic Physical Properties
  • Thermodynamics (White 1.6)
  • Principal components of velocity vectors
  • Pressure, p
  • Density, ?
  • Temperature, T
  • Principal components of work, heat, and energy
    balance.
  • Internal Energy, û
  • Enthalpy, h û ?/p
  • Principal transport properties
  • Viscosity, µ
  • Thermal Conductivity, k
  • Together, these define the state of the fluid.

20
Basic Physical Properties
  • Additional Properties (White 1.6)
  • Specific Weight, ? ?g
  • Specific Gravity
  • SGgas ?gas / ?air
  • SGwater ?liquid / ?water
  • Potential Energy
  • -g?r
  • Kinetic Energy
  • 0.5 V2
  • Total Energy
  • e û 0.5 V2 (-g?r)

21
State Relationships
  • State Relationships for Gases (White 1.6)
  • Thermodynamic properties are related to each
    other by state relationships. For gases, there is
    the ideal gas law (perfect-gas law).
  • p ?RT where R cp cv (gas constant)
  • The gas constant is related to the universal gas
    constant, ? by the following equation
  • ? Rgas Mgas

22
State Relationships
  • State Relationships for Liquids
  • No direct analog of the ideal gas law exists for
    liquids.
  • Why? If fluids involves liquids and gases, why
    can we not get a direct correlation to a liquid
    form?
  • Compressibility. The ideal gas law assumes
    compressibility, whereas most liquids are mostly
    incompressible.

23
State Relationships
  • State Relationships for Liquids
  • As an example of this lack of direct
    relationship, see from White, eq. 1.19
  • Where B and n are dimensionless parameters that
    vary with temperature.

24
Velocity Fields
  • For many of the problems encountered here, the
    velocity field will be the solution to our given
    problem, or an integral part thereof. (White 1.5)
  • The three-dimensional velocity field can be
    expressed in a variety of ways

25
Velocity Fields
  • Simplified problems in White, example 1.5, we
    see the convective result for a 1-Dimensional
    problem. The extended answer for the 3D problem
    is as follows

26
Velocity Fields
  • Dealing with partial differential equations.
  • Cross out terms ahead of time, simplifies
    calculations.
  • For the 2D problem, there are no velocity
    components in the Z direction (no w magnitude,
    and no d() /dz.

27
Velocity Fields
28
Application
  • So, what can we do with all of this stuff? Why
    re-hash over so many of the basics we have seen
    in other courses over the years?
  • While we may have been exposed to all of these
    concepts, they become integral in the study of
    fluid mechanics.
  • Familiarity with these ideas is no longer enough,
    we must master these concepts and learn to apply
    them in new and effective ways.

29
Application
  • With these basics we will be able to
  • Fully describe and define the subject of our
    study Fluids.
  • Perform dimensionally consistent calculations,
    increasing the skill set required of a modern
    professional engineer.
  • Be conversant and capable in both the BG and the
    SI system, able to convert between the two as the
    problem requires.

30
Application
  • With these basics we will be able to
  • Understand the basic thermodynamic concepts
    required to extend our analysis from pure fluid
    mechanics to true energy transport problems.
  • Heat Transfer
  • Temperature-dependent effects
  • Accurately and professionally report our
    findings, accounting for our experimental error
    and/or uncertainty.

31
Application
  • As was mentioned before these skills, though
    ideally common throughout all of our engineering
    courses, become absolute cornerstones of success
    for a subject as complex and difficult as fluid
    mechanics.

32
Fundamental Approaches
  • There are two primary approaches to problem
    solving in fluid mechanics
  • Lagrangian and Eulerian
  • Lagrangian follows a fluid particle as it moves
    through a flow field.
  • Eulerian Observes passing fluid particles from a
    stationary position relative to the flow field

33
Fundamental Approaches
  • Examples
  • Lagrangian
  • A user observes traffic on the freeway as he sits
    in his vehicle, travelling down the freeway along
    with the traffic. Traffic jams, velocity changes,
    etc, are all marked and observed to attempt to
    describe the flow of traffic through a section of
    freeway.
  • Eulerian
  • A state trooper monitors freeway traffic from a
    hidden location under the bridge, monitoring for
    changes in traffic that could indicate potential
    trouble. Multiple state troopers and cameras
    along the road give a big picture perspective
    to traffic managers.

34
Fundamental Approaches
  • Eulerian will be our fundamental approach for
    this course.
  • Probes at different points in the fluid stream
    are much more easy to design and monitor for
    smaller systems that well concern ourselves with
    than large instrumentation designs that follow
    the flow.
  • Can you think of an example of Eulerian
    monitoring and/or Lagrangian monitoring in
    biomedical systems? What are some potential
    benefits of each type of system relative to this
    application?

35
Assignment
  • HW 2 has been posted on blackboard
  • Project Proposals due soon!
  • Individual project sign-ups will be available by
    tonight on blackboard.

36
Questions?
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