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Juan M. Lopez, E.I.T. Research Consultant LeTourneau University Adjunct Lecturer

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 LeTourneau University Adjunct Lecturer Louisiana Tech University. History of Fluid Mechanics.

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Juan M. Lopez, E.I.T. Research Consultant LeTourneau University Adjunct Lecturer

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  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 (200’s B.C.) and Buoyancy / Vector addition – Theoretical work with Experimental roots • 200’s 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. BIEN 301 – Winter 2006-2007

  3. History of Fluid Mechanics • Mariotte (1600’s) built the first wind tunnel – Testing theoretical ideas with experimental work. • Isaac Newton (1600’s-1700’s) generated the mathematics which allowed fluid momentum to be studied. • Bernoulli, D’Alembert, 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. BIEN 301 – Winter 2006-2007

  4. History of Fluid Mechanics • Late 1800’s, 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 1800’s, setting the stage for Prandtl. • In the early 1900’s, 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. BIEN 301 – Winter 2006-2007

  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. BIEN 301 – Winter 2006-2007

  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. BIEN 301 – Winter 2006-2007

  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. BIEN 301 – Winter 2006-2007

  8. What is a Fluid? • Mechanical Description – Mohr’s Circle BIEN 301 – Winter 2006-2007

  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 BIEN 301 – Winter 2006-2007

  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, {Θ} BIEN 301 – Winter 2006-2007

  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. BIEN 301 – Winter 2006-2007

  12. Dimensions vs. Units • Using the tables, perform the following conversion: BIEN 301 – Winter 2006-2007

  13. Dimensions vs. Units BIEN 301 – Winter 2006-2007

  14. Dimensional Consistency • Dimensional Homogeneity (White 1.4) • Theoretical Equations – dimensionally homogeneous BIEN 301 – Winter 2006-2007

  15. Dimensional Consistency • However, much work in fluid mechanics has been empirical, and this can lead to problematic situations. BIEN 301 – Winter 2006-2007

  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. BIEN 301 – Winter 2006-2007

  17. Uncertainty • RMS Formulation: BIEN 301 – Winter 2006-2007

  18. Uncertainty • RMS Example BIEN 301 – Winter 2006-2007

  19. Basic Physical Properties • Thermodynamics (White 1.6) • Principal components of velocity vectors • Pressure, p • Density, ρ • Temperature, T • Principal components of work, heat, and energy balance. • Internal Energy, û • Enthalpy, h = û + ρ/p • Principal transport properties • Viscosity, μ • Thermal Conductivity, k • Together, these define the state of the fluid. BIEN 301 – Winter 2006-2007

  20. Basic Physical Properties • Additional Properties (White 1.6) • Specific Weight, γ = ρg • Specific Gravity • SGgas = ρgas / ρair • SGwater = ρliquid / ρwater • Potential Energy • -g●r • Kinetic Energy • 0.5 V2 • Total Energy • e = û + 0.5 V2 + (-g●r) BIEN 301 – Winter 2006-2007

  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 = ρRT where R = cp – cv(gas constant) • The gas constant is related to the universal gas constant, Λ by the following equation: • Λ = Rgas * Mgas BIEN 301 – Winter 2006-2007

  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. BIEN 301 – Winter 2006-2007

  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. BIEN 301 – Winter 2006-2007

  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: BIEN 301 – Winter 2006-2007

  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: BIEN 301 – Winter 2006-2007

  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 δ() /δz. BIEN 301 – Winter 2006-2007

  27. Velocity Fields BIEN 301 – Winter 2006-2007

  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. BIEN 301 – Winter 2006-2007

  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. BIEN 301 – Winter 2006-2007

  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. BIEN 301 – Winter 2006-2007

  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. BIEN 301 – Winter 2006-2007

  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 BIEN 301 – Winter 2006-2007

  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. BIEN 301 – Winter 2006-2007

  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 we’ll 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? BIEN 301 – Winter 2006-2007

  35. Assignment • HW 2 has been posted on blackboard • Project Proposals due soon! • Individual project sign-ups will be available by tonight on blackboard. BIEN 301 – Winter 2006-2007

  36. Questions? BIEN 301 – Winter 2006-2007

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