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

Fluid Mechanics and Energy Transport BIEN 301 Lecture 16 Compressible Flows Continued – Friction in Ducts. Juan M. Lopez, E.I.T. Research Consultant LeTourneau University Adjunct Lecturer Louisiana Tech University. Compressible Duct Flow with Friction.

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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 16Compressible Flows Continued – Friction in Ducts Juan M. Lopez, E.I.T. Research Consultant LeTourneau University Adjunct Lecturer Louisiana Tech University

  2. Compressible Duct Flow with Friction • Expanding on Nozzle Analysis (White 9.7) • Basic Assumptions • Steady 1D adiabatic flow • Ideal Gas with constant Cp and Cv • Constant-area straight duct • Wall shear stress correlated with a Darcy friction factor. • Like a moody analysis but with very large changes in Kinetic Energy, Enthalpy, and pressure. • Often called “Fanno Flow” • AN IMPORTANT CLARIFICATION: For this chapter, * denotes a critical (sonic point) property. BIEN 301 – Winter 2006-2007

  3. Fanno Flow • From control volume analysis, we end up with the basic relationship between mach number and flow: • This is already a separated variables form of the equation, which we can integrate to obtain the following. (Tabulated in table B.3 in textbook): BIEN 301 – Winter 2006-2007

  4. This relationship leads to a few simple relationships shown as follows: Fanno Flow BIEN 301 – Winter 2006-2007

  5. Fanno Flow • Entropy changes tend towards the maximum entropy change at Ma = 1. • Equations 9.66a-d are used to calculate the ratios between critical throat pressures and entrance or reference pressures. BIEN 301 – Winter 2006-2007

  6. Choking Flow • An interesting property • The theory presened thus far has one interesting consequence: no matter what inlet Ma, in an adiabatic flow the downstream flow shall ALWAYS trend towards Ma = 1. • Are flows truly adiabatic? • No, but for many flow regime ranges this is a good approximation. BIEN 301 – Winter 2006-2007

  7. Additional Fanno Flow Properties • Minor Losses in Compressible Flow • Isothermal flow with friction: Long pipelines • Mass Flow for a given pressure drop in an adiabatic ideal gas: BIEN 301 – Winter 2006-2007

  8. Adding Heat to the Equation • This course is also energy transport. What happens when we add heat to our flow problem? • See equations 9.78a-e for the additional Ma number relationships. BIEN 301 – Winter 2006-2007

  9. Additional Items • Remember, we are skipping shock waves • Read the choking flow due to heat example in the text (E9.15) BIEN 301 – Winter 2006-2007

  10. Chapter 9 Homework • DUE 2/22/2007 - Reminder P9.11P9.43P9.78P9.88EC: P9.114Due with the Ch. 7 and Ch. 8 HW. BIEN 301 – Winter 2006-2007

  11. REVIEW FOR FINAL • Final Exam on Tuesday, Feb. 27th • Chapters 6, 7, 8, 9. Your write-ups on Ch. 5 will be all I need from that chapter. • Same two-part format: closed book and open book. • NO DOCUMENTS OTHER THAN TEXBOOK ALLOWED FOR THIS EXAM. • I am writing the exam to ensure this is all you will need. BIEN 301 – Winter 2006-2007

  12. REVIEW FOR FINAL • Additions to the format: • Closed Book Portion • Mixture of True/False, Short Answer, Fill-In-The-Blank, and Multiple Choice • Open Book Portion • Multiple Choice • Showing work gets you partial credit even if you select the wrong answer. • Showing irrelevant work is the same as showing NO work, so do work the stuff out. • Guessing will NOT help you. You will get a zero. BIEN 301 – Winter 2006-2007

  13. REVIEW FOR FINAL • Concepts we will NOT be covering: • Ch. 6 • 6.5, Moody Charts, Details on flowmeters, correction factors. • Ch. 7 • Airfoils BIEN 301 – Winter 2006-2007

  14. REVIEW FOR FINAL • Concepts we will NOT be covering: • Ch. 8 • 8.3-8.7 • Ch. 9 • 9.5, 9.9, 9.10 BIEN 301 – Winter 2006-2007

  15. REVIEW FOR FINAL • Will Probably be 10 or so questions on Part 1 • 2-3 Questions on Part 2. • You may show up at 7:30 am if you wish. • The exam will not be longer than the rest, but it is the final, so you may have some extra time to work on it if you feel you want to get here earlier. BIEN 301 – Winter 2006-2007

  16. REVIEW FOR FINAL • I will only be handing back your final grade via blackboard. If you want your exam, you’ll have to get in touch with me next quarter. BIEN 301 – Winter 2006-2007

  17. Questions? BIEN 301 – Winter 2006-2007

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