Fluid Mechanics and Energy Transport BIEN 301 Lecture

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

Compressible Duct Flow with Friction Ø Expanding on Nozzle Analysis (White 9. 7) l Basic Assumptions • • l l l Steady 1 D 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. 2/22/2007 BIEN 301 – Winter 2006 -2007

Fanno Flow Ø From control volume analysis, we end up with the basic relationship between mach number and flow: Ø 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): 2/22/2007 BIEN 301 – Winter 2006 -2007

Fanno Flow Ø This relationship leads to a few simple relationships shown as follows: Property p ρ V p 0, ρ 0 T Ma Entropy 2/22/2007 Subsonic Supersonic Decreases Increases Decreases Increases Decreases Increases BIEN 301 – Winter 2006 -2007

Fanno Flow Entropy changes tend towards the maximum entropy change at Ma = 1. Ø Equations 9. 66 a-d are used to calculate the ratios between critical throat pressures and entrance or reference pressures. Ø 2/22/2007 BIEN 301 – Winter 2006 -2007

Choking Flow Ø An interesting property l l 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. 2/22/2007 BIEN 301 – Winter 2006 -2007

Additional Fanno Flow Properties Ø Minor Losses in Compressible Flow Ø Isothermal flow with friction: Long pipelines Ø Mass Flow for a given pressure drop in an adiabatic ideal gas: 2/22/2007 BIEN 301 – Winter 2006 -2007

Adding Heat to the Equation Ø This course is also energy transport. What happens when we add heat to our flow problem? Ø See equations 9. 78 a-e for the additional Ma number relationships. 2/22/2007 BIEN 301 – Winter 2006 -2007

Additional Items Ø Remember, we are skipping shock waves Ø Read the choking flow due to heat example in the text (E 9. 15) 2/22/2007 BIEN 301 – Winter 2006 -2007

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

REVIEW FOR FINAL Ø Final Exam on Tuesday, Feb. 27 th l l l 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. 2/22/2007 BIEN 301 – Winter 2006 -2007

REVIEW FOR FINAL Ø Additions to the format: l Closed Book Portion • Mixture of True/False, Short Answer, Fill-In-The. Blank, and Multiple Choice l Open Book Portion • Multiple Choice l l l 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. 2/22/2007 BIEN 301 – Winter 2006 -2007

REVIEW FOR FINAL Ø Concepts we will NOT be covering: l Ch. 6 • 6. 5, Moody Charts, Details on flowmeters, correction factors. l Ch. 7 • Airfoils 2/22/2007 BIEN 301 – Winter 2006 -2007

REVIEW FOR FINAL Ø Concepts we will NOT be covering: l Ch. 8 • 8. 3 -8. 7 l Ch. 9 • 9. 5, 9. 9, 9. 10 2/22/2007 BIEN 301 – Winter 2006 -2007

REVIEW FOR FINAL Ø Will Probably be 10 or so questions on Part 1 Ø 2 -3 Questions on Part 2. Ø You may show up at 7: 30 am if you wish. l 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. 2/22/2007 BIEN 301 – Winter 2006 -2007

REVIEW FOR FINAL Ø 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. 2/22/2007 BIEN 301 – Winter 2006 -2007

Questions? 2/22/2007 BIEN 301 – Winter 2006 -2007