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

2/22/2007BIEN 301 – Winter Compressible Duct Flow with Friction  Expanding on Nozzle Analysis (White 9.7) Basic Assumptions Basic Assumptions Steady 1D adiabatic flowSteady 1D adiabatic flow Ideal Gas with constant Cp and CvIdeal Gas with constant Cp and Cv Constant-area straight ductConstant-area straight duct Wall shear stress correlated with a Darcy friction factor.Wall shear stress correlated with a Darcy friction factor. Like a moody analysis but with very large changes in Kinetic Energy, Enthalpy, and pressure. Like a moody analysis but with very large changes in Kinetic Energy, Enthalpy, and pressure. Often called “Fanno Flow” Often called “Fanno Flow” AN IMPORTANT CLARIFICATION: For this chapter, * denotes a critical (sonic point) property. AN IMPORTANT CLARIFICATION: For this chapter, * denotes a critical (sonic point) property.

2/22/2007BIEN 301 – Winter 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):

2/22/2007BIEN 301 – Winter Fanno Flow  This relationship leads to a few simple relationships shown as follows: PropertySubsonicSupersonic pDecreasesIncreases ρDecreasesIncreases VIncreasesDecreases p 0, ρ 0 DecreasesDecreases TDecreasesIncreases MaIncreasesDecreases EntropyIncreasesIncreases

2/22/2007BIEN 301 – Winter 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.

2/22/2007BIEN 301 – Winter 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. 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? Are flows truly adiabatic? No, but for many flow regime ranges this is a good approximation.No, but for many flow regime ranges this is a good approximation.

2/22/2007BIEN 301 – Winter 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:

2/22/2007BIEN 301 – Winter 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.

2/22/2007BIEN 301 – Winter Additional Items  Remember, we are skipping shock waves  Read the choking flow due to heat example in the text (E9.15)

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

2/22/2007BIEN 301 – Winter REVIEW FOR FINAL  Final Exam on Tuesday, Feb. 27 th Chapters 6, 7, 8, 9. Your write-ups on Ch. 5 will be all I need from that chapter. 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. Same two-part format: closed book and open book. NO DOCUMENTS OTHER THAN TEXBOOK ALLOWED FOR THIS EXAM. NO DOCUMENTS OTHER THAN TEXBOOK ALLOWED FOR THIS EXAM. I am writing the exam to ensure this is all you will need.I am writing the exam to ensure this is all you will need.

2/22/2007BIEN 301 – Winter REVIEW FOR FINAL  Additions to the format: Closed Book Portion Closed Book Portion Mixture of True/False, Short Answer, Fill-In-The- Blank, and Multiple ChoiceMixture of True/False, Short Answer, Fill-In-The- Blank, and Multiple Choice Open Book Portion Open Book Portion Multiple ChoiceMultiple Choice Showing work gets you partial credit even if you select the wrong answer. 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. 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. Guessing will NOT help you. You will get a zero.

2/22/2007BIEN 301 – Winter REVIEW FOR FINAL  Concepts we will NOT be covering: Ch. 6 Ch , Moody Charts, Details on flowmeters, correction factors.6.5, Moody Charts, Details on flowmeters, correction factors. Ch. 7 Ch. 7 AirfoilsAirfoils

2/22/2007BIEN 301 – Winter REVIEW FOR FINAL  Concepts we will NOT be covering: Ch. 8 Ch Ch. 9 Ch , 9.9, , 9.9, 9.10

2/22/2007BIEN 301 – Winter 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. 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.

2/22/2007BIEN 301 – Winter 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.

2/22/2007BIEN 301 – Winter Questions?