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

Fluid Mechanics and Energy TransportFluid Mechanics and Energy TransportBIEN 301BIEN 301

Lecture 16Lecture 16Compressible Flows Continued – Friction in DuctsCompressible Flows Continued – Friction in Ducts

Juan M. Lopez, E.I.T.Juan M. Lopez, E.I.T.

Research ConsultantResearch ConsultantLeTourneau UniversityLeTourneau University

Adjunct LecturerAdjunct LecturerLouisiana Tech UniversityLouisiana Tech University

2/22/20072/22/2007 BIEN 301 – Winter 2006-2007BIEN 301 – Winter 2006-2007

Compressible Duct Flow with Compressible Duct Flow with FrictionFriction

Expanding on Nozzle Analysis Expanding on Nozzle Analysis (White 9.7)(White 9.7)

Basic AssumptionsBasic 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 Like a moody analysis but with very large changes in Kinetic Energy, Enthalpy, and pressure.Kinetic Energy, Enthalpy, and pressure.

Often called “Fanno Flow”Often called “Fanno Flow” AN IMPORTANT CLARIFICATION: For this chapter, * AN IMPORTANT CLARIFICATION: For this chapter, *

denotes a critical (sonic point) property.denotes a critical (sonic point) property.


Fanno FlowFanno Flow

From control volume analysis, we end up with the basic From control volume analysis, we end up with the basic relationship between mach number and flow:relationship between mach number and flow:

D

dxf

Ma

MakMak

Ma

dMa2

2

22

2

1

121

1

This is already a separated variables form of the equation, which we This is already a separated variables form of the equation, which we can integrate to obtain the following. (Tabulated in table B.3 in can integrate to obtain the following. (Tabulated in table B.3 in textbook):textbook):

2

2

2

2

12

1ln

2

11

Mak

Mak

k

k

Mak

Ma

D

fL



This relationship leads to a few simple This relationship leads to a few simple relationships shown as follows:relationships shown as follows:

PropertyProperty SubsonicSubsonic SupersonicSupersonic

pp DecreasesDecreases IncreasesIncreases

ρρ DecreasesDecreases IncreasesIncreases

VV IncreasesIncreases DecreasesDecreases

p p 00, , ρρ00 DecreasesDecreases DecreasesDecreases

TT DecreasesDecreases IncreasesIncreases

MaMa IncreasesIncreases DecreasesDecreases

EntropyEntropy IncreasesIncreases IncreasesIncreases



Entropy changes Entropy changes tend towards the tend towards the maximum entropy maximum entropy change at Ma = 1.change at Ma = 1.

Equations 9.66a-d Equations 9.66a-d are used to are used to calculate the ratios calculate the ratios between critical between critical throat pressures throat pressures and entrance or and entrance or reference reference pressures.pressures.

1121

2

0

0

0

0

22

2

21

2

2

21

22

1

121

12

1

1

121

12

11

kk

k

xMak

Map

p

Mak

k

a

a

T

T

k

Mak

MaV

V

Mak

k

Map

p


Choking FlowChoking Flow

An interesting propertyAn interesting property The theory presened thus far has one interesting The theory presened thus far has one interesting

consequence: no matter what inlet Ma, in an adiabatic consequence: no matter what inlet Ma, in an adiabatic flow the downstream flow shall ALWAYS trend flow the downstream flow shall ALWAYS trend towards Ma = 1.towards Ma = 1.

Are flows truly adiabatic?Are flows truly adiabatic?• No, but for many flow regime ranges this is a good No, but for many flow regime ranges this is a good

approximation.approximation.


Additional Fanno Flow Additional Fanno Flow PropertiesProperties

Minor Losses in Compressible FlowMinor Losses in Compressible Flow

Isothermal flow with friction: Long pipelinesIsothermal flow with friction: Long pipelines

Mass Flow for a given pressure drop in an adiabatic ideal gas:Mass Flow for a given pressure drop in an adiabatic ideal gas:

tcoefficien loss static ,

22

22

21

Vp

ppK s

point chokingat is ' where''

;1

'2

1

21 kMa

V

V

kMap

p

2

220

21

20

1

2

2

1

1

2

2

1

12

12

Vka

Vka

p

p

T

T

p

p

V

V


Adding Heat to the EquationAdding Heat to the Equation

This course is also energy transport. What This course is also energy transport. What happens when we add heat to our flow happens when we add heat to our flow problem?problem?

21

1

2

1

2

11

22

1

2

T

T

Ma

Ma

aMa

aMa

V

V

See equations 9.78a-e for the additional See equations 9.78a-e for the additional Ma number relationships.Ma number relationships.


Additional ItemsAdditional Items

Remember, we are skipping shock wavesRemember, we are skipping shock waves Read the choking flow due to heat example in the text Read the choking flow due to heat example in the text

(E9.15)(E9.15)


Chapter 9 HomeworkChapter 9 Homework

DUE 2/22/2007 - ReminderDUE 2/22/2007 - Reminder

P9.11P9.11P9.43P9.43P9.78P9.78P9.88P9.88

EC: P9.114EC: P9.114

Due with the Ch. 7 and Ch. 8 HW.Due with the Ch. 7 and Ch. 8 HW.


REVIEW FOR FINALREVIEW FOR FINAL

Final Exam on Tuesday, Feb. 27Final Exam on Tuesday, Feb. 27thth

Chapters 6, 7, 8, 9. Your write-ups on Ch. 5 Chapters 6, 7, 8, 9. Your write-ups on Ch. 5 will be all I need from that chapter.will be all I need from that chapter.

Same two-part format: closed book and open Same two-part format: closed book and open book.book.

NO DOCUMENTS OTHER THAN TEXBOOK NO DOCUMENTS OTHER THAN TEXBOOK ALLOWED FOR THIS EXAM. ALLOWED FOR THIS EXAM. • I am writing the exam to ensure this is all you will I am writing the exam to ensure this is all you will

need.need.



Additions to the format:Additions to the format: Closed Book PortionClosed Book Portion

• Mixture of True/False, Short Answer, Fill-In-The-Mixture of True/False, Short Answer, Fill-In-The-Blank, and Multiple ChoiceBlank, and Multiple Choice

Open Book PortionOpen Book Portion• Multiple ChoiceMultiple Choice

Showing work gets you partial credit even if you select Showing work gets you partial credit even if you select the wrong answer. the wrong answer.

Showing irrelevant work is the same as showing NO Showing irrelevant work is the same as showing NO work, so do work the stuff out. 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.



Concepts we will NOT be covering:Concepts we will NOT be covering: Ch. 6Ch. 6

• 6.5, Moody Charts, Details on flowmeters, 6.5, Moody Charts, Details on flowmeters, correction factors.correction factors.

Ch. 7Ch. 7• AirfoilsAirfoils



Concepts we will NOT be covering:Concepts we will NOT be covering: Ch. 8Ch. 8

• 8.3-8.78.3-8.7 Ch. 9Ch. 9

• 9.5, 9.9, 9.109.5, 9.9, 9.10



Will Probably be 10 or so questions on Will Probably be 10 or so questions on Part 1Part 1

2-3 Questions on Part 2.2-3 Questions on Part 2. You may show up at 7:30 am if you wish.You may show up at 7:30 am if you wish.

The exam will not be longer than the rest, but The exam will not be longer than the rest, but it is the final, so you may have some extra it is the final, so you may have some extra time to work on it if you feel you want to get time to work on it if you feel you want to get here earlier.here earlier.



I will only be handing back your final grade I will only be handing back your final grade via blackboard. If you want your exam, via blackboard. If you want your exam, you’ll have to get in touch with me next you’ll have to get in touch with me next quarter.quarter.


Questions?Questions?

Documents

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