Steady, 1-d, constant area, adiabatic flow with no external work but with friction Conserved quantities

Size: px
Start display at page:

Download "Steady, 1-d, constant area, adiabatic flow with no external work but with friction Conserved quantities"

Transcription

1 School of Aerosace Engineering Stead, -d, constant area, adiabatic flow with no external work but with friction Conserved quantities since adiabatic, no work: h o constant since Aconst: mass fluxρvconstant G combining: h o hg /ρ constant On h-s diagram, can draw Fanno ine line connecting oints with same h o and ρv ρ v τ x, f? As ou change h, ou change ρ (and v) since G and h o const. Fanno Flow - Coright b Jerr. Seitzman. All rights reserved.

2 School of Aerosace Engineering Velocit change (due to friction) associated with entro change Friction can onl increase entro can onl aroach friction alone can not allow flow to transition between sub/suersonic h v0 h < o (ρv) v > s (ρv) wo solutions given (ρv,h o,s): subsonic & suersonic change mass flux: new Fanno line s Fanno Flow - Coright b Jerr. Seitzman. All rights reserved.

3 School of Aerosace Engineering otal friction exerienced b flow increases with length of flow, e.g., h < duct length, h o For long enough duct, e ( ) (ρv) What haens if > flow alread choked > subsonic flow: must move to different Fanno line ( ), i.e., lower mass flux suersonic flow: get a shock ( ) Fanno Flow -3 Coright b Jerr. Seitzman. All rights reserved. s e

4 School of Aerosace Engineering Simlif (X.4-5) for δqda0 d d Fanno Flow -4 Coright b Jerr. Seitzman. All rights reserved. [ ( ) ] fdx ( ) can write each as onl f() o loss due to entro rise fdx (X.6) (X.7) d ds R dρ ρ dh h d o o dv v ( ) dx ( ) fdx 4 f fdx ( ) (X.8) (X.9) (X.0)

5 School of Aerosace Engineering ook at signs of revious equations to see how roerties changed b friction as we move along flow (- ) term makes < different than > s o h, ρ v < > Friction increases s, o dro Friction drives h o, o const: h, oosite to, ρ same as (like isen. flow) ρvconst: v oosite of ρ Fanno Flow -5 Coright b Jerr. Seitzman. All rights reserved.

6 School of Aerosace Engineering Need to integrate (X.6-0) to find how roerties change along length of flow ( fdx/ ) Fanno Flow -6 for examle, need to integrate Searate terms x x f ( ) x d f ( Re, surface ) 4 d ( Re, surface ) dx f ( x x ) Coright b Jerr. Seitzman. All rights reserved. x fdx f dx x x f function of Renolds number (e.g.,velocit) and surface roughness for simlicit, can aroximate f b average value

7 Fanno Flow -7 School of Aerosace Engineering Coright b Jerr. Seitzman. All rights reserved. o erform integral, redefine variables ( ) ( ) 4 d d x x d d ln ln ln

8 School of Aerosace Engineering Combine results into exression for change caused b friction f ln For examle, given f / and x x (X.) could solve X. for Can t invert X. analticall - can t write f(, f /) either use iterative (e.g., numerical or guessing) method or find f / as a function of and tabularize solution Fanno Flow -8 Coright b Jerr. Seitzman. All rights reserved.

9 School of Aerosace Engineering o get change in, use as reference condition (like Prandtl-eer and A/A* table solutions) f f (X.) f f ln f Find values in Aendix E in John,, is reference so if ou know f / and, ) look u f / at ) calculate f / at 3) look u corresonding Fanno Flow -9 Coright b Jerr. Seitzman. All rights reserved.

10 Fanno Flow -0 School of Aerosace Engineering Coright b Jerr. Seitzman. All rights reserved. o get changes in,, o,... can again use condition as reference condition (denoted as *) Integrate (X.7-0), e.g., ( ) * d d,, o,, *,, o

11 Fanno Flow - School of Aerosace Engineering Coright b Jerr. Seitzman. All rights reserved. Summarize results in terms of reference conditions OR in terms of initial and final roerties ( ) * (X.3) * * * v v ρ ρ (X.5) * * (X.4) ( ) * * o o (X.5) (X.7) ( o const) v v ρ ρ (X.0) ( ) o o (X.8) (X.9)

12 School of Aerosace Engineering Given: Exit of suersonic nozzle connected to straight walled test section. est section flows N at test 3.0, o 90. K, o 500. kpa, m, 0 cm, f0.005 test Find: -,, at end of test section - o,exit / o,inlet - for test section Assume: N is tg/cg,.4, stead, adiabatic, no work Fanno Flow - Coright b Jerr. Seitzman. All rights reserved.

13 School of Aerosace Engineering Analsis: e f (X.) e f f 3.0 f 0.005(00) e. (Aendix E) 70 ( o const) e 0.47 test another solution is 0.605, but since started >, can t be subsonic o 8K e Fanno Flow -3 Coright b Jerr. Seitzman. All rights reserved.

14 School of Aerosace Engineering (X.9) (X.7) 500 kpa 3.6kPa kPa.4 6.kPa.7 o,e / o,test o ( ) o o.7 (( ) ) (( ) ) (.4) test.4 5% loss in stagnation ressure due to friction e Fanno Flow -4 Coright b Jerr. Seitzman. All rights reserved.

15 School of Aerosace Engineering f m test 0.m f test 0 m long section would have at exit e Fanno Flow -5 Coright b Jerr. Seitzman. All rights reserved.

16 School of Aerosace Engineering ast roblem (suersonic duct), what would haen if calculated exit ressure ( e,f ) did not match actual back ressure ( b ) b < e,f : exansion outside duct (underexanded) e,f < b < e,sh : oblique shocks outside duct (overexanded) / o */ o shock inside shock at exit e,sh < b : shocks inside duct (until shock reaches ~throat) o test e e O U e,f x b e,sh Fanno Flow -6 Coright b Jerr. Seitzman. All rights reserved.

17 School of Aerosace Engineering Fanno Flow -7 Coright b Jerr. Seitzman. All rights reserved. Can t have flow transition to subsonic with ure Fanno flow shock in duct Shock location fixed b back ressure low enough b, e raise b, shock moves ustream until it reaches sonic location in nozzle / o b */ o o test e e e e b e x x

SPC 407 Sheet 6 - Solution Compressible Flow Fanno Flow

SPC 407 Sheet 6 - Solution Compressible Flow Fanno Flow SPC 407 Sheet 6 - Solution Comressible Flow Fanno Flow 1. What is the effect of friction on flow velocity in subsonic and suersonic Fanno flow? Friction increases the flow velocity in subsonic Fanno flow,

More information

Fanno Flow. Gas Dynamics

Fanno Flow. Gas Dynamics Fanno Flow Simple frictional flow ( Fanno Flow Adiabatic frictional flow in a constant-area duct * he Flow of a compressible fluid in a duct is Always accompanied by :- ariation in the cross sectional

More information

Introduction to Fluid Mechanics. Chapter 13 Compressible Flow. Fox, Pritchard, & McDonald

Introduction to Fluid Mechanics. Chapter 13 Compressible Flow. Fox, Pritchard, & McDonald Introduction to Fluid Mechanics Chapter 13 Compressible Flow Main Topics Basic Equations for One-Dimensional Compressible Flow Isentropic Flow of an Ideal Gas Area Variation Flow in a Constant Area Duct

More information

High speed wind tunnels 2.0 Definition of high speed. 2.1 Types of high speed wind tunnels

High speed wind tunnels 2.0 Definition of high speed. 2.1 Types of high speed wind tunnels Module Lectures 6 to 1 High Seed Wind Tunnels Keywords: Blow down wind tunnels, Indraft wind tunnels, suersonic wind tunnels, c-d nozzles, second throat diffuser, shocks, condensation in wind tunnels,

More information

2013/5/22. ( + ) ( ) = = momentum outflow rate. ( x) FPressure. 9.3 Nozzles. δ q= heat added into the fluid per unit mass

2013/5/22. ( + ) ( ) = = momentum outflow rate. ( x) FPressure. 9.3 Nozzles. δ q= heat added into the fluid per unit mass 9.3 Nozzles (b) omentum conservation : (i) Governing Equations Consider: nonadiabatic ternal (body) force ists variable flow area continuously varying flows δq f ternal force per unit volume +d δffdx dx

More information

Compressible Flow Introduction. Afshin J. Ghajar

Compressible Flow Introduction. Afshin J. Ghajar 36 Comressible Flow Afshin J. Ghajar Oklahoma State University 36. Introduction...36-36. he Mach Number and Flow Regimes...36-36.3 Ideal Gas Relations...36-36.4 Isentroic Flow Relations...36-4 36.5 Stagnation

More information

a) Derive general expressions for the stream function Ψ and the velocity potential function φ for the combined flow. [12 Marks]

a) Derive general expressions for the stream function Ψ and the velocity potential function φ for the combined flow. [12 Marks] Question 1 A horizontal irrotational flow system results from the combination of a free vortex, rotating anticlockwise, of strength K=πv θ r, located with its centre at the origin, with a uniform flow

More information

IX. COMPRESSIBLE FLOW. ρ = P

IX. COMPRESSIBLE FLOW. ρ = P IX. COMPRESSIBLE FLOW Compressible flow is the study of fluids flowing at speeds comparable to the local speed of sound. This occurs when fluid speeds are about 30% or more of the local acoustic velocity.

More information

Applied Gas Dynamics Flow With Friction and Heat Transfer

Applied Gas Dynamics Flow With Friction and Heat Transfer Applied Gas Dynamics Flow With Friction and Heat Transfer Ethirajan Rathakrishnan Applied Gas Dynamics, John Wiley & Sons (Asia) Pte Ltd c 2010 Ethirajan Rathakrishnan 1 / 121 Introduction So far, we have

More information

Compressible Duct Flow with Friction

Compressible Duct Flow with Friction Compressible Duct Flow with Friction We treat only the effect of friction, neglecting area change and heat transfer. The basic assumptions are 1. Steady one-dimensional adiabatic flow 2. Perfect gas with

More information

1. For an ideal gas, internal energy is considered to be a function of only. YOUR ANSWER: Temperature

1. For an ideal gas, internal energy is considered to be a function of only. YOUR ANSWER: Temperature CHAPTER 11 1. For an ideal gas, internal energy is considered to be a function of only. YOUR ANSWER: Temperature 2.In Equation 11.7 the subscript p on the partial derivative refers to differentiation at

More information

Module 4 : Lecture 1 COMPRESSIBLE FLOWS (Fundamental Aspects: Part - I)

Module 4 : Lecture 1 COMPRESSIBLE FLOWS (Fundamental Aspects: Part - I) Module 4 : Lecture COMPRESSIBLE FLOWS (Fundamental Asects: Part - I) Overview In general, the liquids and gases are the states of a matter that comes under the same category as fluids. The incomressible

More information

6.1 According to Handbook of Chemistry and Physics the composition of air is

6.1 According to Handbook of Chemistry and Physics the composition of air is 6. Compressible flow 6.1 According to Handbook of Chemistry and Physics the composition of air is From this, compute the gas constant R for air. 6. The figure shows a, Pitot-static tube used for velocity

More information

Fundamentals of Gas Dynamics (NOC16 - ME05) Assignment - 10 : Solutions

Fundamentals of Gas Dynamics (NOC16 - ME05) Assignment - 10 : Solutions Fundamentals of Gas Dynamics (NOC16 - ME05) Assignment - 10 : Solutions Manjul Sharma & Aswathy Nair K. Department of Aerospace Engineering IIT Madras April 18, 016 (Note : The solutions discussed below

More information

In which of the following scenarios is applying the following form of Bernoulli s equation: steady, inviscid, uniform stream of water. Ma = 0.

In which of the following scenarios is applying the following form of Bernoulli s equation: steady, inviscid, uniform stream of water. Ma = 0. bernoulli_11 In which of the following scenarios is applying the following form of Bernoulli s equation: p V z constant! g + g + = from point 1 to point valid? a. 1 stagnant column of water steady, inviscid,

More information

Chapter 10: Flow Flow in in Conduits Conduits Dr Ali Jawarneh

Chapter 10: Flow Flow in in Conduits Conduits Dr Ali Jawarneh Chater 10: Flow in Conduits By Dr Ali Jawarneh Hashemite University 1 Outline In this chater we will: Analyse the shear stress distribution across a ie section. Discuss and analyse the case of laminar

More information

AE301 Aerodynamics I UNIT A: Fundamental Concepts

AE301 Aerodynamics I UNIT A: Fundamental Concepts AE301 Aerodynamics I UNIT A: Fundamental Concets ROAD MAP... A-1: Engineering Fundamentals Reiew A-: Standard Atmoshere A-3: Goerning Equations of Aerodynamics A-4: Airseed Measurements A-5: Aerodynamic

More information

1. (20 pts total 2pts each) - Circle the most correct answer for the following questions.

1. (20 pts total 2pts each) - Circle the most correct answer for the following questions. ME 50 Gas Dynamics Spring 009 Final Exam NME:. (0 pts total pts each) - Circle the most correct answer for the following questions. i. normal shock propagated into still air travels with a speed (a) equal

More information

Please welcome for any correction or misprint in the entire manuscript and your valuable suggestions kindly mail us

Please welcome for any correction or misprint in the entire manuscript and your valuable suggestions kindly mail us Problems of Practices Of Fluid Mechanics Compressible Fluid Flow Prepared By Brij Bhooshan Asst. Professor B. S. A. College of Engg. And Technology Mathura, Uttar Pradesh, (India) Supported By: Purvi Bhooshan

More information

Introduction to Chemical Engineering Thermodynamics. Chapter 7. KFUPM Housam Binous CHE 303

Introduction to Chemical Engineering Thermodynamics. Chapter 7. KFUPM Housam Binous CHE 303 Introduction to Chemical Engineering Thermodynamics Chapter 7 1 Thermodynamics of flow is based on mass, energy and entropy balances Fluid mechanics encompasses the above balances and conservation of momentum

More information

Lecture 5 Flusso Quasi-Mono-Dimensionale (forma

Lecture 5 Flusso Quasi-Mono-Dimensionale (forma Lecture 5 Dimensionale forma Text: Motori Aeronautici Mar. 6, 2015 Dimensionale forma Mauro Valorani Univeristà La Sapienza 5.50 Agenda Dimensionale forma 1 quasi-monodimensionale 2 5.51 quasi-monodimensionale

More information

16. CHARACTERISTICS OF SHOCK-WAVE UNDER LORENTZ FORCE AND ENERGY EXCHANGE

16. CHARACTERISTICS OF SHOCK-WAVE UNDER LORENTZ FORCE AND ENERGY EXCHANGE 16. CHARACTERISTICS OF SHOCK-WAVE UNDER LORENTZ FORCE AND ENERGY EXCHANGE H. Yamasaki, M. Abe and Y. Okuno Graduate School at Nagatsuta, Tokyo Institute of Technology 459, Nagatsuta, Midori-ku, Yokohama,

More information

Analysis of Shock-plugs in Quasi-One-Dimensional Compressible Flow

Analysis of Shock-plugs in Quasi-One-Dimensional Compressible Flow Proceedings of the World Congress on Mechanical, Chemical, and terial Engineering (MCM 015) Barcelona, Sain Jul 0-1, 015 Paer No. 38 Analsis of Shock-lugs in Quasi-One-Dimensional Comressible Flow Thomas

More information

Gasdynamics 1-D compressible, inviscid, stationary, adiabatic flows

Gasdynamics 1-D compressible, inviscid, stationary, adiabatic flows Gasdynamics 1-D compressible, inviscid, stationary, adiabatic flows 1st law of thermodynamics ρ const Kontrollfläche 1 2 m u 2 u 1 z Q 12 +P 12 = ṁ } h 2 h {{} 1 Enthalpy Q 12 + 1 2 (u2 2 u2 1 }{{} ) +

More information

Fluid Mechanics - Course 123 COMPRESSIBLE FLOW

Fluid Mechanics - Course 123 COMPRESSIBLE FLOW Fluid Mechanics - Course 123 COMPRESSIBLE FLOW Flow of compressible fluids in a p~pe involves not only change of pressure in the downstream direction but also a change of both density of the fluid and

More information

Introduction to Aerospace Engineering

Introduction to Aerospace Engineering Introduction to Aerosace Engineering Lecture slides hallenge the future Introduction to Aerosace Engineering Aerodynamics & Prof. H. Bijl ir. N. Timmer &. Airfoils and finite wings Anderson 5.9 end of

More information

Chapter 5 Mass, Momentum, and Energy Equations

Chapter 5 Mass, Momentum, and Energy Equations 57:00 Mechanics of Fluids and Transort Processes Chater 5 Professor Fred Stern Fall 006 Chater 5 Mass, Momentum, and Energy Equations Flow Rate and Conservation of Mass. cross-sectional area oriented normal

More information

Antony Jameson. Stanford University Aerospace Computing Laboratory Report ACL

Antony Jameson. Stanford University Aerospace Computing Laboratory Report ACL Formulation of Kinetic Energy Preserving Conservative Schemes for Gas Dynamics and Direct Numerical Simulation of One-dimensional Viscous Comressible Flow in a Shock Tube Using Entroy and Kinetic Energy

More information

Introduction to Aerospace Engineering

Introduction to Aerospace Engineering Introduction to Aerospace Engineering Lecture slides Challenge the future 3-0-0 Introduction to Aerospace Engineering Aerodynamics 5 & 6 Prof. H. Bijl ir. N. Timmer Delft University of Technology 5. Compressibility

More information

NUMERICAL AND THEORETICAL INVESTIGATIONS ON DETONATION- INERT CONFINEMENT INTERACTIONS

NUMERICAL AND THEORETICAL INVESTIGATIONS ON DETONATION- INERT CONFINEMENT INTERACTIONS NUMERICAL AND THEORETICAL INVESTIGATIONS ON DETONATION- INERT CONFINEMENT INTERACTIONS Tariq D. Aslam and John B. Bdzil Los Alamos National Laboratory Los Alamos, NM 87545 hone: 1-55-667-1367, fax: 1-55-667-6372

More information

But isentropic (rev./adiab.), so = =

But isentropic (rev./adiab.), so = = School of erospace Engineering Isentropic Flow with rea Change Exaine ass and oentu equations for reersible and adiabatic conditions ass (VI.9) oentu (VI.0) Cobine dρ d + + ρ dρ + ρ ρ d d 0 0 d p ρ L p

More information

GAS DYNAMICS. M. Halük Aksel. O. Cahit Eralp. and. Middle East Technical University Ankara, Turkey

GAS DYNAMICS. M. Halük Aksel. O. Cahit Eralp. and. Middle East Technical University Ankara, Turkey GAS DYNAMICS M. Halük Aksel and O. Cahit Eralp Middle East Technical University Ankara, Turkey PRENTICE HALL f r \ New York London Toronto Sydney Tokyo Singapore; \ Contents Preface xi Nomenclature xiii

More information

Review of Fundamentals - Fluid Mechanics

Review of Fundamentals - Fluid Mechanics Review of Fundamentals - Fluid Mechanics Introduction Properties of Compressible Fluid Flow Basics of One-Dimensional Gas Dynamics Nozzle Operating Characteristics Characteristics of Shock Wave A gas turbine

More information

Lecture-2. One-dimensional Compressible Fluid Flow in Variable Area

Lecture-2. One-dimensional Compressible Fluid Flow in Variable Area Lecture-2 One-dimensional Compressible Fluid Flow in Variable Area Summary of Results(Cont..) In isoenergetic-isentropic flow, an increase in velocity always corresponds to a Mach number increase and vice

More information

HEAT, WORK, AND THE FIRST LAW OF THERMODYNAMICS

HEAT, WORK, AND THE FIRST LAW OF THERMODYNAMICS HET, ORK, ND THE FIRST L OF THERMODYNMIS 8 EXERISES Section 8. The First Law of Thermodynamics 5. INTERPRET e identify the system as the water in the insulated container. The roblem involves calculating

More information

SUPERSONIC WIND TUNNEL Project One. Charles R. O Neill School of Mechanical and Aerospace Engineering Oklahoma State University Stillwater, OK 74078

SUPERSONIC WIND TUNNEL Project One. Charles R. O Neill School of Mechanical and Aerospace Engineering Oklahoma State University Stillwater, OK 74078 41 SUPERSONIC WIND UNNEL Project One Charles R. O Neill School of Mechanical and Aerospace Engineering Oklahoma State University Stillwater, OK 74078 Project One in MAE 3293 Compressible Flow September

More information

Isentropic Duct Flows

Isentropic Duct Flows An Internet Book on Fluid Dynamics Isentropic Duct Flows In this section we examine the behavior of isentropic flows, continuing the development of the relations in section (Bob). First it is important

More information

Fundamentals of Gas Dynamics (NOC16 - ME05) Assignment - 8 : Solutions

Fundamentals of Gas Dynamics (NOC16 - ME05) Assignment - 8 : Solutions Fundamentals of Gas Dynamics (NOC16 - ME05) Assignment - 8 : Solutions Manjul Sharma & Aswathy Nair K. Department of Aerospace Engineering IIT Madras April 5, 016 (Note : The solutions discussed below

More information

Lecture 13 Heat Engines

Lecture 13 Heat Engines Lecture 3 Heat Engines hermodynamic rocesses and entroy hermodynamic cycles Extracting work from heat - How do we define engine efficiency? - Carnot cycle: the best ossible efficiency Reading for this

More information

f self = 1/T self (b) With revolution, rotaton period T rot in second and the frequency Ω rot are T yr T yr + T day T rot = T self > f self

f self = 1/T self (b) With revolution, rotaton period T rot in second and the frequency Ω rot are T yr T yr + T day T rot = T self > f self Problem : Units : Q-a Mathematically exress the relationshi between the different units of the hysical variables: i) Temerature: ) Fahrenheit and Celsius; 2) Fahrenheit and Kelvin ii) Length: ) foot and

More information

Lecture 13. Heat Engines. Thermodynamic processes and entropy Thermodynamic cycles Extracting work from heat

Lecture 13. Heat Engines. Thermodynamic processes and entropy Thermodynamic cycles Extracting work from heat Lecture 3 Heat Engines hermodynamic rocesses and entroy hermodynamic cycles Extracting work from heat - How do we define engine efficiency? - Carnot cycle: the best ossible efficiency Reading for this

More information

Lecture with Numerical Examples of Ramjet, Pulsejet and Scramjet

Lecture with Numerical Examples of Ramjet, Pulsejet and Scramjet Lecture 41 1 Lecture with Numerical Examples of Ramjet, Pulsejet and Scramjet 2 Problem-1 Ramjet A ramjet is flying at Mach 1.818 at an altitude 16.750 km altitude (Pa = 9.122 kpa, Ta= - 56.5 0 C = 216.5

More information

HIGH SPEED GAS DYNAMICS HINCHEY

HIGH SPEED GAS DYNAMICS HINCHEY HIGH SPEED GAS DYNAMICS HINCHEY MACH WAVES Mach Number is the speed of something divided by the local speed of sound. When an infinitesimal disturbance moves at a steady speed, at each instant in time

More information

P 1 P * 1 T P * 1 T 1 T * 1. s 1 P 1

P 1 P * 1 T P * 1 T 1 T * 1. s 1 P 1 ME 131B Fluid Mechanics Solutions to Week Three Problem Session: Isentropic Flow II (1/26/98) 1. From an energy view point, (a) a nozzle is a device that converts static enthalpy into kinetic energy. (b)

More information

FUNDAMENTALS OF GAS DYNAMICS

FUNDAMENTALS OF GAS DYNAMICS FUNDAMENTALS OF GAS DYNAMICS Second Edition ROBERT D. ZUCKER OSCAR BIBLARZ Department of Aeronautics and Astronautics Naval Postgraduate School Monterey, California JOHN WILEY & SONS, INC. Contents PREFACE

More information

One-Dimensional Isentropic Flow

One-Dimensional Isentropic Flow Cairo University Second Year Faculty of Engineering Gas Dynamics AER 201B Aerospace Department Sheet (1) 2011-2012 One-Dimensional Isentropic Flow 1. Assuming the flow of a perfect gas in an adiabatic,

More information

Measurement of cyclone separator

Measurement of cyclone separator Measurement of cyclone searator. Aim of the measurement Cyclones are widely used in industry (in food and chemical industry, in energy technology and in buildings) to remove dust and other articles from

More information

Hypersonic flow: introduction

Hypersonic flow: introduction Hyersonic flow: introduction Van Dyke: Hyersonic flow is flow ast a body at high ach number, where nonlinearity is an essential feature of the flow. Also understood, for thin bodies, that if is the thickness-to-chord

More information

Package Summary. Square Root Equations Absolute Value Equations. Making Math Possible 1 of 9 c Sa diyya Hendrickson

Package Summary. Square Root Equations Absolute Value Equations. Making Math Possible 1 of 9 c Sa diyya Hendrickson Solving Equations Preared by: Sa diyya Hendrickson Name: Date: Package Summary Square Root Equations Absolute Value Equations Making Math Possible 1 of 9 c Sa diyya Hendrickson A square root equation is

More information

Detonation Structure

Detonation Structure Planar Detonations and Detonation Structure Jerry Seitzman. 5 Mole Fraction.5..5 CH4 HO HCO emerature Methane Flame...3 Distance (cm) 5 5 emerature (K) Detonations - Coyright 4-5 by Jerry M. Seitzman.

More information

SPC 407 Sheet 5 - Solution Compressible Flow Rayleigh Flow

SPC 407 Sheet 5 - Solution Compressible Flow Rayleigh Flow SPC 407 Sheet 5 - Solution Compressible Flow Rayleigh Flow 1. Consider subsonic Rayleigh flow of air with a Mach number of 0.92. Heat is now transferred to the fluid and the Mach number increases to 0.95.

More information

COMPENDIUM OF EQUATIONS Unified Engineering Thermodynamics

COMPENDIUM OF EQUATIONS Unified Engineering Thermodynamics COMPENDIUM OF EQUAIONS Unified Engineering hermodynamics Note: It is with some reseration that I suly this comendium of equations. One of the common itfalls for engineering students is that they sole roblems

More information

Tutorial Materials for ME 131B Fluid Mechanics (Compressible Flow & Turbomachinery) Calvin Lui Department of Mechanical Engineering Stanford University Stanford, CA 94305 March 1998 Acknowledgments This

More information

Chapter 8 Internal Forced Convection

Chapter 8 Internal Forced Convection Chater 8 Internal Forced Convection 8.1 Hydrodynamic Considerations 8.1.1 Flow Conditions may be determined exerimentally, as shown in Figs. 7.1-7.2. Re D ρumd μ where u m is the mean fluid velocity over

More information

δq T = nr ln(v B/V A )

δq T = nr ln(v B/V A ) hysical Chemistry 007 Homework assignment, solutions roblem 1: An ideal gas undergoes the following reversible, cyclic rocess It first exands isothermally from state A to state B It is then comressed adiabatically

More information

CHAPTER 2 Fluid Statics

CHAPTER 2 Fluid Statics Chater / Fluid Statics CHAPTER Fluid Statics FE-tye Exam Review Problems: Problems - to -9. (C) h (.6 98) (8.5.54) 96 6 Pa Hg. (D) gh 84. 9.8 4 44 76 Pa. (C) h h. 98. 8 Pa w atm x x water w.4 (A) H (.6

More information

Introduction to Gas Dynamics All Lecture Slides

Introduction to Gas Dynamics All Lecture Slides Introduction to Gas Dynamics All Lecture Slides Teknillinen Korkeakoulu / Helsinki University of Technology Autumn 009 1 Compressible flow Zeroth law of thermodynamics 3 First law of thermodynamics 4 Equation

More information

AOE 3114 Compressible Aerodynamics

AOE 3114 Compressible Aerodynamics AOE 114 Compressible Aerodynamics Primary Learning Objectives The student will be able to: 1. Identify common situations in which compressibility becomes important in internal and external aerodynamics

More information

Rocket Thermodynamics

Rocket Thermodynamics Rocket Thermodynamics PROFESSOR CHRIS CHATWIN LECTURE FOR SATELLITE AND SPACE SYSTEMS MSC UNIVERSITY OF SUSSEX SCHOOL OF ENGINEERING & INFORMATICS 25 TH APRIL 2017 Thermodynamics of Chemical Rockets ΣForce

More information

Chapter 17. For the most part, we have limited our consideration so COMPRESSIBLE FLOW. Objectives

Chapter 17. For the most part, we have limited our consideration so COMPRESSIBLE FLOW. Objectives Chapter 17 COMPRESSIBLE FLOW For the most part, we have limited our consideration so far to flows for which density variations and thus compressibility effects are negligible. In this chapter we lift this

More information

SPC 407 Sheet 2 - Solution Compressible Flow - Governing Equations

SPC 407 Sheet 2 - Solution Compressible Flow - Governing Equations SPC 407 Sheet 2 - Solution Compressible Flow - Governing Equations 1. Is it possible to accelerate a gas to a supersonic velocity in a converging nozzle? Explain. No, it is not possible. The only way to

More information

CHAPTER 2 Fluid Statics

CHAPTER 2 Fluid Statics Chater / Fluid Statics CHAPTER Fluid Statics FE-tye Exam Review Problems: Problems - to -9. (C) h (.6 98) (8.5.54) 96 6 Pa Hg. (D) gh 84. 9.8 4 44 76 Pa. (C) h h. 98. 8 Pa w atm x x water w.4 (A) H (.6

More information

Feedback-error control

Feedback-error control Chater 4 Feedback-error control 4.1 Introduction This chater exlains the feedback-error (FBE) control scheme originally described by Kawato [, 87, 8]. FBE is a widely used neural network based controller

More information

Convective Mass Transfer

Convective Mass Transfer Convective Mass Transfer Definition of convective mass transfer: The transport of material between a boundary surface and a moving fluid or between two immiscible moving fluids separated by a mobile interface

More information

df da df = force on one side of da due to pressure

df da df = force on one side of da due to pressure I. Review of Fundamental Fluid Mechanics and Thermodynamics 1. 1 Some fundamental aerodynamic variables htt://en.wikiedia.org/wiki/hurricane_ivan_(2004) 1) Pressure: the normal force er unit area exerted

More information

CALCULATION OF THE PARTICLE VELOCITY IN COLD SPRAY IN THE ONE-DIMENSIONAL NON-ISENTROPIC APPROACH

CALCULATION OF THE PARTICLE VELOCITY IN COLD SPRAY IN THE ONE-DIMENSIONAL NON-ISENTROPIC APPROACH VOL 10 NO 6 APRIL 015 ISSN 1819-6608 ARPN Journal of Engineering and Alied Sciences 006-015 Asian Research Publishing Network (ARPN) All rights reserved wwwarnjournalscom CALCULATION OF THE PARTICLE VELOCITY

More information

Chapter 1 Fundamentals

Chapter 1 Fundamentals Chater Fundamentals. Overview of Thermodynamics Industrial Revolution brought in large scale automation of many tedious tasks which were earlier being erformed through manual or animal labour. Inventors

More information

Lecture Thermodynamics 9. Entropy form of the 1 st law. Let us start with the differential form of the 1 st law: du = d Q + d W

Lecture Thermodynamics 9. Entropy form of the 1 st law. Let us start with the differential form of the 1 st law: du = d Q + d W Lecture hermodnamics 9 Entro form of the st law Let us start with the differential form of the st law: du = d Q + d W Consider a hdrostatic sstem. o know the required d Q and d W between two nearb states,

More information

dn i where we have used the Gibbs equation for the Gibbs energy and the definition of chemical potential

dn i where we have used the Gibbs equation for the Gibbs energy and the definition of chemical potential Chem 467 Sulement to Lectures 33 Phase Equilibrium Chemical Potential Revisited We introduced the chemical otential as the conjugate variable to amount. Briefly reviewing, the total Gibbs energy of a system

More information

Evolution of Compression Processes in Aero-Engine Thermal Cycles

Evolution of Compression Processes in Aero-Engine Thermal Cycles The Oen Aerosace Engineering Journal, 2008,, -7 Evolution of Comression Processes in Aero-Engine Thermal Cycles Y. Daren, T. Jingfeng * and B. Wen School of Energy Science and Engineering, Harbin Institute

More information

1 One-dimensional analysis

1 One-dimensional analysis One-dimensional analysis. Introduction The simplest models for gas liquid flow systems are ones for which the velocity is uniform over a cross-section and unidirectional. This includes flows in a long

More information

UNIT 1 COMPRESSIBLE FLOW FUNDAMENTALS

UNIT 1 COMPRESSIBLE FLOW FUNDAMENTALS UNIT 1 COMPRESSIBLE FLOW FUNDAMENTALS 1) State the difference between compressible fluid and incompressible fluid? 2) Define stagnation pressure? 3) Express the stagnation enthalpy in terms of static enthalpy

More information

Understanding DPMFoam/MPPICFoam

Understanding DPMFoam/MPPICFoam Understanding DPMFoam/MPPICFoam Jeroen Hofman March 18, 2015 In this document I intend to clarify the flow solver and at a later stage, the article-fluid and article-article interaction forces as imlemented

More information

Notes #4a MAE 533, Fluid Mechanics

Notes #4a MAE 533, Fluid Mechanics Notes #4a MAE 533, Fluid Mechanics S. H. Lam lam@princeton.edu http://www.princeton.edu/ lam October 23, 1998 1 The One-dimensional Continuity Equation The one-dimensional steady flow continuity equation

More information

Richard Nakka's Experimental Rocketry Web Site

Richard Nakka's Experimental Rocketry Web Site Página 1 de 7 Richard Nakka's Experimental Rocketry Web Site Solid Rocket Motor Theory -- Nozzle Theory Nozzle Theory The rocket nozzle can surely be described as the epitome of elegant simplicity. The

More information

PHYS1001 PHYSICS 1 REGULAR Module 2 Thermal Physics Chapter 17 First Law of Thermodynamics

PHYS1001 PHYSICS 1 REGULAR Module 2 Thermal Physics Chapter 17 First Law of Thermodynamics PHYS1001 PHYSICS 1 REGULAR Module Thermal Physics Chater 17 First Law of Thermodynamics References: 17.1 to 17.9 Examles: 17.1 to 17.7 Checklist Thermodynamic system collection of objects and fields. If

More information

2.6 Primitive equations and vertical coordinates

2.6 Primitive equations and vertical coordinates Chater 2. The continuous equations 2.6 Primitive equations and vertical coordinates As Charney (1951) foresaw, most NWP modelers went back to using the rimitive equations, with the hydrostatic aroximation,

More information

AME 436. Energy and Propulsion. Lecture 15 Propulsion 5: Hypersonic propulsion

AME 436. Energy and Propulsion. Lecture 15 Propulsion 5: Hypersonic propulsion AME 436 Energy and Propulsion Lecture 5 Propulsion 5: Hypersonic propulsion Outline!!!!!! Why hypersonic propulsion? What's different about it? Conventional ramjet heat addition at M

More information

Determination of Pressure Losses in Hydraulic Pipeline Systems by Considering Temperature and Pressure

Determination of Pressure Losses in Hydraulic Pipeline Systems by Considering Temperature and Pressure Paer received: 7.10.008 UDC 61.64 Paer acceted: 0.04.009 Determination of Pressure Losses in Hydraulic Pieline Systems by Considering Temerature and Pressure Vladimir Savi 1,* - Darko Kneževi - Darko Lovrec

More information

Aerothermodynamics of High Speed Flows

Aerothermodynamics of High Speed Flows Aerothermodynamics of High Speed Flows Lecture 5: Nozzle design G. Dimitriadis 1 Introduction Before talking about nozzle design we need to address a very important issue: Shock reflection We have already

More information

Notes on pressure coordinates Robert Lindsay Korty October 1, 2002

Notes on pressure coordinates Robert Lindsay Korty October 1, 2002 Notes on ressure coordinates Robert Lindsay Korty October 1, 2002 Obviously, it makes no difference whether the quasi-geostrohic equations are hrased in height coordinates (where x, y,, t are the indeendent

More information

The Role of Momentum Interpolation Mechanism of the Roe. Scheme in the Shock Instability

The Role of Momentum Interpolation Mechanism of the Roe. Scheme in the Shock Instability The Role of Momentum Interolation Mechanism of the Roe Scheme in the Shock Instabilit Xue-song Li Ke Laborator for Thermal Science and Power Engineering of Ministr of Education, Deartment of Thermal Engineering,

More information

AerE 344: Undergraduate Aerodynamics and Propulsion Laboratory. Lab Instructions. Pressure Measurements in a de Laval Nozzle

AerE 344: Undergraduate Aerodynamics and Propulsion Laboratory. Lab Instructions. Pressure Measurements in a de Laval Nozzle AerE 344: Undergraduate Aerodynamics and ropulsion Laboratory Lab Instructions Lab #0: ressure easurements in a de Laval Nozzle Instructor: Dr. Hui Hu Department of Aerospace Engineering Iowa State University

More information

Chapter 6. Thermodynamics and the Equations of Motion

Chapter 6. Thermodynamics and the Equations of Motion Chater 6 hermodynamics and the Equations of Motion 6.1 he first law of thermodynamics for a fluid and the equation of state. We noted in chater 4 that the full formulation of the equations of motion required

More information

4. Score normalization technical details We now discuss the technical details of the score normalization method.

4. Score normalization technical details We now discuss the technical details of the score normalization method. SMT SCORING SYSTEM This document describes the scoring system for the Stanford Math Tournament We begin by giving an overview of the changes to scoring and a non-technical descrition of the scoring rules

More information

Lecture 8, the outline

Lecture 8, the outline Lecture, the outline loose end: Debye theory of solids more remarks on the first order hase transition. Bose Einstein condensation as a first order hase transition 4He as Bose Einstein liquid Lecturer:

More information

Statics and dynamics: some elementary concepts

Statics and dynamics: some elementary concepts 1 Statics and dynamics: some elementary concets Dynamics is the study of the movement through time of variables such as heartbeat, temerature, secies oulation, voltage, roduction, emloyment, rices and

More information

DEVELOPMENT OF A COMPRESSED CARBON DIOXIDE PROPULSION UNIT FOR NEAR-TERM MARS SURFACE APPLICATIONS

DEVELOPMENT OF A COMPRESSED CARBON DIOXIDE PROPULSION UNIT FOR NEAR-TERM MARS SURFACE APPLICATIONS DEVELOPMENT OF A COMPRESSED CARBON DIOXIDE PROPULSION UNIT FOR NEAR-TERM MARS SURFACE APPLICATIONS Erin Blass Old Dominion University Advisor: Dr. Robert Ash Abstract This work has focused on the development

More information

(British) (SI) British Metric L T [V] = L T. [a] = 2 [F] = F = 2 T

(British) (SI) British Metric L T [V] = L T. [a] = 2 [F] = F = 2 T Hydraulics ecture # CWR 40 age () ecture # Outline: Review of terminology in fluid mechanics: Energy or work Hydraulic head Bernoulli s aw, Conductivity (examle) ransient & turbulent Friction head loss

More information

General Physical Chemistry I

General Physical Chemistry I General Physical Cheistry I Lecture 12 Aleksey Kocherzhenko Aril 2, 2015" Last tie " Gibbs free energy" In order to analyze the sontaneity of cheical reactions, we need to calculate the entroy changes

More information

ANALYSIS OF ENTROPY GENERATION IN A CIRCULAR TUBE WITH SHORT LENGTH TWISTED TAPE INSERTS

ANALYSIS OF ENTROPY GENERATION IN A CIRCULAR TUBE WITH SHORT LENGTH TWISTED TAPE INSERTS Proceedings of the th National and 11 th International ISHMT-ASME Heat and Mass Transfer Conference December 8-31, 013, IIT Kharagur, India HMTC13006 ANALYSIS OF ENTROPY GENERATION IN A CIRCULAR TUBE WITH

More information

Chapter 9 Practical cycles

Chapter 9 Practical cycles Prof.. undararajan Chater 9 Practical cycles 9. Introduction In Chaters 7 and 8, it was shown that a reversible engine based on the Carnot cycle (two reversible isothermal heat transfers and two reversible

More information

Rigorous bounds on scaling laws in fluid dynamics

Rigorous bounds on scaling laws in fluid dynamics Rigorous bounds on scaling laws in fluid dynamics Felix Otto Notes written by Steffen Pottel Contents Main Result on Thermal Convection Derivation of the Model. A Stability Criterion........................

More information

Steady waves in compressible flow

Steady waves in compressible flow Chapter Steady waves in compressible flow. Oblique shock waves Figure. shows an oblique shock wave produced when a supersonic flow is deflected by an angle. Figure.: Flow geometry near a plane oblique

More information

Theory of turbomachinery. Chapter 1

Theory of turbomachinery. Chapter 1 Theory of turbomachinery Chater Introduction: Basic Princiles Take your choice of those that can best aid your action. (Shakeseare, Coriolanus) Introduction Definition Turbomachinery describes machines

More information

MONITOR REGULATOR SIZING AND OTHER CONSIDERATIONS

MONITOR REGULATOR SIZING AND OTHER CONSIDERATIONS MONITOR REGULATOR SIZING AND OTHER CONSIDERATIONS 6" 4" 6" 4" 4" 8" 4" 6" 6" 8" 6" 6" OGA 015 Regulator Fundamentals Seminar Monitor Regulator Sizing Theory FLOW in m out USTREAM MONITOR REGULATOR DOWNSTREAM

More information

Ducted Wind/Water Turbines and Propellers Revisited By Michael, J. Werle, PhD 1 and Walter M. Presz, Jr., PhD 2 FLODESIGN, INC. WILBRAHAM, MA.

Ducted Wind/Water Turbines and Propellers Revisited By Michael, J. Werle, PhD 1 and Walter M. Presz, Jr., PhD 2 FLODESIGN, INC. WILBRAHAM, MA. Introduction Ducted Wind/Water Turbines and roellers Revisited By Michael, J. Werle, hd and Walter M. resz, Jr., hd FLODEIGN, IN. WILBRAHAM, MA. 0095 There has been considerable effort and discussion in

More information

OE4625 Dredge Pumps and Slurry Transport. Vaclav Matousek October 13, 2004

OE4625 Dredge Pumps and Slurry Transport. Vaclav Matousek October 13, 2004 OE465 Vaclav Matousek October 13, 004 1 Dredge Vermelding Pumps onderdeel and Slurry organisatie Transport OE465 Vaclav Matousek October 13, 004 Dredge Vermelding Pumps onderdeel and Slurry organisatie

More information

OPTIMIZATION OF EARTH FLIGHT TEST TRAJECTORIES TO QUALIFY PARACHUTES FOR USE ON MARS

OPTIMIZATION OF EARTH FLIGHT TEST TRAJECTORIES TO QUALIFY PARACHUTES FOR USE ON MARS OPTIMIZATION OF EARTH FLIGHT TEST TRAJECTORIES TO QUALIFY PARACHUTES FOR USE ON MARS Christoher L. Tanner (1) (1) Sace Systems Design Laboratory, Daniel Guggenheim School of Aerosace Engineering Georgia

More information

A NEW STREAMLINE CURVATURE THROUGHFLOW METHOD FOR RADIAL TURBOMACHINERY

A NEW STREAMLINE CURVATURE THROUGHFLOW METHOD FOR RADIAL TURBOMACHINERY Proceedings of ASME Turbo Exo 008: Power for Land, Sea and Air GT008 June 9-3, 008, Berlin, Germany GT008-5087 A NEW STREAMLINE CURVATURE THROUGHFLOW METHOD FOR RADIAL TURBOMACHINERY Michael Casey ITSM

More information