Compressible-flow Mach Functionas
Page 5 - Nomenclature
Pages 6 & 7 - Mach Functions
Recommendaitons: Used Equations on Pp. 6 & 7 to
generate any of the results from the table as functions
of specific heat ration, Gamma = Cp/Cv.
Enjoy it as one would enjoy their favorite music.
Structural detailing of fuselage of aeroplane /aircraft.PriyankaKg4
This presentation is about the structural detailing of fuselage of aeroplane .The fuselage or body of the airplane, holds all the pieces together. The pilots sit in the cockpit at the front of the fuselage. Passengers and cargo are carried in the rear of the fuselage. Some aircraft carry fuel in the fuselage; others carry the fuel in the wings.
Atmosphere | Q & A | Topic wise Solutions | Question Analysis | Flight Mechan...Age of Aerospace
Question Analysis, Book Reference, Important Concepts, Formulae and topic wise Solutions for the topic "Atmosphere: Properties and Standard Atmosphere"
This course gets you started with writing device drivers in Linux by providing real time hardware exposure. Equip you with real-time tools, debugging techniques and industry usage in a hands-on manner. Dedicated hardware by Emertxe's device driver learning kit. Special focus on character and USB device drivers.
This project gives an understanding on how an Aircraft is protected from Icy conditions during flight and while on ground. Hence also the systems and devices and fluid used.
ME 438 Aerodynamics is a course taught by Dr. Bilal Siddiqui at DHA Suffa University. This set of lectures start from the basic and all the way to aerodynamic coefficients and center of pressure variations with angle of attack.
This presentation had been prepared for the aircraft propulsion class to my undergraduate and graduate students at Kasetsart University and Chulalongkorn University - Bangkok, Thailand.
Structural detailing of fuselage of aeroplane /aircraft.PriyankaKg4
This presentation is about the structural detailing of fuselage of aeroplane .The fuselage or body of the airplane, holds all the pieces together. The pilots sit in the cockpit at the front of the fuselage. Passengers and cargo are carried in the rear of the fuselage. Some aircraft carry fuel in the fuselage; others carry the fuel in the wings.
Atmosphere | Q & A | Topic wise Solutions | Question Analysis | Flight Mechan...Age of Aerospace
Question Analysis, Book Reference, Important Concepts, Formulae and topic wise Solutions for the topic "Atmosphere: Properties and Standard Atmosphere"
This course gets you started with writing device drivers in Linux by providing real time hardware exposure. Equip you with real-time tools, debugging techniques and industry usage in a hands-on manner. Dedicated hardware by Emertxe's device driver learning kit. Special focus on character and USB device drivers.
This project gives an understanding on how an Aircraft is protected from Icy conditions during flight and while on ground. Hence also the systems and devices and fluid used.
ME 438 Aerodynamics is a course taught by Dr. Bilal Siddiqui at DHA Suffa University. This set of lectures start from the basic and all the way to aerodynamic coefficients and center of pressure variations with angle of attack.
This presentation had been prepared for the aircraft propulsion class to my undergraduate and graduate students at Kasetsart University and Chulalongkorn University - Bangkok, Thailand.
This presentation had been prepared for the aircraft propulsion class to my undergraduate and graduate students at Kasetsart University and Chulalongkorn University - Bangkok, Thailand.
Split Second Analysis Covering High Pressure Gas Flow Dynamics At Pipe Outlet...AEIJjournal2
A detailed investigation covering piped gas flow characteristics in high pressure flow conditions. Such flow
analysis can be resolved using established mathematical equations known as the Fanno condition, which
usually cover steady state, or final flow conditions. However, in real life, such flow conditions are
transient, varying with time. This paper uses CFD analysis providing a split second “snapshot” at what
happens at the pipe outlet, and therefore, a closer understanding at what happens at the pipe’s outlet in
high pressure gas flow condition.
In this example air was selected for simulation purposes. In HVAC applications, such gas flow conditions
can occur in typical applications such as; air compressors releasing high pressure air through a pipe, or
compressor over pressure refrigerant gas being released into the atmosphere via a discharge pipe.
Investigation has shown that rather than a steady mass flow rate condition occurring at the pipe outlet,
calculated by the Fanno flow condition, a spiked increase in flow rate occurs at the beginning,and then
stabilizing after a few seconds, with relatively minor ripples in flow rate. Other observations were also
made and commented.
CFD results in mass flow rate were compared with the mathematically derived results, differences were
recorded. The CFD analysis showed how the k-omega turbulence model performed well, with the processor
stabilizing at an early stage.
SPLIT SECOND ANALYSIS COVERING HIGH PRESSURE GAS FLOW DYNAMICS AT PIPE OUTLET...AEIJjournal2
A detailed investigation covering piped gas flow characteristics in high pressure flow conditions. Such flow analysis can be resolved using established mathematical equations known as the Fanno condition, which usually cover steady state, or final flow conditions. However, in real life, such flow conditions are
transient, varying with time. This paper uses CFD analysis providing a split second “snapshot” at what happens at the pipe outlet, and therefore, a closer understanding at what happens at the pipe’s outlet in high pressure gas flow condition
Apologia - A Call for a Reformation of Christian Protestants Organizations.pdfJulio Banks
This document shows how to know whether an organization claiming to be IRS 501(C)(3) tax exempted nonprofit is being partisan by teaching that the republican party is the party of Jesus Christ violating the nonpartisan IRS requirement are false Christian organizations.
The treatment of large structural systems may be simplified by dividing the system into
smaller systems called components. The components are related through the
displacement, and force conditions at their junction points. Each component is represented
by mode shapes (or functions).
The synchronicity time or common time of two (2) independent and asynchronous events can be readily
completed in a four (4) steps algorithm to be described in this article. Additionally, two (2) illustrative
examples are also provided for completeness of presentation of the Synchronicity Algorithm.
Math cad prime the relationship between the cubit, meter, pi and the golden...Julio Banks
It has been reported that the ancient Egyptians knew pi, the golden ration (phi) and the meter. This paper summarizes the relationship of pi, and phi via the cubit.
Jannaf 10 1986 paper by julio c. banks, et. al.-ballistic performance of lpg ...Julio Banks
This paper is the result of the response of LPG (Liquid Propellant Gun) to high-temperate simulated-desert condition using ANSYS FEA (Finite Element Analysis) and Mica Heating Banks.
web site: http://www.joycenter.net/wp-content/uploads/2013/04/Mans-Search-for-Meaning-Viktor-Frankl.pdf
A case can be made that since the main basis of "The Theory" of evolution is the "Self-preservation principle". That is, how could the propagation of the a specie be enhanced by the demeaning action of a group against its constituents and even self-against-self. The only explanation is that humas were created and not a result of a random sett of actions causing consciousness arriving from non-conscious matter. Life comes from life, and intelligence (DNA), comes from intelligence. This book can be contrasted with: The Lucifer Effect Understanding How Good People Turn Evil by Philip Zimbardo' and also with the Bible for a view of The Meaning of Life from ancient to contemporary writings for balance understanding of the physical (Psyche) to the metaphysical (Spiritual). We can view the human condition as the effect of gravity of interacting physical objects and human interaction as the response to spiritual influence (angels and demons).
When the Scriptures command us to “love your enemies”, “bless those who curse you” as well as “Judge not because as you judge you will also be judged and the very same standard you apply in condemning others you also be condemned”. One can see, in the context of this essay, that we are actually harming ourselves if we do not love our “perceived enemies” since it is well known that “There are no greater flaws than the ones we perceive in others than the ones residing within ourselves (known as “our personal demons” or “small judging sub-self)”. This is in essence the basis of psychological projection which is a form of psychological dissonance (the closer one is to danger, the more one tends to minimize or even ignore its potential harm to us). Psychological dissonance is a defense mechanism by which “the human mind minimizes the pain of being less than the person that we all believe we are and we seek to find. The true self is the enlightened being who has discovered the meaning of love. Finally, we are home when we feel at peace at being who we are; unique individuals just as our DNA and fingerprints identifies us from billions of other humans. Be yourself and celebrate your uniqueness then you will be truly enlightened - you have arrived at the place call true self and therefore happy
The first step required to defeating an enemy is by first thoroughly defining it. A physician runs tests of their patients to determine the type of pathogen ailing such patients. Similarly, we must be clear that A Muslim Terrorist is indeed a Fundamentalist and not a Radical Terrorist since the method of striking terror is explicitly and clearly defined in the Qur'an. Christianity is the only religion that needs not attack any other religion such as the Islam religion since God is the author and finisher of our faith and also commands the Christians to allow God to avenge Himself for our attacks even from Islamic Terrorist. A Christian is commanded to live at peace with all humans and when such a peaceful coexistence is not achieved then we must simply stay away from such toxic humans.
The primary test for a true religion is that "The Judeo-Christian God does not need nor require that mere mortal human beings to defend Him".
NASA-TM-X-74335 --U.S. Standard Atmosphere 1976Julio Banks
NASA-TM-X-74335 --U.S. Standard Atmosphere 1976. This information is useful for airframes (e.g., missiles and aircrafts) aero-thermos analysis and design.
Mathcad P-elements linear versus nonlinear stress 2014-t6Julio Banks
This work couples the classical ESED (Equivalent Strain Energy Density) Method; aka, Glinka. The most expedient method of solving a structural problem using FEA (Finite Element Analysis). There would be occasions when stress concentrations would be calculated due to interior corners, holes, sudden change of geometry (aka stress raisers). Although some software would allow regions in the vicinity of such stress risers to be defined by nonlinear material models such as "Elastic Perfectly-plastic", "Bilinear (Elastic and linear plastic), or the fundamental Ramberg-Osgood metal strain-stress models. Once the Linear-elastic FEA solution is obtained one can readily determine that Pseduo nonlinear strain, the corresponding stress and the implicit stress-intensification factor, Kt. It should be noted that once the analyst-designer is ready for final analysis, it would be most prudent to create a FEA model in which the regions of high concentration of stress to be modeled with local nonlinear models of the metal using St. Vennants' Principle of load-and-resistance distance from area of interest. The P-method is an excellent FEA element that can "find the actual nonlinear stress" by the simple iterative increase of the order of the polynomial representing the stress fields within every P-element. It should be noted that this research was facilitated by the use of the P-element FEA software called StressCheck which is 100% P-element solution which I am quite pleased to have had the opportunity of utilizing for this research.
Apologia - The martyrs killed for clarifying the bibleJulio Banks
I know all the things you do, that you are neither hot nor cold. I wish that you were one or the other! 16But since you are like lukewarm water, neither hot nor cold, I will spit you out of my mouth!” - Revelation 3:15-16
“A man who does not have something for which he is willing to die is not fit to live.” - Martin Luther King Jr.
Spontaneous creation of the universe ex nihil by maya lincoln and avi wasserJulio Banks
Questions regarding the formation of the Universe and ‘what was there ’ before it came to existence have
been of great interest to mankind at all times. Several suggestions have been presented during the ages –
mostly assuming a preliminary state prior to creation. Nevertheless, theories that require initial conditions
are not considered complete, since they lack an explanation of what created such conditions. We therefore
propose the ‘Creatio Ex Nihilo ’ (CEN) theory, aimed at describing the origin of the Universe from ‘nothing ’ in
information terms. The suggested framework does not require amendments to the laws of physics: but rather
provides a new scenario to the Universe initiation process, and from that point merges with state-of-the-art
cosmological models. The paper is aimed at providing a first step towards a more complete model of the
Universe creation – proving that creation Ex Nihilo is feasible. Further adjustments, elaborations, formalisms
and experiments are required to formulate and support the theory.
The “necessary observer” that quantum mechanics require is described in the b...Julio Banks
This essay is intended to share the vies of the author of his Judeo-Christian belief and the physical validation of such believes based upon the theories of Quantum Mechanics.
A fund way to remember how to "fix our manifested creation" by means of observation is as follows: "Keep an eye on the ball", "Do not drop the ball"
Advances in fatigue and fracture mechanics by grzegorz (greg) glinkaJulio Banks
Professor Grzegorz (Greg) Glinka has made substantial contributions to the field of stress concentration evaluation using linear FEA results using the ESED (Equivalent Striain Energy Density). ESED aka Glinka methods allows the determination of strain-stress state at a point of local concentration by equating the strain energy from the linear FEA area in the material strain-stress curve to that of the actual strain-stress of the material using a models such as Ramberg-Osgood. The ESED method is more accurate than the Neuber requiring the equating of SED (Strain Energy Densities) of linear FEA results that Stress is proportional to strain even when the FEA predicts a stress greater than the ultimate strength of the material. One easy method of remember when to use ESED versus Neuber is that ESED, more accurate, should be use on the stress analysis of rocket structures and Neuber delegated to aerospace engines and components.
Quality defects in TMT Bars, Possible causes and Potential Solutions.PrashantGoswami42
Maintaining high-quality standards in the production of TMT bars is crucial for ensuring structural integrity in construction. Addressing common defects through careful monitoring, standardized processes, and advanced technology can significantly improve the quality of TMT bars. Continuous training and adherence to quality control measures will also play a pivotal role in minimizing these defects.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
NO1 Uk best vashikaran specialist in delhi vashikaran baba near me online vas...Amil Baba Dawood bangali
Contact with Dawood Bhai Just call on +92322-6382012 and we'll help you. We'll solve all your problems within 12 to 24 hours and with 101% guarantee and with astrology systematic. If you want to take any personal or professional advice then also you can call us on +92322-6382012 , ONLINE LOVE PROBLEM & Other all types of Daily Life Problem's.Then CALL or WHATSAPP us on +92322-6382012 and Get all these problems solutions here by Amil Baba DAWOOD BANGALI
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Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
TECHNICAL TRAINING MANUAL GENERAL FAMILIARIZATION COURSEDuvanRamosGarzon1
AIRCRAFT GENERAL
The Single Aisle is the most advanced family aircraft in service today, with fly-by-wire flight controls.
The A318, A319, A320 and A321 are twin-engine subsonic medium range aircraft.
The family offers a choice of engines
2. The scope of engineering activity at Pratt & Whitney involves the
use of many compressible flow relatwnships. While there is
generaUy available a great wealth oftabulated data on this subject,
much ofit is specialized or limited in scope.
This book accumulates a number ofthese diverse tables under one
cover and adds certain thrustfunctions not to be found elsewhere.
It is published in order that others who also have a usefor this type
of information may enjoy the convenience of a single source of
aerodynamic tables.
PRATT & WHITNEY
3. TABLE OF CONTENTS
Page
Introduction ...................................................................................... vii
Nomenclature for List of Mach Functions .................................... viii
List of Mach Functions .................................................................... ix
Functional Relationships and Examples ........................................ x
References .........................." ........................................................... xi
Mach Number Tables
y = 1.100 ................................................................................ 2
Y = 1.150 ................................................................................ 30
Y = 1.200 ................................................................................ 58
Y = 1.250 ................................................................................ 86
Y = 1.286 ....................................................................,........... 114
Y = 1.300 ................................................................................ 142
Y= 1.350 ................................................................................ 170
Y = 1.400 ................................................................................ 198
Y = 1.667 ................................................................................ 226
Table of Mach Number vs. Mach Angle ...................................... 255
y
4. INTRODUCTION
These tables contain the Mach number functions most frequently used in the analysis
of steady or nonsteady, inviscid, compressible flow. The Mach number range includes
values from M = 0 to M = 20; the ratio of specific heats (gamma) varies from
1.10 to 1.667; ideal thrust and non-steady flow functions are presented; and special
flow functions extremely useful for solving the heat-addition problem in a constant
area duct and the mixing of parallel streams in a constant area duct have also been
included. For the above reasons it is believed that these tables are the most com
prehensive of their kind available. Though they were intended primarily for pre
liminary air breathing and rocket powerplant calculations, they can be used to assist
in solving a wide range of practical aerodynamic problems.
Functions are presented for different specific heat ratios as functions of Mach number.
In the calculations the gas is assumed to be a calorically perfect, ideal fluid. This
implies the equation of state PV = RT, and that the specific heat ratio and molecular
weight are constant. A mean or effective gamma gives a satisfactory first approxima
tion where chemical reactions do occur, as in the rocket nozzle process. Derivations
of the various functions presented may be found in References 1 through 5.
All functions were computed on an IBM 7090 computer and are given to five sig~
nificant figures. A fixed-point notation is used except where otherwise indicated.
The appearance of x lo±n at the top of a column indicates that the tabulated
value should be multiplied by 10±n. The Mach numbers are tabulated in .01 inter
vals for M = 0.00 to M = .85, in .001 intervals from M = .851 to M = 1.149,
in .01 intervals from M =1.15 to 5.00, and in .1 intervals from M =5.00 to
M = 20.0. Values of gamma are calculated in .05 intervals from values of 1.10 to
1.40. Gamma values of 5/3 {1.667} and 9/7 (1.286) have also been included.
The tables have been reproduced directly from the mM printout. Spot checks for
accuracy have been made, but it is obviously infeasible to check every point. There
fore, it would be appreciated if errors are found that they be brought to the attention
of Pratt & Whitney.
vii
5. NOMENCLATURE FOR LIST OF MACH FUNCTIONS
A = Stream tube cross-sectional area, sound speed
D =Mass flow function
F = Stream thrust (or Vacuum thrust), lbs.
FsA = Vacuum Thrust Coefficient
A*
Fip = Ideal Thrust for Complete Expansion to
Ambient Pressure, lbs.
M =Mach Number
M DOT = Mass flow parameter
m = Mass flow, slugs/sec
N = Mass flow parameter
p = Pressure,lbs./ft.2
Q =Dynamic Pressure,lbs./ft.2
SUBSCRIPTS
A =Ambient Conditions
s = Stream
T = Isentropic stagnation conditions
1 =Condition upstream of normal shock
2 =Condition downstream of normal shock
R =Gas Constant, ft.lb./slug OR
T = Temperature OR
V =Velocity
a = Mach Angle
y = Specific heat ratio, CP/CV
.6.U Non-steady flow function
A
p = Density
<.0 = Prandtl-Meyer expansion angle
SUPERSCRIPT
• Refers to condition where M = 1.0
viii
6. LIST OF MACH FUNCTIONS
PRESSURE RATIO VS MACH NUMBER STATIC PRESSURE RATIO ACROSS A
NORMAL SHOCK
.!:. == (1 + y-1 M2 ) 1":1'
2
PI y+l y+l
PT (t) P2
== (2L)M12- 1'-1
AREA RATIO VS MACH NUMBER
TOTAL PRESSURE RATIO ACROSS A
NORMAL SHOCK
:* == ~ [2 (1+ 7 M2 )]2;:::'1)
PT2
y+1 (t) ==PT1
NON·DIMENSIONAL VELOCITY
V ( -1 )-% 7-Ml2 1/....1 (2LM12 y-l) 1":1'
~ =M 1+7M2 1 + Y2 I Ml2 y+l y+1[
TEMPERATURE RATIO VS MACH NUMBER
~ == (1 + y-1 M2 ) -1
TT 2
PRANDTL-MEYER TURNING ANGLE VS
MACH NUMBER
(t) w ==
Y+ 1
tan-IVY-1 (M2-1) - tan-l
VW-lVy-l y+l
MASS FLOW PARAMETER
M DOT = M ( 1 + 'Y 21M2) 1/2
DYNAMIC PRESSURE/TOTAL PRESSURE
VS MACH NUMBER
~==~~yM2
PT 2 PT
VACUUM THRUST/THROAT AREA X TOTAL
PRESSURE VS MACH NUMBER
A P A ( M'»Fs-==---~ l+y
A* p,!, A:
IDEAL THRUST VS PRESSURE RATIO
~ ==1/ 2y2 (_2) ~~~ [ 1 _ (PA
) 1'~l ]
A* PT y-1 y+1 PT
MASS FLOW FUNCTIONS VS MACH NUMBER
N == M ( 1+7 W ) 1h (1+y W ) -1
ID M (~+ M2 F(~~; Ii1
~', "" ." " ~. ,.= ... ~. __~. __"__ .::r"'" .~~
CHANGE IN VELOCITY/NON DIMENSIONAL
SPEED OF SOUND FOR NON-STEADY FLOW
(t) flU == _2_(W-l)A y+l M
MACH NUMBER AFTER NORMAL SHOCK
(t) M2 = (y-l) M12V2+
2 yM12_y + 1
DYNAMIC PRESSURE(fOTAL PRESSURE
STATIC PRESSURE
Q/(PT - P) = ¥z yM2
(PT/P-l)
STATIC TEMPERATURE RATIO ACROSS A
NORMAL SHOCK
(
1 + y-l Ml2 ) (2LM I 2_ 1 )
(t) T2 == 2 y-l
Tl (y+l)2 M12
2 (y-l)
STATIC DENSITY RATIO ACROSS A
NORMAL SHOCK
(t) P2 == (P2
) (TI)PI PI T2
MACH ANGLE VS MACH NUMBER (SEE PAGE 255)
• 1 1
a=slO-
M
Equations marked (t) are valid for M > 1.0.only.
ix
7. FUNCTIONAL RELATIONSHIPS
The functions N, D, Fe, Fe :.' and F1P arepa.t#cu1arly
useful for solutions of one-dimensional steady Bow prob
lems. The continuity equation between any two stations,
1 and 2, for a calorically imperfect gas may be written as,
VYl PT1 At Dl - VY2 PT2 A2 D2
Rl y~ - R2 yTT2
For a calorically perfect gas,
PT1 Al Dl _ ,PT2 A2 D2
~- yTT2
or
For adiabatic Bow,
PTI Al Dl = 'PT2 A2 D2
or
FINI = F2N2
For isentropic Bow,
AlDl =A2 D 2
Stream thrust or vacuum thrust is defined as,
F=PA+mV
or in terms of the stream thrust coefficient Fs,
F=PTAFs
Similarly in terms of the vacuum thrust coefficient Fs ~
A·'
The reaction on the gas between any two stations 1 and
2is
R = PT2 A2 FS2 - PTI Al FSI
The ideal thrust of a nozzle is defined as,
F1P =mV
which is identical to the thrust,
Fg=mV + (Pe-PA ) Ae
when
PA = Pe = NOZZLE EXIT PRESSURE
For heat addition in a constant area duct between sta
qons 1 and 2,
N1 Nl-3
YTTI = y'T;;
where N1-2 is obtained for an average gamma between
stations 1 and 2.
Mixing of p.allel streams in a constant .ea duct. Given
n streams, the conditions after mixing, denoted by sub
script f, may be found by applying the continuity, mo
mentum and energy equations.
COQt•. _~q:
PTiA1D1
VY. P,..A.O. = 1:VYl
Rt yTTi i=l Rl yTTl
Momentum eq:
l=n
PTf At Fst = EPTl Ai FSi
1=1
Energy eq: (assuming constant sl'eciDc heats)
i=n
mtTTt= EmiTTi
i=l
Combining these equations yields the following expres
sion for the mixed Mach number,
Nt = iti ~i~ ymlTT1/!~; VTTIYtRi
i~ i'=t i'=t Yl Rt1
For the case of two streams, denoted by subscripts 1
and 2, and a constant gamma, this expression reduces to
[(~ + 1 ) (m2 TT2 + 1 )] *
Nt = ~_m_l____m_I=T=T=l=--____
Nl m2 NI VTT2 + 1
ml N2 TTl
Station., Normal Shock
Let subscript 1 and 2 refer to conditions before and
after a. normal shock respectively; then, since the Bow
is adiabatic
Vy, P",O, =V y. p...O.
Rl Rs
Hence
x
8. REFERENCES
1. uEqua.tions, Tables and Charts for Compressible Flow", N.A.C.A. Report 1135
2. Rudinger, G., uWave Diagrams for Nonsteady Flow in Ducts", D. Van Nostrand
Co., Inc., 1955
3. Foa, J. V., "Mach Number Functions For Ideal Diatomic Gas", Cornell Aero
nautical Laboratory, Inc., Oct. 1949
4. Shapiro, A. H., "The Dynamics and Thermodynamics of Compressible Fluid
Flow", Vol 1, The Ronald Press Co., 1953
5. Foa, J. V., "Theory of Propulsion In Air"~ Aeronautical Engineenng Dept.,
Rensselaer Polytechnic lost., 1958
6. Weatherson, R., tCMixing of Any Number of Streams In a Duct of Constant Cross
Sectional Area", Journal of the Aeronautical Sciences, Vol. 16, No. 11, Nov.
1949
7. "New Mach Number Tables for Ram-Jet Flow Analysis", OAL MEMO 50,
April 1952
xi
9.
10. TABLES OF MACH NUMBER FUNCTIONS FOR STEADY
AND NONSTEADY, INVISCID, COMPRESSIBLE FLOW
y = 1.10, 1.15, 1.20, 1.25, 1.286
1.30, 1.35, 1.40, 1.667
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