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Scilab Textbook Companion for

Gas Dynamics and Jet Propulsion

by P. Murugaperumal1

Created byBathini Maheswara Reddy

B.TechMechanical Engineering

SASTRA UNIVERSITYCollege Teacher

Prof. D. VenkatesanCross-Checked by

Chaitanya

June 8, 2014

1Funded by a grant from the National Mission on Education through ICT,http://spoken-tutorial.org/NMEICT-Intro. This Textbook Companion and Scilabcodes written in it can be downloaded from the ”Textbook Companion Project”section at the website http://scilab.in


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Book Description

Title: Gas Dynamics and Jet Propulsion

Author: P. Murugaperumal

Publisher: Scitech Publications, Chennai

Edition: 1

Year: 2005

ISBN: 8188429937

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Scilab numbering policy used in this document and the relation to theabove book.

Exa Example (Solved example)

Eqn Equation (Particular equation of the above book)

AP Appendix to Example(Scilab Code that is an Appednix to a particularExample of the above book)

For example, Exa 3.51 means solved example 3.51 of this book. Sec 2.3 meansa scilab code whose theory is explained in Section 2.3 of the book.

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Contents

List of Scilab Codes 4

1 Compressible Flow Fundamentals 12

2 Flow through Variable Area Ducts 46

3 Flow Through Constant Area Duct Adiabatic Flow 74

4 Flow Through Constant Area Ducts Rayleigh Flow 104

5 Normal and Oblique Shock 124

6 Aircraft Propulsion 170

7 Rocket Propulsion 195

8 Two Marks Questions and Answers 209

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List of Scilab Codes

Exa 1.1 To calculate the work done . . . . . . . . . . . . . . . 12Exa 1.2 To calculate heat transfer internal energy change and

work done . . . . . . . . . . . . . . . . . . . . . . . . . 13Exa 1.3 To determine temperature enthalpy drop and internal

energy change . . . . . . . . . . . . . . . . . . . . . . 14Exa 1.4 To determine properties at outlet and area ratio of dif-

fuser . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Exa 1.5 To determine static pressure and axial force of turbojet

engine . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Exa 1.6 To determine mach number at a point . . . . . . . . . 17Exa 1.7 To find direction of flow . . . . . . . . . . . . . . . . . 17Exa 1.8 To calculate the bulk modulus . . . . . . . . . . . . . 18Exa 1.9 To calculate mass of water to be pumped to obtain de-

sired pressure . . . . . . . . . . . . . . . . . . . . . . . 19Exa 1.10 To find sonic velocity . . . . . . . . . . . . . . . . . . 20Exa 1.11 To find velocity of sound . . . . . . . . . . . . . . . . 20Exa 1.12 To find highest pressure acting on surface of a body . 22Exa 1.13 To find air velocity for different types of flow . . . . . 22Exa 1.14 To find number of nozzles . . . . . . . . . . . . . . . . 23Exa 1.15 To find properties of a gas in vessel at a point . . . . . 24Exa 1.16 To find mach number and velocity of flow . . . . . . . 25Exa 1.17 To find distance covered before sonic boom is heard on

ground . . . . . . . . . . . . . . . . . . . . . . . . . . 25Exa 1.18 To calculate time elapsed to feel disturbance due to air-

craft . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Exa 1.19 To find mach number at a point . . . . . . . . . . . . 27Exa 1.20 To find Mach number . . . . . . . . . . . . . . . . . . 28Exa 1.21 To find speed of sound and Mach number . . . . . . . 28

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Exa 2.11 To find properties at throat and test section mass flow

rate and Power required in nozzle of wind tunnel . . . 59Exa 2.12 To find cross section at throat and exit . . . . . . . . . 60Exa 2.13 To find ratio of areas velocity and back pressure in CD

nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . 62Exa 2.14 To find how duct acts . . . . . . . . . . . . . . . . . . 63Exa 2.15 To find mass flow rate static and stagnation conditions

and entropy change of subsonic diffuser . . . . . . . . 63Exa 2.16 To find throat area reservoir conditions and mass flow

rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65Exa 2.17 To find throat conditions ratio of velocities and mass

flow rate . . . . . . . . . . . . . . . . . . . . . . . . . 66

Exa 2.18 To find mass flow rate and exit conditions . . . . . . . 67Exa 2.19 To find mach number change in stagnation pressure en-

tropy change and static temperature and efficiency of nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

Exa 2.20 To find pressure rise coefficient and ratio of area . . . 70Exa 2.21 To find area at throat and exit Mach number total pres-

sure loss and entropy change . . . . . . . . . . . . . . 71Exa 2.22 To find required throat and exit area of nozzle . . . . 72Exa 3.1 To find length of pipe . . . . . . . . . . . . . . . . . . 74Exa 3.2 To find length of required duct and length required to

obtain critical condition . . . . . . . . . . . . . . . . . 75Exa 3.3 To find length of pipe and mass flow rate . . . . . . . 76Exa 3.4 To find temperature velocity at a section and distance

between two sections . . . . . . . . . . . . . . . . . . . 77Exa 3.5 To find length of pipe and properties of air at exit . . 78Exa 3.6 To find mach number properties at a section and critical

section and length of the duct . . . . . . . . . . . . . 80Exa 3.7 TO find final pressure and velocity of duct . . . . . . 82Exa 3.8 To find inlet mach number mass flow rate and exit tem-

perature . . . . . . . . . . . . . . . . . . . . . . . . . 83Exa 3.9 To find length diameter of the duct pressure at exit Stag-

nation pressure lose and to verify exit mach number . 84Exa 3.10 To find length of the pipe Mach number percent of stag-

nation pressure loss and length required to reach chokingcondition . . . . . . . . . . . . . . . . . . . . . . . . . 86

Exa 3.11 To find length of the pipe and mass flow rate . . . . . 87

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Exa 3.12 To find length and Mach number of given pipe and at

required section . . . . . . . . . . . . . . . . . . . . . 88Exa 3.13 To find length of the pipe percent of stagnation pressurechange and entropy change . . . . . . . . . . . . . . . 89

Exa 3.14 To find maximum length of pipe and conditions of airat exit . . . . . . . . . . . . . . . . . . . . . . . . . . 91

Exa 3.15 To find Maximum and required length of the pipe andproperties of air at a section . . . . . . . . . . . . . . . 93

Exa 3.16 To find exit mach number and inlet temperature andpressure . . . . . . . . . . . . . . . . . . . . . . . . . . 95

Exa 3.17 To find Static and Stagnation conditions velocity lengthand mass flow rate of air in pipe . . . . . . . . . . . . 96

Exa 3.18 To find length of pipe and properties of air at a sectionand limiting mach number . . . . . . . . . . . . . . . . 98

Exa 3.19 To find diameter of pipe . . . . . . . . . . . . . . . . 100Exa 3.20 To determine required inlet conditions . . . . . . . . . 101Exa 3.21 To find mach number at sections and mean value of

friction . . . . . . . . . . . . . . . . . . . . . . . . . . 102Exa 4.1 To find heat transferred per unit mass flow and temper-

ature change . . . . . . . . . . . . . . . . . . . . . . . 104Exa 4.2 To calculate flow properties at the exit . . . . . . . . . 105Exa 4.3 To find mass flow rate per unit area Final temperature

and heat added per kg of air flow . . . . . . . . . . . . 107Exa 4.4 To calculate pressure and Mach number after combus-tion in combustion chamber . . . . . . . . . . . . . . 108

Exa 4.5 To find total temperature static pressure at exit Stag-nation pressure and exponent of polytropic equation . 109

Exa 4.6 To determine Mach number pressure temperature of gasat entry and amount of heat added and maximum heatcan be added . . . . . . . . . . . . . . . . . . . . . . 111

Exa 4.7 To determine Mach number pressure temperature andvelocity of gas at exit . . . . . . . . . . . . . . . . . . 112

Exa 4.8 To find Mach number pressure and temperature after

cooling . . . . . . . . . . . . . . . . . . . . . . . . . . 114Exa 4.9 To determine heat added per kg of air flow maximum

possible heat transfer and heat transfer required to getmaximum static temperature . . . . . . . . . . . . . . 115

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Exa 4.10 To find exit properties Maximum stagnation tempera-

ture percentage of pressure loss and initial mach number. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116Exa 4.11 To find Mach number and percentage drop in pressure 118Exa 4.12 To find inlet mach number and percentage loss in static

pressure . . . . . . . . . . . . . . . . . . . . . . . . . . 119Exa 4.13 To find inlet and exit mach number . . . . . . . . . . 120Exa 4.14 To find properties at exit and sonic condition and heat

required to accelerate gas from inlet to sonic condition 121Exa 5.1 To find Mach number before shock properties after shock

density increase loss of stagnation pressure and entropychange of air in pipe . . . . . . . . . . . . . . . . . . . 124

Exa 5.2 To find properties across normal shock and entropy change 125Exa 5.3 To find properties downstream of shock . . . . . . . . 127Exa 5.4 To find velocities across shock and stagnation pressure

change . . . . . . . . . . . . . . . . . . . . . . . . . . 128Exa 5.5 To find properties downstream of shock . . . . . . . . 129Exa 5.6 To find pressure acting on front of the body . . . . . . 130Exa 5.7 To find mass flow rate and properties at exit of CD nozzle 130Exa 5.8 To find properties upstream of wave front . . . . . . . 133Exa 5.9 To find properties downstream of shock total head pres-

sure ratio entropy change strength of shock . . . . . . 134

Exa 5.10 To determine Mach number across shock and area atshock . . . . . . . . . . . . . . . . . . . . . . . . . . . 135Exa 5.11 To find Mach number across shock Static pressure and

area at shock . . . . . . . . . . . . . . . . . . . . . . . 136Exa 5.12 To find properties at various sections . . . . . . . . . . 137Exa 5.13 To find mass flow rate and properties at throat and exit

at various sections of CD nozzle . . . . . . . . . . . . 139Exa 5.14 To estimate the difference in mercury in limbs of U tube

manometer at various velocities . . . . . . . . . . . . 146Exa 5.15 To estimate Mach number and properties across the nor-

mal shock of tube . . . . . . . . . . . . . . . . . . . . 147

Exa 5.16 To find Mach number and velocity in pitot tube . . . . 148Exa 5.17 To find shock speed and air velocity inside the shock . 149Exa 5.18 To compute speed of wave pressure and temperature of

air at rest . . . . . . . . . . . . . . . . . . . . . . . . 150

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Exa 5.19 To find Mach number pressure temperature at exit and

diffuser efficiency . . . . . . . . . . . . . . . . . . . . 151Exa 5.20 To find length of duct across shock mass flow rate en-tropy change across and downstream of shock . . . . . 153

Exa 5.21 To find length across the shock properties of air at exitand mass flow rate through the duct . . . . . . . . . . 156

Exa 5.22 To find properties after shock and exit and exit Machnumber . . . . . . . . . . . . . . . . . . . . . . . . . . 158

Exa 5.23 To find length diameter of pipe and properties at pipeexit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

Exa 5.24 To estimate amount of heat added in two pipe sectionand properties . . . . . . . . . . . . . . . . . . . . . . 161

Exa 5.25 To find deflection angle Downstream Mach number Staticpressure and total pressure loss through the shock . . 164

Exa 5.26 To determine static pressure temperature behind waveMach number and Wedge angle . . . . . . . . . . . . 165

Exa 5.27 To find property ratios at strong and weak shock atwedge . . . . . . . . . . . . . . . . . . . . . . . . . . 166

Exa 5.28 To find deflection angle final Mach number and temper-ature of gas . . . . . . . . . . . . . . . . . . . . . . . 168

Exa 6.1 To calculate thrust and specific thrust of jet propulsion 170Exa 6.2 To find thrust developed thrust power and propulsive

efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 172Exa 6.3 To determine specific thrust and thrust specific fuel con-sumption for turbojet engine . . . . . . . . . . . . . . 173

Exa 6.4 To estimate properties at exit and propulsive efficiencyof a turbojet aircraft . . . . . . . . . . . . . . . . . . 175

Exa 6.5 To calculate absolute velocity drag overall and turbineefficiency of jet . . . . . . . . . . . . . . . . . . . . . 176

Exa 6.6 To Calculate propulsive and thrust power total fuel con-sumption and propulsive thermal and overall efficiency 177

Exa 6.7 To find specific thrust jet velocity TSFC and propulsivethermal and overall efficiency . . . . . . . . . . . . . . 179

Exa 6.8 To calculate fuel air and pressure ratios and Mach num-ber of jet . . . . . . . . . . . . . . . . . . . . . . . . . 180

Exa 6.9 To determine air flow rate thrust power thrust producedspecific thrust and specific impulse . . . . . . . . . . 181

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Exa 6.10 To calculate pressure rise pressured developed by com-

pressor and air standard efficiency of the engine . . . . 182Exa 6.11 To estimate diameter power output AFR and absolutevelocity of the jet . . . . . . . . . . . . . . . . . . . . 184

Exa 6.12 To determine jet velocity thrust specific thrust TSFCthrust power and efficiencies . . . . . . . . . . . . . . 185

Exa 6.13 To jet velocity fuel rate TSFC propulsive power andefficiencies . . . . . . . . . . . . . . . . . . . . . . . . 186

Exa 6.14 To find absolute jet velocity volume of air compresseddiameter power output and air fuel ratio of the jet . . 187

Exa 6.15 To estimate AFR nozzle thrust propeller thrust andmass flow rate . . . . . . . . . . . . . . . . . . . . . . 188

Exa 6.16 To find various parameters of ramjet engine through outits operation . . . . . . . . . . . . . . . . . . . . . . . 190

Exa 6.17 To find power input power output Fuel air ratio ExitMach number thrust and thrust power developed in the

jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192Exa 7.1 To find thrust of the motor of a rocket . . . . . . . . . 195Exa 7.2 To calculate area ratio thrust characteristic velocity thrust

coefficient exit velocity and possible maximum velocity 196Exa 7.3 To estimate thrust per unit area and specific impulse 197Exa 7.4 To find specific impulse specific propellant consumption

effective and absolute jet velocity of rocket . . . . . . 198Exa 7.5 To find propulsive efficiency thrust and thrust power of rocket . . . . . . . . . . . . . . . . . . . . . . . . . . 199

Exa 7.6 To find velocity and maximum height that rocket willreach . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

Exa 7.7 To determine thrust coefficient propellant weight flowcoefficient SPC and characteristic velocity of rocket . 201

Exa 7.8 To find various parameters of rocket projectile duringits operation . . . . . . . . . . . . . . . . . . . . . . . 202

Exa 7.9 To propulsive power engine output and efficiencies . . 203Exa 7.10 To find thrust specific impulse and efficiencies . . . . 204

Exa 7.11 To find specific impulse SPC effective and actual jetvelocity and efficiencies . . . . . . . . . . . . . . . . . 204

Exa 7.12 To find propellant flow rate thrust developed and heightattained during powered and coasting flights . . . . . 206

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Exa 7.13 To find effective jet velocity mass ratio and propellant

mass fraction maximum slight speed Altitude gain dur-ing powered and coasting flights . . . . . . . . . . . . 207Exa 7.14 To find orbital and escape velocities of a rocket . . . . 208Exa 8.1.34 To find Mach angle . . . . . . . . . . . . . . . . . . . 209Exa 8.1.35 To find values of back pressure . . . . . . . . . . . . . 210Exa 8.1.37 To find temperature at nose of aircraft . . . . . . . . 210Exa 8.1.38 To determine stagnation pressure and stagnation tem-

perature . . . . . . . . . . . . . . . . . . . . . . . . . 211Exa 8.1.39 To calculate bulk modulus of elasticity of a liquid . . 212Exa 8.1.40 To find highest possible velocity . . . . . . . . . . . . 212Exa 8.3.10 To find the length of the pipe . . . . . . . . . . . . . 213

Exa 8.3.15 To find length of the pipe to achieve deceleration . . . 213Exa 8.3.31 To find maximum possible amount of heat transfer of

combustion chamber . . . . . . . . . . . . . . . . . . 214Exa 8.3.32 To find increase in specific entropy of the fluid . . . . 214Exa 8.3.33 To pipe maximum heat transfer in a pipe . . . . . . . 215Exa 8.5.16 To find pressure acting on the front of the body . . . . 216Exa 8.5.17 To find strength of shock wave . . . . . . . . . . . . . 216Exa 8.5.20 To find irreversibility of duct . . . . . . . . . . . . . . 217Exa 8.5.21 To find mach number and air velocity of pitot tube . 217Exa 8.5.22 To find properties downstream of the shock . . . . . . 218

Exa 8.6.41 To find propulsive efficiency for an optimum thrust power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219Exa 8.6.42 To find propulsive efficency . . . . . . . . . . . . . . . 219Exa 8.7.42 To find thrust of the rocket . . . . . . . . . . . . . . . 220Exa 8.7.44 To find the thrust developed . . . . . . . . . . . . . . 221Exa 8.7.45 To find the jet velocity of a rocket . . . . . . . . . . . 221Exa 8.7.46 To calculate thrust propulsive efficiency and thrust power

of a rocket . . . . . . . . . . . . . . . . . . . . . . . . 222Exa 8.7.47 To determine orbital velocity and escape velocity of a

rocket . . . . . . . . . . . . . . . . . . . . . . . . . . 222Exa 8.7.48 To determine propulsive efficiency and propulsive power

of a rocket . . . . . . . . . . . . . . . . . . . . . . . . 223

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Chapter 1

Compressible Flow

Fundamentals

Scilab code Exa 1.1 To calculate the work done

1 clc

2 clear

3

4 / / I n p ut d at a5 m = 0 . 7 5 // Mass o f a i r i n kg6 T 1 = 8 0 0 / / I n t i a l T em pe ra tu re i n K7 P 1 = 4 0 0 / / I n i t i a l P r e s s u r e i n kPa8 P 2 = 1 5 0 / / F i n a l P r e s s u r e i n kPa9 k = 1 . 4 / / A d i a b a ti c c o n s t a n t

10 R = 0 . 2 8 7 / / S p e c i f i c Gas c o n st a n t i n J /kg−K11

12 / / C a l c u l a t i o n13 p 1 = P 2 / P 1 // p r e s s u r e r a t i o o f p r oc e ss14 T 2 = T 1 * p 1 ^ ( ( k - 1 ) / k ) / / F i n a l t e mp e r at u r e i n K

15 W = ( ( m * R * ( T 1 - T 2 ) ) / ( k - 1 ) ) / / Wo rk do ne i n k J1617 //P−V Di agr am18 s c f ( )

19 c l f ( )

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20 V 1 = ( ( ( m * R * T 1 ) / P 1 ) ^ ( 1 / k ) ) * 1 0 ^ 3 / / I n l e t volume i n c c

21 V 2 = ( ( ( m * R * T 2 ) / P 2 ) ^ ( 1 / k ) ) * 1 0 ^ 3 / / F i n a l vo lu me i n c c22 V = V 1 :( V2 - V 1 ) / 10 0: V 2 / / R e p r e s e n t i n g v ol um e o ngraph , a d i a b a t i c e xp a ns i on

23 P = P1 * V1 ^ k ./ V ^k / / R e p r e se n t i n g p r e s s u r e on g ra ph24 plot (V , P ) / / P l o t t i n g25 l e g e n d ( ’ P∗Vˆk=C ’ ) / / D e f i n i n g c u r v e26 xtitle ( ”PV Diagram” , ”V ( cc ) ” , ” P ( k P a ) ” ) / / T i t l e s

o f a xe s27

28 //Output29 printf ( ’ W orkdone i s %3 . 2 f k J ’ ,W )

Scilab code Exa 1.2 To calculate heat transfer internal energy change andwork done

1 clc

2 clear

3

4 / / I n p ut d at a

5 V 1 = 0 . 3 5 / / Volume o f g a s i n mˆ 36 P 1 = 1 1 0 / / I n i t i a l P r e s s u r e i n kPa7 T 1 = 3 0 0 / / I n t i a l T em pe ra tu re i n K8 P 2 = 6 0 0 // F i n a l P r e s s u r e i n kPa , m i s s i n g d at a9 k = 1 . 4 / / A d i a b a ti c c o n s t a n t

10 C v = 7 1 8 // S p e c i f i c h ea t a t c o n st a n t volume i n J /kg−K11 R = 2 8 7 / / S p e c i f i c Gas c o n st a n t i n J /kg−K12

13 / / C a l c u l a t i o n14 d Q = 0 // Heat t r a n s f e r i n J , S i nc e A di a ba t i c p r o c e s s

15 m = ( P 1 * 1 0 ^ 3 * V 1 ) / ( R * T 1 ) // Mass o f a i r i n kg16 p 1 = P 2 / P 1 // P r e ss u r e r a t i o17 T 2 = T 1 * p 1 ^ ( ( k - 1 ) / k ) / / F i n a l t e mp e r at u r e i n K18 d U = ( m * C v * ( T 2 - T 1 ) ) * 1 0 ^ - 3 // Change i n i n t e r n a l e ne rg y

i n kJ

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19 d W = - d U / / W ork do ne i n kJ , S i n c e dQ=0

2021 //P−V Di agr am22 s c f ( )

23 c l f ( )

24 V 1 c c = V 1 * 1 0 ^ 3 / / I n l e t volume i n c c25 V 2 c c = V 1 c c * ( T 2 / T 1 ) ^ ( 1 / ( k - 1 ) ) / / F i n a l vo lu me i n c c26 V = V 1 cc : ( V 2 cc - V 1 c c ) / 1 00 : V 2 c c / / R e p r e s e n t i n g

v ol ume on g ra ph , a d i a b a t i c e x p an s i o n27 P = P 2 * V1 cc ^ k . / V^ k / / R e p r e s en t i n g p r e s s u r e on g ra ph28 plot (V , P ) / / P l o t t i n g29 l e g e n d ( ’ P∗Vˆk=C ’ ) / / D e f i n i n g c u r v e

30 xtitle ( ”PV Diagram” , ”V ( cc ) ” , ” P ( k P a ) ” ) / / T i t l e so f a xe s

31

32 //Output33 printf ( ’ (A) H eat t r a n s f e r i s %3i J\n ( B) C h an ge i n

i n t e r n a l e ne rg y i s %3 . 3 f kJ\n ( C) W orkdone i s %3 . 3f kJ\n ’ , d Q , d U , d W )

Scilab code Exa 1.3 To determine temperature enthalpy drop and internalenergy change

1 clc

2 clear

3

4 / / I n p ut d at a5 P 1 = 3 . 2 / / I n i t i a l P r e s s u r e i n b a r6 P 2 = 1 / / F i n al P r e ss u r e i n b ar7 T 1 = 4 7 5 / / I n i t i a l t e m p e r a t u r e i n K

8 M o l = 4 4 // M o l ec u l ar w e ig h t o f c a r b o n d i o x i d e i n kg / mol9 R i = 8 3 1 4 / / I d e a l g as c o n st a n t i n J /mol−K10 k = 1 . 3 / / A d i a b a ti c c o n s t a n t11

12 / / C a l c u l a t i o n

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13 R = R i / M o l // S p e c i f i c g as c on s ta n t i n J /kg−K

14 C p = ( k * R ) / ( k - 1 ) // S p e c i f i c h ea t c a p ac i t y a t c o ns t a n tp r e s s ur e i n J /kg−K15 C v = C p / k / / S p e c i f i c h ea t c a pa c i ty a t c on s ta n t volume

i n J /kg−K16 p 1 = P 2 / P 1 // P r e ss u r e r a t i o17 T 2 = T 1 * p 1 ^ ( ( k - 1 ) / k ) / / F i n a l T e m p er a t u re18 d h = C p * ( T 1 - T 2 ) * 1 0 ^ - 3 / / E nt ha lp y d ro p i n kJ / kg19 d U = C v * ( T 2 - T 1 ) * 1 0 ^ - 3 // Change i n i n t e r n a l e ne rg y i n

kJ/ kg , −ve s i g n i n d i c a t e s l o s s20

21 //Output

22 printf ( ’ ( A) T e m p er a t u r e i s %3 . 3 f K\n ( B) E n t ha l p y d r opi s %3 . 3 f kJ / kg\n (C) Change i n i n t e r n a l e ne rg y i s

%3 . 2 f k J / kg i . e . %3 . 2 f k J / kg ( l o s s ) ’ , T 2 , d h , d U , abs( d U ) )

Scilab code Exa 1.4 To determine properties at outlet and area ratio of diffuser

1 clc2 clear

3

4 / / I n p ut d at a5 P 1 = 0 . 5 / / I n i t i a l P r e s s u r e i n b a r6 T 1 = 5 0 + 2 7 3 / / I n t i a l T em pe ra tu re i n K7 C 1 = 2 4 0 / / I n l e t v e l o c i t y i n m/ s8 C 2 = 1 2 0 / / O ut l et v e l o c i t y i n m/ s , m i s s in g d at a9 C p = 1 0 0 5 // S p e c i f i c h ea t c a pa c i ty a t c on s ta n t

p r e s s ur e i n J /kg−K

10 k = 1 . 4 / / A d i a b a ti c c o n s t a n t1112 / / C a l c u l a t i o n13 T 2 = T 1 + ( ( C 1 ^ 2 - C 2 ^ 2 ) / ( 2 * C p ) ) / / F i n a l T em pe ra tu re i n K14 t 1 = T 2 / T 1 // T e m pe ra tu re r a t i o

15


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15 P 2 = P 1 * t 1 ^ ( k / ( k - 1 ) ) // F i n al P r e s su r e i n b ar

16 a r = ( P 1 * T 2 * C 1 ) / ( P 2 * T 1 * C 2 ) // R a ti o o f o u t l e t t o i n l e ta r e a17

18 //Output19 printf ( ’ (A) A t o u t l e t : \ n T empe r at ure i s %3 . 2 f K\n

P r e s su r e i s %3 . 4 f b ar \n (B) R at io o f o u t l e t t oi n l e t a re a i s %3 . 4 f ’ , T 2 , P 2 , a r )

Scilab code Exa 1.5 To determine static pressure and axial force of tur-bojet engine

1 clc

2 clear

3

4 / / I n p ut d at a5 m = 2 5 // Mass f lo w r a t e o f a i r i n kg / s6 C 2 = 1 1 5 / / O ut l et v e l o c i t y i n m/ s7 P 1 = 1 0 0 / / / / I n i t i a l P r e s s u r e i n kPa8 T 1 = 3 0 0 / / I n t i a l T em pe ra tu re i n K

9 C 1 = 4 0 / / I n l e t v e l o c i t y i n m/ s10 R = 0 . 2 8 7 / / S p e c i f i c g as c o ns t a n t i n kJ /kg−K11 C p = 1 0 0 5 // S p e c i f i c h ea t c a pa c i ty a t c on s ta n t

p r e s s ur e i n J /kg−K12 k = 1 . 4 / / A d i a b a ti c c o n s t a n t13

14 / / C a l c u l a t i o n15 T 2 = T 1 + ( ( C 1 ^ 2 - C 2 ^ 2 ) / ( 2 * C p ) ) / / F i n a l T em pe ra tu re i n K16 t 1 = T 2 / T 1 // T e m pe ra tu re r a t i o17 P 2 = P 1 * t 1 ^ ( k / ( k - 1 ) ) // F i n al P r e s su r e i n b ar

18 A 1 = ( m * R * T 1 ) / ( P 1 * C 1 ) // Area a t i n l e t i n mˆ219 A 2 = ( m * R * T 2 ) / ( P 2 * C 2 ) // Area a t o u t l e t i n mˆ220 F = ( ( P 1 * A 1 ) - ( P 2 * A 2 ) ) + ( m * ( C 1 - C 2 ) ) * 1 0 ^ - 3 / / A x i a l f o r c e

on m o u t h p ie c e r e s u l t i n g from a c c e l e r a t i o n o f a i ri n kN

16


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21

22 //Output23 printf ( ’ (A) S t a t i c p r e s s ur e a t i n t ak e f a c e i s %3 . 3 f kPa\n (B) M ag ni tu de o f a x i a l f o r c e on m o ut hp ie cer e s u l t i n g from a c c e l e r a t i o n o f a i r i s %3 . 3 f kN ’ ,P 2 , F )

Scilab code Exa 1.6 To determine mach number at a point

1 clc2 clear

3

4 / / I n p ut d at a5 P = 2 0 0 / / P r e s s u r e i n kPa6 C = 5 0 // V e l oc i t y o f a i r i n m/ s7 d = 2 . 9 / / D e n s i t y i n k g /mˆ 38 M o l = 3 2 / / M o l ec u l ar w e ig h t o f o xy ge n i n kg / mol9 k = 1 . 4 / / A d i a b a ti c c o n s t a n t

10 R i = 8 3 1 4 / / I d e a l g as c o n st a n t i n J /mol−K11

12 / / C a l c u l a t o r13 R = R i / M o l // S p e c i f i c g as c on s ta n t i n J /kg−K14 T = P * 1 0 ^ 3 / ( R * d ) / / T e mp er at ur e i n K15 a = sqrt ( k * R * T ) // V e l o c i t y o f s ou nd i n m/ s16 M = C / a //Mach number17

18 //Output19 printf ( ’ Mach n um be r i s %3 . 2 f ’ ,M )

Scilab code Exa 1.7 To find direction of flow

1 clc

2 clear

17


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3

4 / / I n p ut d at a5 P a = 1 . 3 // P r e s su r e a t s e c t i o n −A i n ba r6 T a = 5 0 + 2 7 3 // T e mp er at ur e a t s e c t i o n −A i n K7 P b = 1 / / P r e s su r e a t s e c t i o n −B i n b ar8 T b = 1 3 + 2 7 3 // T e mp er at ur e a t s e c t i o n −B i n K9 C p = 1 0 0 5 // S p e c i f i c h ea t c a pa c i ty a t c on s ta n t

p r e s s ur e i n J /kg−K10 R = 2 8 7 // S p e c i f i c g as c o ns t an t i n J /kg−K11

12 / / C a l c u l a t i o n13 d s = ( ( C p * log ( T b / T a ) ) - ( R * log ( P b / P a ) ) ) * 1 0 ^ - 3 //The

c ha ng e i n t he e nt ro py i s kJ /kg14 / /+ve s i g n i n d i c a t e s A t o B15 //−ve s i g n i n d i c a t e s B t o A16

17 //Output18 printf ( ’ The c ha ng e i n t he e nt ro p y i s %3 . 4 f kJ / kg\n

S i n ce v al ue i s −ve , p r o c e s s must t a k e s p l a c e fro mB t o A ’ , d s )

Scilab code Exa 1.8 To calculate the bulk modulus

1 clc

2 clear

3

4 / / I n p ut d at a5 V 1 = 8 / / I n t i a l v ol um e i n l i t r e6 V 2 = 7 . 8 / / F i n a l v ol um e i n l i t r e7 P 1 = 0 . 7 / / I n t i a l P r e ss u r e i n MPa

8 P 2 = 2 . 7 / / F i n a l P r e s s u r e i n MPa910 / / C a l c u l a t i o n s11 K = ( P 2 - P 1 ) / ( log ( V 1 / V 2 ) ) // Bulk modulus o f l i q u i d i n

kPa

18


20/224

12

13 //Output14 printf ( ’ B ulk modulus o f l i q u i d i s %3 . 3 f kPa ’ ,K )

Scilab code Exa 1.9 To calculate mass of water to be pumped to obtaindesired pressure

1 clc

2 clear

34 / / I n p ut d at a5 V 1 = 0 . 5 / / Voume o f Water r e q u i r e d t o f i l l p r e s s u r e

v e s s e l i n mˆ36 P = 3 0 0 0 // T es t p r e s s ur e i n ba r7 d v = 0 . 6 // Change o f empty v ol um e o f c o n t a i n e r due t o

p r e s s u r i s a t i o n i n p e r c e nt ag e8 K = 2 0 0 0 0 / / Bu lk m od ul us o f w a te r i n MPa9

10 / / C a l c u l a t i o n11 m 1 = V 1 * 1 0 ^ 3 / / Mass o f w at er r e q u i r e d t o f i l l p r e s s u r e

v e s s e l i n kg12 V r = ( P * V 1 ) / K // R ed uc ed v ol um e o f w a te r d ue t o

c o m p r e s s i o n i n mˆ 313 V i = d v * V 1 / 1 0 0 / / I n c r e a s e d volume o f c o n t a i n e r i n mˆ314 V = V r + V i // Volume o f a d d i t i o n a l w at er r e q u i r e d i n mˆ315 m = V * 1 0 ^ 3 // Mass o f a d d i t i o n a l w a te r r e q ui r e d i n kg16 m t = m 1 + m // T ot al mass o f w at er r e q ui r e d i n l i t r e ,

S i n c e 1 k g=1 L i t17

18 //Output

19 printf ( ’ Mass o f w at er t o be pumped i n t o t he v e s e l t oo bt ai n t he d e s i r e d p r e s s u r e i s %3i l i t ’ , m t )

19


21/224

Scilab code Exa 1.10 To find sonic velocity

1 clc

2 clear

3

4 / / I n p ut d at a5 S G _ o i l = 0 . 8 // S p e c i f i c g r a v i t y o f c r ud e o i l6 K _ o i l = 1 5 3 0 3 6 * 1 0 ^ 4 / / B ul k m od ul us o f O i l i n N/mˆ 27 K _ h g = 2 6 4 8 7 0 0 * 1 0 ^ 4 / / B u lk m od ul us o f M er cu ry i n N/mˆ 28 d _ s t e e l = 7 8 6 0 / / D en s it y o f s t e e l i n kg /mˆ39 E _ s t e e l = 2 0 0 * 1 0 ^ 9 //M odulus of e l a s t i c i t y i n Pa

10 d _ h g = 1 3 6 0 0 / / D e n s i t y o f m er cu ry i n k g /mˆ 3

11 d _ w a t e r = 1 0 0 0 / / D e n s i t y o f w a te r i n kg /mˆ 312

13 / / C a l c u l a t i o n14 d _ o i l = S G _ o i l * d _ w a t e r / / D en s it y o f o i l i n kg /mˆ315 a _ o i l = sqrt ( K _ o i l / d _ o i l ) // S on i c v e l o c i t y o f c ru de

o i l i n m/ s16 a _ h g = sqrt ( K _ h g / d _ h g ) / / S on i c v e l o c i t y o f mer cury i n

m/ s17 a _ s t e e l = sqrt ( E _ s t e e l / d _ s t e e l ) / / S on ic v e l o c i t y o f

s t e e l i n m/ s18

19 //Output20 printf ( ’ (A) S on i c v e l o c i t y o f c ru de o i l i s %3 . 2 f m/ s \

n (B) S o ni c v e l o c i t y o f me rcu ry i s %3 . 2 f m/ s \n (A)S on ic v e l o c i t y o f s t e e l i s %3 . 1 f m/ s \n ’ , a _ o i l ,a _ h g , a _ s t e e l )

Scilab code Exa 1.11 To find velocity of sound

1 clc

2 clear

3


20


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5 T = 2 0 + 2 7 3 / / T e m pe r ar t ur e o f medium i n K

6 C p _ f r = 6 7 8 // S p e c i f i c h ea t c a p ac i t y a t c o ns t a n tp r e s s u r e o f f r e o n i n J /kg−K7 C v _ f r = 5 4 3 // S p e c i f i c h ea t c a p ac i t y a t c o ns t a n t

v ol im e o f f r eo n i n J / kg−K8 T _ a i r = 0 + 2 7 3 // T em pe ra tu re o f a i r i n K9 R i = 8 3 1 4 / / I d e a l g as c o n st a n t i n J /mol−K

10 m o l _ h = 2 / / M o l e c u l a r w e i g ht o f H yd ro ge n i n kg / m ol11 m o l _ w a t e r = 1 8 / / M o l ec u l a r w ei g ht o f w at er i n kg / mol12 R _ a i r = 2 8 7 // S p e c i f i c g a s c on st an t o f a i r i n J / kg−K13 k = 1 . 4 / / A d i a b a ti c c o n s t a n t o f h yd ro ge n14 k _ w a t e r = 1 . 3 / / A d i a b a t ic c o n s t a n t o f w at er

1516 / / C a l c u l a t i o n17 R _ h = R i / m o l _ h // S p e c i f i c g as c o ns t a n t o f h yd ro ge n i n

J /k g−K18 a _ h = sqrt ( k * R _ h * T ) // V e l o c i t y o f so un d i n h yd ro ge n i n

m/ s19 R _ w a t e r = R i / m o l _ w a t e r // S p e c i f i c g as c on s ta n t o f

w at er i n J / kg−K20 a _ w a t e r = sqrt ( k _ w a t e r * R _ w a t e r * T ) / / V e l o c i t y o f s ou nd

i n w at er v ap ou r i n m/ s21 k _ f r = C p _ f r / C v _ f r

/ / A d i ab a t ic c o n st a n t o f f e oa n22 R _ f r = C p _ f r - C v _ f r // S p e c i f i c g as c on st an t o f f r e o n i nJ/kg−K

23 a _ f r = sqrt ( k _ f r * R _ f r * T ) / / V e l oc i t y o f sound i n f r e o ni n m / s

24 a _ a i r = sqrt ( k * R _ a i r * T _ a i r ) // S on ic V e l o c i t y o f a i r a ti n m / s

25

26 //Output27 printf ( ’ (A) V e l o c i t y o f s ou nd i n h yd ro ge n i s %3 . 2 f m/

s \n (B) V e l o c i t y o f s oun d i n w at er v ap ou r i s %3 . 2 f

m/ s \n (C) V e l o c i t y o f so un d i n f r e o n i s %3 . 2 f m/ s\n (D) S on i c V e l oc i t y o f a i r a t %3i K i s %3 . 4 f m/ s’ , a _h , a _ w a t er , a _ fr , T _ a ir , a _ a i r )

21


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Scilab code Exa 1.12 To find highest pressure acting on surface of a body

1 clc

2 clear

3

4 / / I n p ut d at a5 M = 0 . 8 5 // Mach number6 P = 8 0 / / P r e s s u r e i n kPa7 k = 1 . 4 / / A d i a b a t i c C o n s ta n t8

9 / / C a l c u l a t i o n10 P o = P * ( 1 + ( ( ( k - 1 ) / 2 ) * M ^ 2 ) ) ^ ( k / ( k - 1 ) ) / / P r e s s u r e a c t i n g

on t he s u r f a c e o f t he body i n kPa11

12 //Output13 printf ( ’ The h i g h e s t p r e s s u r e a c ti n g on t h e s u r f a c e

o f t h e body i s %3 . 1 f kPa ’ , P o )

Scilab code Exa 1.13 To find air velocity for different types of flow

1 clc

2 clear

3

4 / / I n p ut d at a5 P = 9 6 / / P r e s s u r e i n kPa6 T = 2 7 + 2 7 3 / / T e mp er at ur e i n K7 d P = 3 2 // D i f f e r e n c e b et w ee n p i v o t and s t a t i c p r e s s ur e

8 k = 1 . 4 / / A d i a b a t i c C o n s ta n t9 R = 2 8 7 / / S p e c i f i c Gas c o n st a n t i n J /kg−K

10

11 / / C a l c u l a t i o n12 d = ( P * 1 0 ^ 3 ) / ( R * T ) / / D e n s i t y i n k g /mˆ 3

22


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13 Ci = sqrt ( ( 2 * ( d P * 1 0 ^ 3 ) ) / d ) // V e l o c i t y o f

i n c o m pr e s s i b l e f l o w i n m/ s14 p r = ( d P ) / P // P r e s su r e r a t i o15 p 1 = p r + 1 // S ta gn at i o n t o s t a t i c p r e s s u r e r a t i o16 M = sqrt ( ( ( p 1 ^ ( ( k - 1 ) / k ) - 1 ) * 2 ) / ( k - 1 ) ) //Mach number17 C c = M * sqrt ( k * R * T ) // V e l oc i t y o f c o m pr e s si b l e f l o w i n

m/ s18

19 //Output20 printf ( ’ (A) A ir v e l o c i t y i n i n c o m pr e s s i b l e f l o w i s %3

. 1 f m/ s \n (B) A i r v e l o c i t y i f f lo w i s c o mp r es s i b l ei s %3 . 3 f m/ s ’ , C i , C c )

Scilab code Exa 1.14 To find number of nozzles

1 clc

2 clear

3

4 / / I n p ut d at a5 T 1 = 2 0 0 + 2 7 3 / / I n t i a l T em pe ra tu re i n K

6 P 1 = 1 . 7 / / I n i t i a l P r e s s u r e i n b a r7 P 2 = 1 / / F i n al P r e ss u r e i n b ar8 C 1 = 3 0 / / I n l e t v e l o c i t y i n m/ s9 m =1 // Mass f l o w r a t e i n kg / s

10 D = 0 . 0 2 5 / / N o zz l e d i a me t er i n m11 k = 1 . 4 / / A d i a b a t i c C o n s ta n t12 R = 2 8 7 / / S p e c i f i c Gas c o n st a n t i n J /kg−K13 C p = 1 0 0 5 // S p e c i f i c h ea t c a pa c i ty a t c on s ta n t

p r e s s ur e i n J /kg−K14

15 / / C a l c u l a t i o n16 p 1 = P 2 / P 1 // P r e ss u r e r a t i o17 T 2 = T 1 * p 1 ^ ( ( k - 1 ) / k ) / / F i n a l t e mp e r at u r e i n K18 E 1 = T 1 + ( C 1 ^ 2 / ( 2 * C p ) ) //LHS o f S te ad y f l o w e n er g y

e q u a t i o n

23


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19 C2 = sqrt ( ( E 1 - T 2 ) * 2 * C p ) // E x i t v e l o c i t y o f t h e a i r i n

m/ s20 d 2 = ( P 2 * 1 0 ^ 5 ) / ( R * T 2 ) / / D e ns i t y a t o u t l e t i n kg /mˆ 321 A 2 = % p i * D ^ 2 / 4 // Area a t o u t l e t i n mˆ222 n = ceil ( m / ( d 2 * A 2 * C 2 ) ) // Number o f n o z z l e s t o be u se d23

24 //Output25 printf ( ’ (A) E xi t v e l o c i t y o f t he a i r i s %3 . 2 f m/ s \n (

B) Number o f n o z z l e s t o be u se d a r e %1 . 0 f ’ , C 2 , n )

Scilab code Exa 1.15 To find properties of a gas in vessel at a point

1 clc

2 clear

3

4 / / I n p ut d at a5 P o = 3 0 0 // P r es s ur e i n t he v e s s e l i n kPa6 T o = 5 0 + 2 7 3 // T em pe ra tu re i n v e s s e l i n K7 M =1 //Mach number8 k = 1 . 6 6 7 / / A d i a b a ti c c o n s t a n t

9 R i = 8 3 1 4 / / I d e a l g as c o n st a n t i n J /mol−K10 M o l = 4 // M o l ec u l a r w ei g h t o f h el i um i n kg / mol11

12 / / C a l c u l a t i o n13 R = R i / M o l // S p e c i f i c g as c on s ta n t i n J /kg−K14 C p = ( k * R ) / ( k - 1 ) // S p e c i f i c h ea t c a p ac i t y a t c o ns t an t

p r e s s ur e i n J /kg−K15 p 1 = ( 2 / ( k + 1 ) ) ^ ( k / ( k - 1 ) ) // P r e s su r e r a t i o16 P t = P o * p 1 // P r es s ur e a t t e s t c o n d i t i o n i n kPa17 t 1 = ( 2 / ( k + 1 ) ) // T e m pe ra tu re r a t i o

18 T t = T o * t 1 // T emper at ur e a t t e s t c o n d i t i o n i n K19 at = sqrt ( k * R * T t ) / / V e l o c i t y o f s ou nd i n m/ s20 C t = a t // V e l o c it y o f g as a t t e s t c o n d i t i o n i n m/ s21 C m a x = sqrt ( 2 * C p * T o ) / /Maximum v e l o c i t y d ue t o

e xp an di ng o f g a s e s t hr ou gh n o z z l e s ys te m i n m/ s

24


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22

23 //Output24 printf ( ’ (A) At t e s t p o i n t :\ n P r e s s u r e i s %3 . 2 f kPa\n Te mper at ur e i s %3 . 2 f K\n V e l o c i t y i s %3. 1 f m/ s \n (B )Maximum v e l o c i t y d ue t o e x pa n d in g o f

g a s e s t hr ou gh n o z z l e s ys te m i s %3 . 2 f m/ s ’ , P t , T t ,C t , C m a x )

Scilab code Exa 1.16 To find mach number and velocity of flow

1 clc

2 clear

3

4 / / I n p ut d at a5 T = 4 0 + 2 7 3 / / T e mp er at ur e i n K6 p 1 = 0 . 5 // S t a t i c t o S t a g na t io n p r e s su r e r a t i o7 k = 1 . 6 7 / / A d i a b a t i c c o n s t a n t8 R i = 8 3 1 4 / / I d e a l g as c o n st a n t i n J /mol−K9 M o l = 3 9 . 9 4 / / M o l ec u l ar w e ig h t o f a r go n i n kg / mol

10

11 / / C a l c u l a t i o n12 R = R i / M o l // S p e c i f i c g as c on s ta n t i n J /kg−K13 p 2 = 1 / p 1 // P r e s su r e r a t i o14 M = sqrt ( ( ( p 2 ^ ( ( k - 1 ) / k ) - 1 ) * 2 ) / ( k - 1 ) ) //Mach number15 C = M * sqrt ( k * R * T ) / / V e l o ci t y i n t he f l ow i n m/ s16

17 //Output18 printf ( ’ ( A) M ach numbe r i s %3. 3 f \n (B) V e l o c i t y i n t he

f l o w i s %3 . 1 f m/ s ’ , M , C )

Scilab code Exa 1.17 To find distance covered before sonic boom is heardon ground

25


27/224

1 clc

2 clear3

4 / / I n p ut d at a5 M = 2 . 5 //Mach number6 h = 1 0 / / H e ig h t i n km7

8 / / C a l c u l a t i o n9 a l p = a s i n d ( 1 / M ) // Mach c on e a n g l e i n d e g r e e

10 d = 1 0 / t a n d ( a l p ) // D i s ta n ce t he j e t would c o ve r b e f o r ea s o n i c boom i s h ea rd on g ro un d i n km

11

12 //Output13 printf ( ’ D i s t a n ce t he j e t would c ov er b e f o r e a s o n i c

boom i s h ea rd on g ro un d i s %3 . 2 f km ’ ,d )

Scilab code Exa 1.18 To calculate time elapsed to feel disturbance due toaircraft

1 clc

2 clear3

4 / / I n p ut d at a5 h = 1 1 0 0 // H e ig ht i n m6 M 1 = 2 . 5 / /Mach number o f a i r c r a f t @h7 T = 2 8 0 // T e mpe r at ur e @h8 M 2 = 0 . 5 / /Mach nu mber o f o b s e r v e r9 k = 1 . 4 / / A d i a b a t i c C o n s ta n t

10 R = 2 8 7 // S p e c i f i c g as c o ns t an t i n J /kg−K11

12 / / C a l c u l a t i o n13 a l p = a s i n d ( 1 / M 1 ) // Mach c on e a n g l e i n d e g r e e14 a = sqrt ( k * R * T ) // V e l o c i t y o f s ou nd i n m/ s15 C 1 = M 1 * a // V e lo c i t y o f a i r c r a f t when t h e o b se r v e r i s

s t a t i o n a r y i n m/ s

26


28/224

16 t 1 = h / ( C 1 * t a n d ( a l p ) ) // Time e l a p s e d when t h e o b s e r v e r

i s s t a t i o n a r y i n s ec17 C 2 = ( M 1 - M 2 ) * a // V e l oc i t y o f a i r c r a f t when t heo b s e r v e r i s moving i n t h e d i r e c t i o n o f a i r c r a f ti n m / s

18 t 2 = h / ( C 2 * t a n d ( a l p ) ) // Time e l a p s e d when t h e o b s e r v e ri s moving i n t h e d i r e c t i o n o f a i r c r a f t i n s ec

19 C 3 = ( M 1 + M 2 ) * a // V e l oc i t y o f a i r c r a f t when t heo b se r v e r i s moving i n t h e o p po s i t e d i r e c t i o n i n m/ s

20 t 3 = h / ( C 3 * t a n d ( a l p ) ) // Time e l a p s e d when t h e o b s e r v e ri s moving i n t h e o p po s i t e d i r e c t i o n i n s e c

2122 //Output23 printf ( ’ (A) Time e l a p s e d when t h e o b s e r v e r i s

s t a t i o n a r y i s %3 . 3 f s e c \n ( B) Time e l a p s e d whent h e o b se r v e r i s moving i n t h e d i r e c t i o n o f a i r c r a f t w it h M=%3 . 1 f i s %3 . 2 f s e c \n ( C) Ti mee l a p s e d when t he o b s e r v er i s moving i n t heo p po s i t e d i r e c t i o n i s %3 . 2 f s e c \n ’ , t 1 , M 2 , t 2 , t 3 )

Scilab code Exa 1.19 To find mach number at a point

1 clc

2 clear

3

4 / / I n p ut d at a5 P = 2 0 0 / / P r e s s u r e i n kPa6 d = 2 . 9 / / D e n s i t y i n k g /mˆ 37 C = 5 0 / / V e l o c i t y i n m/ s

8 m o l = 3 2 / / M o l ec u l ar w e ig h t o f o xy ge n i n kg / mol9 k = 1 . 4 / / A d i a b a ti c c o n s t a n t10 R i = 8 3 1 4 / / I d e a l g as c o n st a n t i n J /mol−K11

12 / / C a l c u l a t i o n

27


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13 R = R i / m o l // S p e c i f i c g as C on st an t i n J /kg−k

14 T = ( P * 1 0 ^ 3 ) / ( R * d ) / / T e mp er at ur e i n K15 a = sqrt ( k * R * T ) // V e l o c i t y o f s ou nd i n m/ s16 M = C / a //Mach number17


Scilab code Exa 1.20 To find Mach number

1 clc

2 clear

3

4 / / I n p ut d at a5 C = 2 0 0 / / V e l o ci t y o f o b j e ct i n m/ s6 m o l = 4 // M o l ec u l a r w ei g h t o f h el i um i n kg / mol7 k = 1 . 6 7 / / A d i a b a t i c c o n s t a n t8 R i = 8 3 1 4 / / I d e a l g as c o n st a n t i n J /mol−K9 T = 2 8 8 / / T e mp er at ur e i n K

10

11 / / C a l c u l a t i o n12 R = R i / m o l // S p e c i f i c g as C on st an t i n J /kg−k13 a = sqrt ( k * R * T ) // V e l o c i t y o f s ou nd i n m/ s14 M = C / a //Mach number15


Scilab code Exa 1.21 To find speed of sound and Mach number

1 clc

2 clear

3

28


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5 Z 1 = 0 // H ei gh t fr om s ea l e v e l i n m6 Z 2 = 1 1 // H ei g ht from s ea l e v e l i n m7 T 1 = 2 8 8 / / T em pe ra tu re @Z1 i n K , f ro m g a s t a b l e s8 T 2 = 2 1 6 . 5 / / Te mp er at ur e @Z2 i n K , f ro m g a s t a b l e s9 C = 1 0 0 0 * ( 5 / 1 8 ) // V e l o c i t y i n m/ s

10 k = 1 . 4 / / A d i a b a t i c C o n s ta n t11 R = 2 8 7 // S p e c i f i c g as c o ns t an t i n J /kg−k12

13 / / C a l c u l a t i o n14 a1 = sqrt ( k * R * T 1 ) / / Sound v e l o c i t y @Z1 i n m/ s15 M 1 = C / a 1 // Mach number @Z1

16 a2 = sqrt ( k * R * T 2 ) / / Sound v e l o c i t y @Z2 i n m/ s17 M 2 = C / a 2 // Mach number @Z218

19 //Output20 printf ( ’ (A) S p ee d o f s o un d a t : \ n s e a l e v e l i s %3 . 2

f \n an a l t i t u d e o f %3i km i s %3 . 2 f m/ s\n (B)Mach numbeer at :\ n s e a l e v e l i s %3 . 2 f \n ana l t i t u d e o f %3i km i s %3 . 2 f ’ , a 1 , Z 2 , a 2 , M 1 , Z 2 , M 2 )

Scilab code Exa 1.22 To find maximum possible velocity of air

1 clc

2 clear

3

4 / / I n p ut d at a5 T = 3 0 0 + 2 7 3 / / S t a t i c T em pe ra tu re i n K6 C = 2 0 0 / / V e l o c i t y i n m/ s7 C p = 1 0 0 5 // S p e c i f i c h ea t c a pa c i ty a t c on s ta n t

p r e s s ur e i n J /kg−K89 / / C a l c u l a t i o n

10 T o = T + ( C ^ 2 / ( 2 * C p ) ) / / S t a g n a t i o n T em pe ra tu re i n K11 C _ m a x = sqrt ( 2 * C p * T o ) // Maximum p o s s i b l e v e l o c i t y

29


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o b ta i ne d by a i r i n m/ s

1213 //Output14 printf ( ’ Maximum p o s s i b l e v e l o c i t y o b ta i n ed by a i r i s

%3. 2 f m/ s ’ , C _ m a x )

Scilab code Exa 1.23 To find exit velocity of air

1 clc

2 clear3

4 / / I n p ut d at a5 d T = 3 7 // T em per at ur e d i f f e r e n c e b et we en a i r i n s i d e

t h e t y r e and n o z z l e e x i t6 C p = 1 0 0 5 // S p e c i f i c h ea t c a pa c i ty a t c on s ta n t


8 / / C a l c u l a t i o n9 C = sqrt ( 2 * C p * d T ) // E xi t v e l o c i t y o f a i r i n m/ s

10

11 //Output12 printf ( ’ E xi t v e l o c i t y o f a i r i s %3 . 1 f m/ s ’ ,C )

Scilab code Exa 1.24 To find static conditions and Flight Mach number

1 clc

2 clear

3

4 / / I n p ut d at a5 C = 8 0 0 * ( 5 / 1 8 ) / / V e l o c i t y i n m/ s6 P o = 1 0 5 / / S t ag n a ti o n p r e s s u r e i n kPa7 T o = 3 5 + 2 7 3 / / S t a g n a t io n t e m pe r a tu r e i n K

30


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8 C p = 1 0 0 5 // S p e c i f i c h ea t c a pa c i ty a t c on s ta n t

p r e s s ur e i n J /kg−K9 k = 1 . 4 / / A d i a b a t i c C o n s ta n t10 R = 2 8 7 // S p e c i f i c g as c o ns t an t i n J /kg−k11

12 / / C a l c u l a t i o n13 T = T o - ( C ^ 2 / ( 2 * C p ) ) / / S t a t i c t em p er at u re i n K14 P = P o * ( T / T o ) ^ ( k / ( k - 1 ) ) / / S t a t i c p r e s s ur e i n kPa15 a = sqrt ( k * R * T ) // Sound V e l o c i t y i n m/ s16 M = C / a //Mach number17

18 //Output

19 printf ( ’ (A) S t a t i c c o n d i t i o n s : \ n P r e s s u r e i s %3 . 2 f kPa\n T empe r at ure i s %3 . 2 f K\n Sound

V e l o c i t y i s %3 . 2 f m/ s \n ( B) Mach n um ber i s %3 . 2 f ’ ,P , T , a , M )

Scilab code Exa 1.25 To find stagnation pressure and mach number

1 clc

2 clear3

4 / / I n p ut d at a5 C = 2 1 5 / / V e l o c i t y i n m/ s6 T = 3 0 + 2 7 3 / / S t a t i c t em p er a tu re i n K7 P =5 // S t a t i c p r e s s ur e i n b ar8 R = 2 8 7 // S p e c i f i c g as c o ns t an t i n J /kg−k9 k = 1 . 4 / / A d i a b a t i c C o n s ta n t

10

11 / / C a l c u l a t i o n s

12 a = sqrt ( k * R * T ) // Sound V e l o c i t y i n m/ s13 M = C / a //Mach number14 T o = T * ( 1 + ( ( ( k - 1 ) / 2 ) * M ^ 2 ) ) / / S t a g n a t io n t e m pe r a tu r e i n

K15 P o = P * ( T o / T ) ^ ( k / ( k - 1 ) ) / / S t ag n a ti o n p r e s s u r e i n kPa

31


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16

17 //Output18 printf ( ’ (A) S t a g n a t i o n P r e s s u r e i s %3 . 4 f b ar \n (B)Mach n um be r i s %3 . 3 f ’ , P o , M )

Scilab code Exa 1.26 To determine different velocities stagnation enthalpyand crocco number

1 clc

2 clear3

4 / / I n p ut d at a5 T = 4 0 0 / / S t a t i c t em p er at u re i n K6 k = 1 . 4 / / A d i a b a t i c C o n s ta n t7 C p = 1 0 0 5 // S p e c i f i c h ea t c a pa c i ty a t c on s ta n t

p r e s s ur e i n J /kg−K8 R = 2 8 7 // S p e c i f i c g as c o ns t an t i n J /kg−k9

10 / / C a l c u l a t i o n11 a = sqrt ( k * R * T ) // Sound v e l o c i t y i n m/ s

12 C = a // V e l o c i t y o f j e t i n m/ s , S i n c e j e t h as s o n i cv e l o c i t y

13 T o = T + ( C ^ 2 / ( 2 * C p ) ) / / S t a g n a t i on t e m pe r a tu r e i n K14 ao = sqrt ( k * R * T o ) // Sound v e l o c i t y a t S t a gn a t io n

c o n d i t i o n i n m/ s15 h o = ( C p * T o ) * 1 0 ^ - 3 / / S t a g n a t io n e n t h al p y i n kJ / kg16 C _ m a x = sqrt ( 2 * C p * T o ) //Maximum v e l o c i t y o f j e t i n m/ s17 c r = C / C _ m a x / / C r o c c o n um be r18

19 //Output

20 printf ( ’ (A) V e l o c i t y o f s ou nd a t %3i K i s %3 . 3 f m/ s \n(B) V e l oc i t y o f sound a t s t a g na t i o n c o n d i t i o n i s%3. 3 f m/ s \n (C) Maximum v e l o c i t y o f j e t i s %3 . 3 f m/ s \n (D) S t a g n a t i on e n t ha l p y i s %3 . 3 f kJ / kg\n ( E )C r o cc o nu mber i s %3 . 4 f ’ , T , C , a o , C _ m a x , h o , c r )

32


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Scilab code Exa 1.27 To find stagnation conditions and mass flow rate

1 clc

2 clear

3

4 / / I n p ut d at a5 C = 2 5 0 // V e l o ci t y o f a i r i n m/ s6 D = 1 0 // D i am et er i n d uc t i n cm

7 T = 5 + 2 7 3 / / S t a t i c t em p er at u re i n K8 P = 4 0 / / S t a t i c p r e s s ur e i n kPa9 k = 1 . 4 / / A d i a b a ti c c o n s t a n t

10 C p = 1 0 0 5 // S p e c i f i c h ea t c a pa c i ty a t c on s ta n tp r e s s ur e i n J /kg−K

11 R = 2 8 7 // S p e c i f i c g as c o ns t an t i n J /kg−k12

13 / / C a l c u l a t i o n14 T o = T + ( C ^ 2 / ( 2 * C p ) ) / / S t a g n a t i on t e m pe r a tu r e i n K15 P o = P * ( T o / T ) ^ ( k / ( k - 1 ) ) / / S t ag n a ti o n p r e s s u r e i n kPa16 d = ( P * 1 0 ^ 3 ) / ( R * T ) / / D e n s i t y i n k g /mˆ 317 A = ( % p i * D ^ 2 / 4 ) * 1 0 ^ - 4 / / A re a i n mˆ 218 m = d * A * C // Mass f l o w r a t e i n kg / s19

20 //Output21 printf ( ’ (A) S t a g n a t i o n p r e s s u r e i s %3 . 2 f kPa\n (B)

S t a gn a t io n t em p er a tu re i s %3 . 2 f K\n (C) M ass f l o wr a t e i s %3 . 4 f kg / s ’ , P o , T o , m )

Scilab code Exa 1.28 To find stagnation conditions and velocity at dy-namic condition

1 clc

33


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2 clear

34 / / I n p ut d at a5 C = 3 0 0 // V e l o ci t y o f a i r i n m/ s6 P =1 / / S t a t i c p r e s s ur e i n kPa7 T = 2 9 0 / / S t a t i c t em p er at u re i n K8 k = 1 . 4 / / A d i a b a ti c c o n s t a n t9 R = 2 8 7 // S p e c i f i c g as c o ns t an t i n J /kg−k

10 C p = 1 0 0 5 // S p e c i f i c h ea t c a pa c i ty a t c on s ta n tp r e s s ur e i n J /kg−K

11

12 / / C a l c u l a t i o n

13 T o = T + ( C ^ 2 / ( 2 * C p ) ) / / S t a g n a t i on t e m pe r a tu r e i n K14 P o = P * ( T o / T ) ^ ( k / ( k - 1 ) ) / / S t ag n a ti o n p r e s s u r e i n kPa15 a = sqrt ( k * R * T ) // Sound v e l o c i t y i n m/ s16 Co = sqrt ( k * R * T o ) // Sound v e l o c i t y a t S t a gn a t io n

c o n d i t i o n i n m/ s17

18 //Output19 printf ( ’ (A) S t a g n a t i o n p r e s s u r e and t e mp e r at u r e a r e

%3 . 4 f b a r a nd %3 . 2 f K\n (B) V e l o c i t y o f s ound i nt he dynamic and s t a g n a t i o n c o n d i t i o n s a r e %3 . 2 f m

/ s a nd %3 . 2 f m/ s ’, P o , T o , a , C o )

Scilab code Exa 1.29 To find flow velocity for compressible and incom-pressible flow

1 clc

2 clear

3

4 / / I n p ut d at a5 d P = 4 9 0 * ( 1 . 0 1 3 2 5 / 7 6 0 ) / / P r es s ur e i n p i v o t t u be i n ba r6 P = 0 . 3 5 4 6 + 1 . 0 1 3 2 5 // S t a t i c p r e s s u r e ( a b s o l u t e ) i n b ar7 T o = 2 5 + 2 7 3 / / S t a g n a t io n t e m pe r a tu r e i n K8 k = 1 . 4 / / A d i a b a a t i c c o n s t a n t

34


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9 R = 2 8 7 // S p e c i f i c g as c o ns t an t i n J /kg−k

10 C p = 1 0 0 5 // S p e c i f i c h ea t c a pa c i ty a t c on s ta n tp r e s s ur e i n J /kg−K11

12 / / C a l c u l a t i o n13 P o = d P + P // S t a gn a t io n p r e s s u r e i n b ar14 T = T o * ( P / P o ) ^ ( ( k - 1 ) / k ) // S t a t i c t e m pe r a tu r e15 C1 = sqrt ( 2 * C p * ( T o - T ) ) // Flow v e l o c i t y f o r

C o m p re s s ib l e f l o w i n m/ s16 d i = P o / ( R * T o ) / / D e n s i t y i n k g /mˆ 317 C2 = sqrt ( ( 2 * d P ) / d i ) // Flow v e l o c i t y f o r

i n c o m pr e s s i b l e f l o w i n m/ s

1819 //Output20 printf ( ’ Flow v e l o c i t y f o r : \ n (A) C o m p re s s i bl e f l o w i s

%3. 2 f m/ s \n (B) I n c o m p r e s s i b l e f l o w i s %3 . 2 f m/ s ’, C 1 , C 2 )

Scilab code Exa 1.30 To find Mach number velocity and area at a point

1 clc2 clear

3

4 / / I n p ut d at a5 T o = 2 7 + 2 7 3 / / S t a g n a t io n t e m pe r a tu r e i n K6 P o = 8 / / S t a gn a t io n P r e ss u r e i n b ar7 P = 5 . 6 / / S t a t i c p r e s s u r e i n bar , t ak en fro m d ia gr am

g i v e n8 m =2 // Mass f l o w r a t e i n kg / s9 k = 1 . 4 / / A d i a b a a t i c c o n s t a n t

10 C p = 1 0 0 5 // S p e c i f i c h ea t c a pa c i ty a t c on s ta n tp r e s s ur e i n J /kg−K11 R = 2 8 7 // S p e c i f i c g as c o ns t an t i n J /kg−k12

13 / / C a l c u l a t i o n

35


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14 T = T o * ( P / P o ) ^ ( ( k - 1 ) / k ) / / S t a t i c t em p er a tu re i n K

15 a = sqrt ( k * R * T ) // Sound v e l o c i t y i n m/ s16 C = sqrt ( 2 * C p * ( T o - T ) ) / / V e l o c i t y i n m/ s17 M = C / a //Mach number18 A = ( ( m * R * T ) / ( P * 1 0 ^ 5 * C ) ) * 1 0 ^ 4 // Area a t a p oi nt i n t h e

c h a n na l i n cm ˆ219

20 //Output21 printf ( ’ ( A) M ach numbe r i s %3. 4 f \n (B) V e l o c i t y i s %3

. 1 f m/ s \n (C) A rea a t a p o in t i n t he c ha nn al i s %3

. 3 f cmˆ2 ’ , M , C , A )

Scilab code Exa 1.31 To find velocity and mass flow rate

1 clc

2 clear

3

4 / / I n p ut d at a5 P o = 1 . 8 / / S t ag n a ti o n p r e s s u r e i n atm6 T o = 2 0 + 2 7 3 / / S t a g n a t io n t e m pe r a tu r e i n K

7 P =1 / / S u rr o un d in g p r e s s u r e i n atm8 k = 1 . 4 / / A d i a b a ti c c o n s t a n t9 R = 2 8 7 // S p e c i f i c g as c o ns t an t i n J /kg−k

10

11 / / C a l c u l a t i o n12 p 1 = 0 . 5 2 8 / / S t a t i c t o S t a gn a t io n p r e s s u r e r a t i o @Mach

number =1 , f ro m g a s t a b l e s13 P t = p 1 * P o / / C r i t i c a l p r e s su r e i n atm , S i nc e Pt


38/224

a i r f l o w which w i l l t ak e p l a ce from chamber t o

t h e o u t s i d e t h r o ug h a u ni t a re a h o l e i n m/ s18 G = d i * a o * sqrt ( 2 / ( k - 1 ) ) * ( P / P o ) ^ ( 1 / k ) * sqrt ( ( 1 - ( P / P o ) ^ ( (k - 1 ) / k ) ) ) // Mass f l ow r a t e p er u n it a re a i n kg / s−mˆ2

19

20 //Output21 printf ( ’ (A) V e l oc i t y o f a i r f l o w whi ch w i l l t ak e

p l a c e fro m c hamber t o t he o u t s i d e t hr ou gh a u n i ta r ea h o l e i s %3 . 3 f m/ s \n (B) Mass f l o w r a t e p eru n i t a r e a i s %3 . 3 f kg / s−mˆ2 ’ , C , G )

Scilab code Exa 1.32 To find various properties at one section in duct

1 clc

2 clear

3

4 / / I n p ut d at a5 A 1 = 4 6 5 . 1 2 5 // C ro ss s e c t i o n a l a re a a t e nt r y i n cmˆ26 T 1 = 2 6 . 6 6 + 2 7 3 / / S t a t i c t em p er at u re a t s e c t i o n −1 i n K

7 P 1 = 3 . 4 4 7 3 / / S t a t i c P r es s ur e a t s e c ti o n −1 i n ba r8 C 1 = 1 5 2 . 5 / / V e l o c i t y a t s e c t i o n −1 i n m / s9 P 2 = 2 . 0 6 8 3 8 / / S t a t i c P r es s ur e a t s e c t i o n −2 i n b a r

10 T 2 = 2 7 7 . 4 4 / / S t a t i c t em pe ra t ur e a t s e c t i o n −2 i n K11 C 2 = 2 6 0 . 7 7 5 / / V e l o c i t y a t s e c t i o n −2 i n m / s12 C p = 1 0 0 5 // S p e c i f i c h ea t c a pa c i ty a t c on s ta n t

p r e s s ur e i n J /kg−K13 k = 1 . 4 / / A d i a b a ti c c o n s t a n t14 R = 2 8 7 // S p e c i f i c g as c o ns t an t i n J /kg−k15

16 / / C a l c u l a t i o n s17 T o 1 = T 1 + ( C 1 ^ 2 / ( 2 * C p ) ) / / S t a g n a t i on t e mp e ra t u re a te nt ry i n K

18 T o 2 = T 2 + ( C 2 ^ 2 / ( 2 * C p ) ) / / S t a g n a t i on t e mp e ra t u re a te x i t i n K

37


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19 // he r e To1=To2 f r om ans w e r s

20 d 1 = ( P 1 * 1 0 ^ 5 ) / ( R * T 1 ) / / D e ns i t y a t s e c t i o n −121 d 2 = ( P 2 * 1 0 ^ 5 ) / ( R * T 2 ) / / D e ns i t y a t s e c t i o n −222 a r = ( d 2 * C 2 ) / ( d 1 * C 1 ) // R a ti o o f i n l e t t o o u t l e t a re a23 A 2 = A 1 / a r // C ro ss s e c t i o n a l a r e a a t e x i t i n cmˆ224 C _ m a x = sqrt ( 2 * C p * T o 1 ) //Maximum v e l o c i t y a t e x i t i n m

/ s25 m = d 1 * A 1 * C 1 * 1 0 ^ - 4 // Mass f l ow r a t e i n kg / s26 F = ( ( P 1 * 1 0 ^ 5 * A 1 * 1 0 ^ - 4 ) - ( P 2 * 1 0 ^ 5 * A 2 * 1 0 ^ - 4 ) ) + ( m * ( C 1 - C 2 )

) // F o rc e a c t i n g on t he d uc t w a l l b et we en twos e c t i o n s i n N

27

28 //Output29 printf ( ’ (A) Maximum v e l o c i t y a nd s t a g n a t i o n

t e mp e r at u r e a t e x i t a r e %3 . 2 f m/ s and %3 . 2 f K\n (B) S i n c e S t a g n a t i on t e m pe r a tu r e %3i K a t e n t r y and

%3i K at e x i t a re e q u a l , t h e f lo w i s a d i a b a t i c \n(C) C ro ss s e c t i o n a l a r e a a t e x i t i s %3 . 2 f cmˆ2\n

(D) F or ce a c t i n g on t h e d uc t w a l l b et we en twos e c t i o n s i s %3 . 2 f N ’ , C _ m a x , T o 2 , T o 1 , T o 2 , A 2 , F )

Scilab code Exa 1.33 To find various properties at one section in duct

1 clc

2 clear

3

4 / / I n p ut d at a5 P 1 = 2 5 0 / / S t a t i c P r es s ur e a t s e c t i o n −1 i n kPa6 T 1 = 2 6 + 2 7 3 / / S t a t i c t em pe ra t ur e a t s e c t i o n −1 i n K7 M 1 = 1 . 4 / / Mach n um be r a t e n t r y

8 M 2 = 2 . 5 / / Mach nu mber a t e x i t9 k = 1 . 4 / / A d i a b a ti c c o n s t a n t10 R = 2 8 7 // S p e c i f i c g as c o ns t an t i n J /kg−k11

12 / / C a l c u l a t i o n

38


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13 C1 = sqrt ( k * R * T 1 ) * M 1 // A ir v e l o c i t y a t e nt ry i n m/ s

14 T o = T 1 * ( 1 + ( ( ( k - 1 ) / 2 ) * M 1 ^ 2 ) ) / / S t a g n a t i o n t e m p e r at u r ei n K15 t 1 = ( 1 + ( ( ( k - 1 ) / 2 ) * M 2 ^ 2 ) ) / / S t a gn a t io n t o e x i t

T em pe ra tu re r a t i o16 T 2 = T o / t 1 / / E x it t e m pe r a tu r e i n K17 C2 = sqrt ( k * R * T 2 ) * M 2 // A ir v e l o c i t y a t e x i t i n m/ s18 P 2 = P 1 * ( T 2 / T 1 ) ^ ( k / ( k - 1 ) ) // E xi t s t a t i c p r e s s u re i n

kPa19 d 2 = ( P 2 * 1 0 ^ 3 ) / ( R * T 2 ) / / D e ns i t y a t s e c t i o n −2 i n k g /mˆ 320 G = d 2 * C 2 // ) M ass f l o w r a t e t hr ou gh t he d uc t p er

s q ua r e m etr e i n kg / s−mˆ2

2122 //Output23 printf ( ’ (A) At s e c o nd s e c t i o n : \ n Te mper at ure i s %3

. 2 f K\n P r e s s u r e i s %3 . 2 f kPa\n V e l o c i t y i s%3. 4 f m/ s \n (B) Mass f l o w r a t e t hr ou gh t he d uc t

p er s q ua r e m et re i s %3 . 1 f kg / s−mˆ2 ’ , T 2 , P 2 , C 2 , G )

Scilab code Exa 1.34 To find maximum temperature encountered by skin

1 clc

2 clear

3

4 / / I n p ut d at a5 M =2 //Mach number6 h = 2 0 / / A l t i t u d e i n km7 T c = - 5 6 // A mbient t e mp e r at u r e i n d e g r e e C e n ti g r a d e8 T a = - 5 6 + 2 7 3 / / Am bi ent t e m p e r a tu r e i n K9 k = 1 . 4 / / A d i a b a ti c c o n s t a n t

10 R = 2 8 7 // S p e c i f i c g as c o ns t an t i n J /kg−k11 C p = 1 0 0 5 // S p e c i f i c h ea t c a pa c i ty a t c on s ta n tp r e s s ur e i n J /kg−K

12

13 / / C a l c u l a t i o n

39


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14 a = sqrt ( k * R * T a ) // Sound v e l o c i t y i n m/ s

15 C = M * a // V e l o c i t y o f f l i g h t i n m/ s16 T o = T c + ( C ^ 2 / ( 2 * C p ) ) //The maximum te mp er at ur ee n co u nt e re d i s %3 . 1 f d e g re e C en t ig r ad e

17

18 //Output19 printf ( ’ The maximum t e m p e r a t u r e e n c o u n t e r e d i s %3 . 1 f

d e g r e e C e n t ig r a d e ’ , T o )

Scilab code Exa 1.35 To find rate of heat transfer

1 clc

2 clear

3

4 / / I n p ut d at a5 W = 2 0 0 0 0 / / Po wer d e v e l o p e d i n kW6 m = 1 2 // Mass f l o w r a t e i n kg / s7 C 1 = 5 0 / / V e l o c it y o f a i r e n t e r i n g i n m/ s8 T 1 = 7 0 0 + 2 7 3 // T emper at ur e o f a i r e n t e r i n g i n K9 T 2 = 2 9 8 // T empe ra tur e o f a i r l e a v i n g i n K

10 C 2 = 1 2 5 / / V e l o c i t y o f a i r l e a v i n g i n m/ s11 C p = 1 . 0 0 5 // S p e c i f i c h ea t c a p ac i t y a t c o ns t an t

p r e s s u r e i n kJ /kg−K12

13 / / C a l c u l a t i o n14 d h = C p * ( T 2 - T 1 ) // Change i n e n t ha l p y i n kJ / kg15 Q = ( ( m * d h ) + W - ( m * ( 1 / 2 0 0 0 ) * ( C 2 ^ 2 - C 1 ^ 2 ) ) ) // The r a t e o f

h ea t t r a n s f e r i n k J / s16

17 //Output18 printf ( ’ The r a t e o f h ea t t r a n s f e r i s %3 . 2 f kJ / s ’ ,Q )

Scilab code Exa 1.36 To find various properties in a nozzle

40


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1 clc

2 clear3

4 / / I n p ut d at a5 m o l = 3 9 . 9 // M o l ec u l a r w e ig h t o f g a s i n kg / mol6 k = 1 . 6 7 / / A d i a b a t i c c o n s t a n t7 P o = 5 0 0 / / P r e s s u r e i n c ha mb er i n kPa8 T o = 3 0 + 2 7 3 / / T em pe ra tu re i n c ha mb er i n K9 P 1 = 8 0 // P r e ss u r e o f n o z z l e a t g iv en s e c t i o n i n kPa

10 D = 0 . 0 1 2 // C ro ss s e c t i o n d ia me te r o f n o z z l e i n m11 R i = 8 3 1 4 / / I d e a l g as c o n st a n t i n J /mol−K12

13 / / C a l c u l a t i o n14 R = R i / m o l // S p e c i f i c g as c on s ta n t i n J /kg−K15 p 1 = P o / P 1 // S t a gn at io n t o s t a t i c p r e s s u r e r a t i o16 M1 = sqrt ( ( ( ( p 1 ^ ( ( k - 1 ) / k ) ) - 1 ) * 2 ) / ( k - 1 ) ) //Mach number

a t s e c t i o n17 T 1 = T o * ( ( 1 + ( ( ( k - 1 ) / 2 ) * M 1 ^ 2 ) ) ^ ( - 1 ) ) / / T e m pe r at u re a t

s e c t i o n i n K18 a = sqrt ( k * R * T 1 ) // Sound V e l o c i t y i n m/ s19 C 1 = M 1 * a // Gas V e l oc i t y a t s e c t i o n i n m/ s20 d = ( P 1 * 1 0 ^ 3 ) / ( R * T 1 ) / / D e n s i t y i n k g /mˆ 321 A 1 = % p i * D ^ 2 / 4

/ / C r o s s−s e c t i o n a l Area22 m = d * A 1 * C 1 // Mass f l o w r a t e t hr ou gh n o z z l e i n kg / s23

24 //Output25 printf ( ’ (A) At s e c t i o n :\ n Mach number i s %3 . 1 f \n

T em p er at ur e i s %3 . 1 f K\n V e l o c i t y i s %3 . 3 f m/ s \n (B) Mass f l o w r a t e t hr ou gh n o z z l e i s %3 . 3 f k g / s ’ , M 1 , T 1 , C 1 , m )

Scilab code Exa 1.37 To find Mach number velocity and pressure at asection in duct

1 clc

41


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2 clear

34 / / I n p ut d at a5 m o l = 4 // M o l ec u l a r w ei g h t o f g a s i n kg / mol6 k = 1 . 3 / / A d i a b a ti c c o n s t a n t7 C 1 = 1 5 0 // Gas V e l o c i t y a t s e c t i o n −1 i n m / s8 P 1 = 1 0 0 // P r e s su r e o f d uc t a t s e c t i o n −1 i n kPa9 T 1 = 1 5 + 2 7 3 // T e mp er at ur e a t s e c t i o n −1 i n K

10 T 2 = - 1 0 + 2 7 3 // T e m pe ra tu re a t s e c t i o n −2 i n K11 R i = 8 3 1 4 / / I d e a l g as c o n st a n t i n J /mol−K12

13 / / C a l c u l a t i o n

14 R = R i / m o l // S p e c i f i c g as c on s ta n t i n J /kg−K15 a1 = sqrt ( k * R * T 1 ) // Sound v e l o c i t y a t s e c ti o n −1 i n m / s16 M 1 = C 1 / a 1 / / Mach n um ber a t s e c t i o n −117 t 1 = 0 . 9 9 5 5 // S t a t i c t o S t a gn a t io n t em p er a tu re r a t i o

a t e n t r y f ro m g a s t a b l e s @M1, k = 1. 318 T o = T 1 / t 1 / / S t a g a n t i o n t e mp e r at u r e i n K19 p 1 = 0 . 9 8 1 5 / / S t a t i c t o S ta gn at io n p r e s s u re r a t i o a t

e n t r y f ro m g a s t a b l e s @M1, k = 1. 320 P o = P 1 / p 1 / / S t a gn a t io n p r e s s u r e i n kPa21 t 2 = T 2 / T o // S t a t i c t o S t ag n at i o n t em pe ra tu re r a t i o a t

e x i t22 M 2 = 0 . 8 2 / /Amch n u mb er a t s e c t i o n −2 f rom g as t a b l e s@t2 , k=1. 3

23 p 2 = 0 . 6 5 9 // S t a t i c t o S t a gn at io n p r e s s u r e r a t i o a te x i t f ro m g a s t a b l e s @M2, k = 1. 3

24 P 2 = P o * p 2 / / P r e ss u r e a t s e c t i o n −2 i n kPa25 a2 = sqrt ( k * R * T 2 ) // Sound v e l o c i t y a t s e c ti o n −2 i n m / s26 C 2 = M 2 * a 2 // Gas V e l o c i t y a t s e c t i o n −2 i n m / s27

28 //Output29 printf ( ’ At t h e s e co n d p o i n t :\ n Mach number i s %3

. 2 f \n P r e s s u r e i s %3 . 3 f kPa\n V e l o c i t y i s%3. 2 f m/ s ’ , M 2 , P 2 , C 2 )

42


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Scilab code Exa 1.38 To find mass flow rate and velocity at exit

1 clc

2 clear

3

4 / / I n p ut d at a5 A 1 = 1 0 / / I n l e t a r ea i n cmˆ26 C 1 = 8 0 / / I n l e t A i r v e l o c i t y i n m/ s7 T 1 = 2 8 + 2 7 3 / / I n l e t t em p er a tu re i n K8 P 1 = 7 0 0 / / I n l e t P r e s su r e i n kPa9 P 2 = 2 5 0 / / E xi t p r e s s u r e i n kPa

10 k = 1 . 4 / / A d i a b a ti c c o n s t a n t11 R = 2 8 7 // S p e c i f i c g as c o ns t an t i n J /kg−K12

13 / / C a l c u l a t i o n14 a1 = sqrt ( k * R * T 1 ) // Sound v e l o c i t y a t i n l e t i n m/ s15 M 1 = C 1 / a 1 / /Mach number a t i n l e t16 t 1 = 0 . 9 8 9 // S t a t i c t o S t ag n at i o n t em pe ra tu re r a t i o a t

e n t r y f ro m g a s t a b l e s @M1, k = 1. 4

17 T o = T 1 / t 1 / / S t a g a n t i o n t e mp e r at u r e i n K18 p 1 = 0 . 9 6 4 // S t a t i c t o S t a gn at io n p r e s s u r e r a t i o a t

e n t r y f ro m g a s t a b l e s @M1, k = 1. 419 P o = P 1 / p 1 / / S t a gn a t io n p r e s s u r e i n kPa20 p 2 = P 2 / P o // S t a t i c t o S t ag n at i o n p r e s s ur e r a t i o21 M 2 = 1 . 3 3 5 / / Mach n um ber a t e x i t22 t 2 = 0 . 7 3 7 // S t a t i c t o S t ag n at i o n t em pe ra tu re r a t i o a t

e x i t f ro m g a s t a b l e s @M2, k = 1. 423 T 2 = T o * t 2 / / S t a g n a t i o n t e mp e ra t ur i n K24 a2 = sqrt ( k * R * T 2 ) // Sound v e l o c i t y a t e x i t i n m/ s25 C 2 = M 2 * a 2 / / E xi t A ir v e l o c i t y i n m/ s26 d 1 = ( P 1 * 1 0 ^ 3 ) / ( R * T 1 ) / / D en s it y a t i n l e t i n kg /mˆ327 m = d 1 * A 1 * C 1 * 1 0 ^ - 4 // Mass f l ow r a t e i n kg / s28

29 //Output

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30 printf ( ’ (A) Mass f l o w r a t e i s %3 . 3 f kg / s \n (B )

V e l oc i t y a t t he e x i t i s %3 . 2 f m/ s ’ , m , C 2 )

Scilab code Exa 1.39 To find time required for a value of pressure de-crease

1 clc

2 clear

3

4 / / I n p ut d at a5 V =5 // Volume o f a i r i n mˆ36 A e = 1 0 * 1 0 ^ - 4 / / E x i t a r e a i n cm ˆ27 T o = 6 0 + 2 7 3 // T em pe ra tu re i n s i d e i n t he t an k i n K8 P o 1 = 4 0 // I n t i a l t o t a l p r e s s u r e i n ba r9 P o 2 = 2 // F i n a l t o t a l p r e s s u r e i n b ar

10 P =1 // D i sc h ar g e p r e s s u r e i n b ar11 R = 2 8 7 // S p e c i f i c g as c o ns t an t i n J /kg−K12

13 / / C a l c u l a t i o n14 / / H er e p r e s s u r e r a t i o s P/ Po1 a nd P/ Po2 a r e a l wa y s

l e s s t han c r i t i c a l p r e s s ur e r a t i o t h e r e f o r e f l o wi s c ho ke d i . e . M=1 a t e x i t

15 G p = ( 0 . 0 4 0 4 1 8 4 * A e ) / sqrt ( T o ) // Mass f l o w r a t e byS t a g n a t i o n p r e s s u r e i . e . m/ Po

16 / / D i f f e r e n t i a t i n g m=(P∗V) /(R∗To ) w . r . t . t i m e a ndi n t r g r a t i n g r e s u l t i n g e qu at io n we g e t f o l l o w i n ge x p r e s s i o n .

17 t = - ( V / ( R * T o * G p ) ) * log ( P o 2 / P o 1 ) // The t im e r e q u i r e df o r t a nk p r e s s ur e t o d e c re a s e from Po1 t o Po2 i ns e c

1819 //Output20 printf ( ’ The t im e r e q u i r e d f o r t a nk p r e s su r e t o

d e c re a s e from %i ba r t o %i ba r i s %3 . 2 f s e c ’ , P o 1 ,P o 2 , t )

44


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45


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Chapter 2

Flow through Variable Area

Ducts

Scilab code Exa 2.1 To find mass flow rate temperature and pressure atthroat

1 clc

2 clear

3

4 / / I n p ut d at a5 d o 1 = 1 . 1 2 // D en si ty o f a i r i r e s e r v o i r i n kg /mˆ36 a o 1 = 5 0 0 // V e l oc i t y o f sound i n r e s e r v o i r i n m/ s7 d = 0 . 0 1 // T h ro at d i a m et e r i n m8 k = 1 . 4 / / A d i a b a t i c C o n s ta n t9 R = 2 8 7 // S p e c i f i c g as c o ns t an t i n J /kg−K

10

11 / / C a l c u l a t i o n12 T o 1 = a o 1 ^ 2 / ( k * R ) / / S t a g n a t i on t e mp e ra t u re i n K13 P o 1 = d o 1 * R * T o 1 / / S t a gn a t io n p r e s s u r e i n Pa

14 p 1 = 0 . 5 2 8 // R a ti o o f c r i t i c a l p r e s s u r e t o S t a g n a t i o np r e s s u r e f ro m g a s t a b l e s @M=115 P t = ( P o 1 * p 1 ) * 1 0 ^ - 5 // T hro at p r e s s u r e i n b ar16 t 1 = 0 . 8 3 4 / / R a t i o o f c r i t i c a l t e m p e r a t u r e t o

S t a g n a t i o n t e m p e r a tu r e f ro m g a s t a b l e s @M=1

46


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17 T t = T o 1 * t 1 / / c r i t i c a l t e m p e r a t u r e i n K

18 d _ t = ( P t * 1 0 ^ 5 ) / ( R * T t ) // D en si ty o f a i r a t t h r o a t i nkg/mˆ319 a _ t = sqrt ( k * R * T t ) // Sound v e l o c i t y a t t h r o a t i n m/ s20 C t = a _ t // A i r v e l o c i t y t t h r o a t i n m/ s , S i n ce M=121 A _ t = % p i * d ^ 2 / 4 // T h r oa t a r e a i n mˆ 222 m = d _ t * A _ t * C t // Maximum m a ss f l o w r a t e i n k g / s23

24 //Output25 printf ( ’ (A) Maximum m as s f l o w r a t e i s %3 . 5 f k g / s \n (B

) P r e ss u r e and t e mp e ra r at u re a t t he t h r o a t a r e %3. 3 f b ar and %3 . 4 f K ’ , m , P t , T t )

Scilab code Exa 2.2 To find properties at throat and exit in ConvergentDivergent nozzle

1 clc

2 clear

3


5 P 1 = 2 // I n t i a l p r e s s u r e i n ba r6 C 1 = 1 7 0 // I n i t i a l v e l o c i t y o f a i r i n m/ s7 T 1 = 4 7 3 / / I n t i a l t em pe ra tu re i n K8 A 1 = 1 0 0 0 / / I n l e t a r e a i n mmˆ 29 P 2 = 0 . 9 5 // E xi t p r e s s u r e i n b ar

10 k = 1 . 4 / / A d i a b a t i c C o n s ta n t11 R = 2 8 7 // S p e c i f i c g as c o ns t an t i n J /kg−K12

13 / / C a l c u l a t i o n14 a _ 1 = sqrt ( k * R * T 1 ) // V e l oc i t y o f sound a t i n l e t i n m/ s

15 M 1 = C 1 / a _ 1 / / I n l e t mach n um be r16 t 1 = 0 . 9 7 0 / / R at io o f i n l e t t em pe ra tu re t o S t ag n at i o nt e m p e r a t u r e f ro m g a s t a b l e s @M=1

17 T o 1 = T 1 / t 1 / / S t a g n a t io n t e m pe r a tu r e i n K18 p 1 = 0 . 9 0 0 // R at io o f i n l e t p r e s s ur e t o S t a g na t i o n

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p r e s s u r e f ro m g a s t a b l e s @M=1

19 P o 1 = P 1 / p 1 / / S t a gn a t io n p r e s s u r e i n b ar20 a 1 = 1 . 6 2 3 // R a ti o o f i n l e t a r e a t o c r i t i c a l a r e a f ro mi s e n t r o p i c g a s t a b l e s @M=1

21 A t = A 1 / a 1 // c r i t i c a l ar ea in mmˆ222 p 2 = 0 . 5 2 8 // P r e s s u r e r a t i o a t c r i t i c a l s t a t e f ro m

i s e n t r o p i c g a s t a b l e s @M=123 P t = P o 1 * p 2 // T hr oa t p r e s s u r e i n b ar24 t 2 = 0 . 8 3 4 / / T em pe ra tu re r a t i o a t c r i t i c a l s t a t e f ro m

i s e n t r o p i c g a s t a b l e s @M=125 T t = T o 1 * t 2 / / Th ro at t e mp e ra t u re i n K26 a _ t = sqrt ( k * R * T t ) // V e l o c i t y o f s ound a t t h r o at i n m/

s27 C _ t = a _ t // C r i t i c a l v e l o c i t y o f a i r i n m/ s28 p 3 = P 2 / P o 1 / / P r e s s u r e r a t i o a t e x i t29 M 2 = 1 . 1 7 // Mach n umber a t e x i t fro m i s e n t r o p i c g as

t a b l e s @p330 t 3 = 0 . 7 8 5 // T emper at ur e r a t i o a t e x i t from i s e n t r o p i c

g a s t a b l e s @M231 T 2 = T o 1 * t 3 / / E x it t e mp e r at u r e i n K32 a 3 = 1 . 0 2 2 // Area r a t i o a t e x i t from i s e n t r o p i c g as

t a b l e s @M233 A 2 = A t * a 3

/ / E x i t a r e a i n mmˆ 2 , wr on g a n sw er i nt e x t b o o k34 C 2 = M 2 * sqrt ( k * R * T 2 ) / / E xi t v e l o c i t y i n m/ s35

36 //Output37 printf ( ’ (A) S t a g n a t i o n t e mp e r at u r e and p r e s s u r e a r e

%3 . 2 f K a nd %3 . 3 f b a r\n (B) S o ni c v e l o c i t y andmach nu mb er a t e n t r y a r e %3 . 2 f m/ s a nd %3 . 2 f \n (C) V e l o c i ty , Mach number and f l o w a r e a a t o u t l e ts e c t i o n a r e %3 . 2 f m/ s , %3 . 2 f a nd %3 . 2 f mmˆ 2\n (D)P re ss ur e , a r e a a t t h ro a t o f t he n o z z l e a r e %3 . 5 f

bar and %3. 3 f mmˆ2 ’ , T o 1 , P o 1 , a _ 1 , M 1 , C 2 , M 2 , A 2 , P t , A t)

48


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Scilab code Exa 2.3 To find properties at throat and exit maximum pos-sible velocity of gas and type of nozzle

1 clc

2 clear

3

4 / / I n p ut d at a5 P o 1 = 1 0 // S t ag n a ti o n p r e s s u r e i n b ar6 T o 1 = 7 9 8 / / S t a g n a t i on t e m pe r a tu r e i n K7 P t = 7 . 6 // T hr oa t p r e s s u r e i n b ar8 m = 1 . 5 // Mass f l o w r a t e i n kg / s9 k = 1 . 4 / / A d i a b a t i c C o n s ta n t

10 R = 2 8 7 // S p e c i f i c g as c o ns t an t i n J /kg−K11 C p = 1 0 0 5 // S p e c i f i c h ea t c a pa c i ty a t c on s ta n t


13 / / C a l c u l a t i o n14 p 1 = 0 . 5 2 8 // R a ti o o f c r i t i c a l p r e s s u r e t o S t a g n a t i o n

p r e s s u r e fro m i s e n t r o p i c g as t a b l e s @M=1 ,k =1 .4

15 P c = p 1 * P o 1 // C r i t i c a l p r e s s u r e i n b a r16 P 2 = P t / / E xi t p r e s s u r e i n bar , S i n ce Pc


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27 printf ( ’ (A) At t h e n o z z l e t h r o a t / e x i t :\ n P r e s s u r e

i s %3 . 2 f b ar \n Te mper at ure i s %3 . 2 f K\nV e l o c i t y i s %3 . 2 f \n (B )Maximum p o s s i b l e v e l o c i t yi s %3 . 2 f m/ s \n (C) Type o f t h e n o z z l e i s ac on v e rg e n t n o z z l e and i t s t h ro a t a r e a i s %3 . 3 f mmˆ2 ’ , P 2 , T 2 , C 2 , C _ m a x , A t )

Scilab code Exa 2.4 To find properties at exit in Convergent Divergentnozzle

1 clc

2 clear

3

4 / / I n p ut d at a5 P o 1 = 3 . 3 4 4 / / S t a gn a t io n p r e s s u r e i n b ar6 T o 1 = 9 0 0 / / S t a g n a t i on t e m pe r a tu r e i n K7 P 2 = 1 . 0 5 // E xi t p r e s s u r e i n b ar8 k = 1 . 4 / / A d i a b a t i c C o n s ta n t9 R = 2 8 7 // S p e c i f i c g as c o ns t an t i n J /kg−K

10 C p = 1 0 0 5 // S p e c i f i c h ea t c a pa c i ty a t c on s ta n t


12 / / C a l c u l a t i o n13 p 1 = P 2 / P o 1 // P r e s su r e r a t i o14 M 2 = 1 . 4 0 / / E x i t mach n umb er f ro m g a s t a b l e s @p1 , k = 1. 415 t 1 = 0 . 7 1 8 // R at io o f e x i

gas dynamics and jet propulsion_p. murugaperumal (1)

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