table gas dynamics

Gas Dynamics TablesGenick Bar-MeirDecember 4, 2007

Version 1.3

This document started as a collection of the tables made in the bookFundamentals of compressible Flow Mechanics. However, since theinitial phase it has grown and now has additional tables for variousvalues of specific heat, k = 1.2, 1.3, 1.4 and 1.67 etc. Furthermore,the tables are more detailed than those in the book. In fact, there areno known tables that match the depth, variety, and quality of thiscollection. So, as far as it is known, this collection of gas dynamicstables is the biggest in the world.These tables supposed to be used by professionals and students whowould like to have handy gas dynamics tables without going throughthe pages of the whole books. These tables are intended to replacecommercial tables.

These Tables were created by Potto-GDC and later where translatedby using latex2html versions 1.7. Then they were translated fromhtml to php by toPHP script (our script). The oblique shock figureswere generate by a new script that use gd (non graphical part of gdc)and produces a gle file. The simple operation is:./obliqueFigur 1.4

and later use gle ob.jpg to generate a eps file. If you interested inthis php scrip or the figure script drop me a line.

2copyright c, 2007, by Dr. BarMeir www.potto.org

Contents

1 Isentropic Flow 71.1 Regular Isentropic Flow Tables . . . . . . . . . . . . . . . . . 7

1.1.1 Isentropic Flow for k=1.2 . . . . . . . . . . . . . . . . 71.1.2 Isentropic Flow for k=1.3 . . . . . . . . . . . . . . . . 91.1.3 Isentropic Flow for k =1.4 . . . . . . . . . . . . . . . . 121.1.4 Isentropic Flow k=1.67 . . . . . . . . . . . . . . . . . . 14

1.2 Naughty Professor Tables (NPT) for Isentropic Flow . . . . 171.2.1 NPT for Isentropic Flow k=1.2 . . . . . . . . . . . . . 171.2.2 NPT for Isentropic Flow k=1.3 . . . . . . . . . . . . . 191.2.3 NPT for Isentropic Flow k=1.4 . . . . . . . . . . . . . 221.2.4 NPT for Isentropic Flow k=1.67 . . . . . . . . . . . . . 24

2 Isothermal Nozzle 292.1 Isothermal Nozzle for k=1.2 . . . . . . . . . . . . . . . . . . . 292.2 Isothermal Nozzle for k=1.3 . . . . . . . . . . . . . . . . . . . 332.3 Isothermal Nozzle for k=1.4 . . . . . . . . . . . . . . . . . . . 352.4 Isothermal Nozzle for k=1.67 . . . . . . . . . . . . . . . . . . 38

3 Normal Shock 413.1 Normal Shock Standard tables . . . . . . . . . . . . . . . . . . 41

3.1.1 Normal Shock Standard Table for k=1.2 . . . . . . . . 413.1.2 Normal Shock Standard Table for k=1.3 . . . . . . . . 433.1.3 Normal Shock Standard Table for k=1.4 . . . . . . . . 453.1.4 Normal shock Standard Table for k=1.67 . . . . . . . . 47

3.2 Open Valve maximum values . . . . . . . . . . . . . . . . . . . 503.3 Shock Reflecting from a Suddenly Closed Valve . . . . . . . . 50

3.3.1 Reflecting Shock (closed Valve) k =1.2 . . . . . . . . . 503.3.2 Reflecting Shock (closed Valve) k =1.3 . . . . . . . . . 53

3

4 CONTENTS

3.3.3 Reflecting Shock (closed Valve) k =1.4 . . . . . . . . . 553.3.4 Reflecting Shock (closed Valve) k =1.67 . . . . . . . . 56

3.4 Shock propagating from suddenly open valve . . . . . . . . . . 583.4.1 Shock from suddenly open valve k =1.2 . . . . . . . . . 583.4.2 Shock from suddenly open valve k =1.3 . . . . . . . . . 603.4.3 Shock from suddenly open valve k =1.4 . . . . . . . . . 633.4.4 Shock from suddenly open valve k =1.67 . . . . . . . . 65

4 Isothermal Flow 694.1 Isothermal Flow k=1.2 . . . . . . . . . . . . . . . . . . . . . . 694.2 Isothermal Flow k=1.3 . . . . . . . . . . . . . . . . . . . . . . 724.3 Isothermal Flow k=1.4 . . . . . . . . . . . . . . . . . . . . . . 754.4 Isothermal Flow k=1.67 . . . . . . . . . . . . . . . . . . . . . 784.5 Unchoked Isothermal Flow k=1.4 . . . . . . . . . . . . . . . . 81

5 Fanno Flow 835.1 Standard Fanno Flow Table for k=1.2 . . . . . . . . . . . . . 835.2 Standard Fanno Flow Table for k=1.3 . . . . . . . . . . . . . 1195.3 Standard Fanno Flow Table for k=1.4 . . . . . . . . . . . . . 1555.4 Standard Fanno Flow Table for k=1.67 . . . . . . . . . . . . 191

6 Rayleigh Flow 2296.1 Rayleigh Flow Table for k=1.2 . . . . . . . . . . . . . . . . . . 2296.2 Rayleigh Flow Table for k=1.3 . . . . . . . . . . . . . . . . . . 2656.3 Rayleigh Flow Table for k=1.4 . . . . . . . . . . . . . . . . . . 3006.4 Rayleigh Flow Table for k=1.67 . . . . . . . . . . . . . . . . . 336

7 Prandtl-Meyer Function 3737.1 Prandtl-Meyer Function for k=1.2 . . . . . . . . . . . . . . . . 3737.2 Prandtl-Meyer Function for k=1.3 . . . . . . . . . . . . . . . . 4037.3 Prandtl-Meyer Function for k=1.4 . . . . . . . . . . . . . . . . 4327.4 PrandtlMeyer Function for k=1.67 . . . . . . . . . . . . . . . 462

8 Oblique Shock 4938.1 Values at the Deflection Point . . . . . . . . . . . . . . . . . . 493

8.1.1 Deflection Point for k=1.2 . . . . . . . . . . . . . . . . 4938.1.2 Deflection Point for k=1.3 . . . . . . . . . . . . . . . . 5238.1.3 Deflection Point for k=1.4 . . . . . . . . . . . . . . . . 553

copyright c, 2007, by Dr. BarMeir www.potto.org

CONTENTS 5

8.1.4 Deflection Point for k=1.67 . . . . . . . . . . . . . . . 5828.2 Regular Oblique Shock Figures . . . . . . . . . . . . . . . . . 613

8.2.1 Oblique Shock k=1.2 . . . . . . . . . . . . . . . . . . . 6138.2.2 Oblique Shock k=1.3 . . . . . . . . . . . . . . . . . . . 6148.2.3 Oblique Shock k=1.4 . . . . . . . . . . . . . . . . . . . 6158.2.4 Oblique Shock k=1.67 . . . . . . . . . . . . . . . . . . 616

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6 CONTENTS


Chapter 1

Isentropic Flow

1.1 Regular Isentropic Flow Tables

1.1.1 Isentropic Flow for k=1.2

Table 1.1: Isentropic Flow k = 1.2

M TT0

0

AA

PP0

APAP0

FF

0.00 1.00000 1.00000 5.9E+5 1.00000 5.9E+5 2.7E+50.05 0.99975 0.99875 11.86 0.99850 11.84 5.3970.10 0.99900 0.99501 5.953 0.99402 5.917 2.7220.20 0.99602 0.98024 3.026 0.97633 2.954 1.4070.25 0.99379 0.96933 2.451 0.96331 2.361 1.1540.30 0.99108 0.95619 2.073 0.94766 1.965 0.989440.35 0.98790 0.94094 1.809 0.92955 1.681 0.876530.40 0.98425 0.92370 1.615 0.90915 1.468 0.795590.45 0.98015 0.90462 1.469 0.88667 1.302 0.735910.50 0.97561 0.88385 1.356 0.86230 1.170 0.691080.55 0.97064 0.86156 1.268 0.83627 1.060 0.657020.60 0.96525 0.83792 1.199 0.80880 0.96941 0.63100.65 0.95946 0.81309 1.144 0.78013 0.89216 0.611130.70 0.95329 0.78727 1.100 0.75049 0.82576 0.596050.75 0.94675 0.76062 1.067 0.72011 0.76806 0.584770.80 0.93985 0.73332 1.041 0.68921 0.71743 0.57655

7

8 CHAPTER 1. ISENTROPIC FLOW

Table 1.1: Isentropic Flow k = 1.2 (continue)

M TT0

0

AA

PP0

APAP0

FF

0.85 0.93262 0.70554 1.022 0.65800 0.67263 0.570810.90 0.92507 0.67744 1.010 0.62668 0.63268 0.567110.95 0.91722 0.64919 1.002 0.59545 0.59683 0.565091.0 0.90909 0.62092 1.000 0.56447 0.56447 0.564471.05 0.90070 0.59278 1.002 0.53392 0.53511 0.565021.10 0.89206 0.56490 1.009 0.50393 0.50833 0.566561.15 0.88320 0.53739 1.019 0.47462 0.48381 0.568911.20 0.87413 0.51035 1.034 0.44611 0.46126 0.571961.25 0.86486 0.48388 1.052 0.41849 0.44046 0.575601.30 0.85543 0.45807 1.075 0.39184 0.42120 0.579731.35 0.84584 0.43297 1.101 0.36622 0.40332 0.584271.40 0.83612 0.40864 1.132 0.34167 0.38668 0.589151.45 0.82628 0.38515 1.166 0.31824 0.37114 0.594331.50 0.81633 0.36251 1.205 0.29593 0.35660 0.599741.55 0.80629 0.34076 1.248 0.27475 0.34297 0.605341.60 0.79618 0.31993 1.296 0.25472 0.33016 0.611101.65 0.78601 0.30001 1.349 0.23581 0.31810 0.616981.70 0.77580 0.28102 1.407 0.21801 0.30674 0.622951.75 0.76555 0.26295 1.470 0.20130 0.29600 0.629001.80 0.75529 0.24579 1.540 0.18564 0.28584 0.635091.85 0.74502 0.22953 1.615 0.17100 0.27622 0.641201.90 0.73475 0.21415 1.697 0.15734 0.26709 0.647331.95 0.72451 0.19962 1.787 0.14463 0.25842 0.653452.00 0.71429 0.18593 1.884 0.13281 0.25018 0.659562.25 0.66390 0.12898 2.504 0.085628 0.21439 0.689472.50 0.61538 0.088254 3.421 0.054310 0.18577 0.717742.75 0.56940 0.059851 4.767 0.034079 0.16245 0.743943.00 0.52632 0.040386 6.735 0.021256 0.14317 0.767893.25 0.48632 0.027203 9.602 0.013230 0.12703 0.789633.50 0.44944 0.01833813.76 0.00824 0.11340 0.809253.75 0.41558 0.01239619.76 0.00515 0.10177 0.826924.00 0.38462 0.00842 28.36 0.00324 0.091790 0.842804.25 0.35635 0.00575 40.61 0.00205 0.083155 0.85706


1.1. REGULAR ISENTROPIC FLOW TABLES 9

Table 1.1: Isentropic Flow k = 1.2 (continue)

M TT0

0

AA

PP0

APAP0

FF

4.50 0.33058 0.00395 57.96 0.00131 0.075642 0.869894.75 0.30710 0.00273 82.34 0.000839 0.069070 0.881425.00 0.28571 0.00190 1.2E+2 0.000544 0.063290 0.891825.25 0.26622 0.00134 1.6E+2 0.000356 0.058184 0.901195.50 0.24845 0.000947 2.3E+2 0.000235 0.053653 0.909665.75 0.23222 0.000675 3.2E+2 0.000157 0.049616 0.917336.00 0.21739 0.000486 4.4E+2 0.000106 0.046006 0.924296.25 0.20382 0.000352 6.0E+2 7.17E5 0.042765 0.930626.50 0.19139 0.000257 8.1E+2 4.91E5 0.039846 0.936386.75 0.17998 0.000189 1.1E+3 3.40E5 0.037209 0.941647.00 0.16949 0.000140 1.5E+3 2.37E5 0.034819 0.946447.25 0.15984 0.000104 2.0E+3 1.67E5 0.032647 0.950857.50 0.15094 7.84E5 2.6E+3 1.18E5 0.030668 0.954897.75 0.14273 5.92E5 3.4E+3 8.45E6 0.028860 0.958618.00 0.13514 4.51E5 4.5E+3 6.09E6 0.027204 0.962048.25 0.12810 3.45E5 5.8E+3 4.42E6 0.025684 0.965208.50 0.12158 2.66E5 7.5E+3 3.23E6 0.024286 0.968128.75 0.11552 2.06E5 9.7E+3 2.38E6 0.022997 0.970839.00 0.10989 1.60E5 1.2E+4 1.76E6 0.021806 0.973349.25 0.10464 1.25E5 1.6E+4 1.31E6 0.020704 0.975689.50 0.099751 9.88E6 2.0E+4 0.0 0.019682 0.977859.75 0.095181 7.81E6 2.5E+4 0.0 0.018733 0.9798710.0 0.090909 6.21E6 3.2E+4 0.0 0.017850 0.9817620.0 0.024390 0.0 2.2E+7 0.0 0.00462 1.01130.0 0.010989 0.0 1.2E+9 0.0 0.00207 1.01640.0 0.00621 0.0 2.0E+10 0.0 0.00117 1.01950.0 0.00398 0.0 1.9E+11 0.0 0.000747 1.019

1.1.2 Isentropic Flow for k=1.3



Table 1.2: Isentropic Flow k =1.3

M TT0

0

AA

PP0

APAP0

FF

0.00 1.00000 1.00000 5.9E+5 1.00000 5.9E+5 2.5E+50.05 0.99963 0.99875 11.72 0.99838 11.70 5.1040.10 0.99850 0.99502 5.886 0.99353 5.848 2.5760.20 0.99404 0.98026 2.994 0.97441 2.917 1.3340.25 0.99071 0.96937 2.426 0.96037 2.330 1.0950.30 0.98668 0.95629 2.054 0.94355 1.938 0.941060.35 0.98196 0.94111 1.793 0.92413 1.657 0.835130.40 0.97656 0.92399 1.602 0.90233 1.446 0.759370.45 0.97052 0.90507 1.459 0.87839 1.281 0.703680.50 0.96386 0.88452 1.348 0.85255 1.149 0.661990.55 0.95659 0.86250 1.261 0.82506 1.041 0.630420.60 0.94877 0.83920 1.193 0.79620 0.95007 0.606390.65 0.94040 0.81479 1.139 0.76623 0.87311 0.588110.70 0.93153 0.78945 1.097 0.73540 0.80691 0.574310.75 0.92219 0.76337 1.064 0.70397 0.74933 0.564030.80 0.91241 0.73671 1.040 0.67218 0.69876 0.556580.85 0.90222 0.70965 1.021 0.64026 0.65398 0.551400.90 0.89166 0.68234 1.009 0.60842 0.61402 0.548080.95 0.88077 0.65494 1.002 0.57685 0.57814 0.546281.0 0.86957 0.62759 1.000 0.54573 0.54573 0.545731.05 0.85809 0.60041 1.002 0.51521 0.51630 0.546211.10 0.84638 0.57353 1.008 0.48542 0.48946 0.547551.15 0.83446 0.54705 1.018 0.45649 0.46487 0.549611.20 0.82237 0.52106 1.032 0.42850 0.44226 0.552251.25 0.81013 0.49565 1.049 0.40154 0.42140 0.555371.30 0.79777 0.47089 1.070 0.37566 0.40209 0.558901.35 0.78531 0.44683 1.095 0.35090 0.38416 0.562751.40 0.77280 0.42353 1.123 0.32730 0.36748 0.566871.45 0.76024 0.40102 1.154 0.30487 0.35191 0.571201.50 0.74766 0.37933 1.189 0.28361 0.33735 0.575701.55 0.73509 0.35849 1.228 0.26352 0.32372 0.580331.60 0.72254 0.33849 1.271 0.24457 0.31091 0.585051.65 0.71004 0.31935 1.318 0.22675 0.29887 0.58985



Table 1.2: Isentropic Flow k=1.3 (continue)

M TT0

0

AA

PP0

APAP0

FF

1.70 0.69759 0.30107 1.369 0.21003 0.28753 0.594681.75 0.68522 0.28365 1.424 0.19436 0.27682 0.599531.80 0.67295 0.26706 1.484 0.17972 0.26671 0.604391.85 0.66077 0.25129 1.549 0.16605 0.25715 0.609241.90 0.64872 0.23633 1.618 0.15331 0.24808 0.614061.95 0.63679 0.22215 1.693 0.14147 0.23949 0.618852.00 0.62500 0.20874 1.773 0.13046 0.23133 0.623592.25 0.56838 0.15210 2.268 0.086453 0.19609 0.646362.50 0.51613 0.11029 2.954 0.056923 0.16818 0.667222.75 0.46852 0.079879 3.892 0.037425 0.14567 0.685973.00 0.42553 0.057957 5.160 0.024663 0.12725 0.702663.25 0.38694 0.042216 6.857 0.016335 0.11201 0.717423.50 0.35242 0.030918 9.110 0.010896 0.099263 0.730453.75 0.32161 0.02279112.07 0.00733 0.088503 0.741934.00 0.29412 0.01692015.94 0.00498 0.079346 0.752064.25 0.26959 0.01265720.95 0.00341 0.071497 0.761014.50 0.24768 0.00954 27.39 0.00236 0.064723 0.768934.75 0.22808 0.00725 35.59 0.00165 0.058841 0.775965.00 0.21053 0.00555 45.96 0.00117 0.053704 0.782215.25 0.19477 0.00428 58.98 0.000834 0.049195 0.787795.50 0.18059 0.00333 75.22 0.000601 0.045217 0.792785.75 0.16780 0.00261 95.34 0.000437 0.041692 0.797256.00 0.15625 0.00205 1.2E+2 0.000321 0.038555 0.801286.25 0.14579 0.00163 1.5E+2 0.000238 0.035752 0.804916.50 0.13629 0.00130 1.9E+2 0.000178 0.033238 0.808196.75 0.12764 0.00105 2.3E+2 0.000134 0.030976 0.811177.00 0.11976 0.000847 2.9E+2 0.000101 0.028932 0.813887.25 0.11256 0.000689 3.5E+2 7.75E5 0.027082 0.816357.50 0.10596 0.000563 4.3E+2 5.97E5 0.025400 0.818607.75 0.099906 0.000463 5.2E+2 4.62E5 0.023868 0.820668.00 0.094340 0.000382 6.2E+2 3.61E5 0.022469 0.822568.25 0.089211 0.000317 7.5E+2 2.83E5 0.021188 0.824308.50 0.084477 0.000265 9.0E+2 2.23E5 0.020011 0.82590




M TT0

0

AA

PP0

APAP0

FF

8.75 0.080100 0.000222 1.1E+3 1.77E5 0.018929 0.827389.00 0.076046 0.000186 1.3E+3 1.42E5 0.017932 0.828759.25 0.072284 0.000157 1.5E+3 1.14E5 0.017010 0.830029.50 0.068788 0.000133 1.8E+3 9.17E6 0.016157 0.831209.75 0.065533 0.000113 2.1E+3 7.44E6 0.015366 0.8322910.0 0.062500 9.69E5 2.4E+3 6.06E6 0.014631 0.8333120.0 0.016393 0.0 2.0E+5 0.0 0.00375 0.8486730.0 0.00735 0.0 2.9E+6 0.0 0.00167 0.8516540.0 0.00415 0.0 2.0E+7 0.0 0.000942 0.8527150.0 0.00266 0.0 8.7E+7 0.0 0.000604 0.85320

1.1.3 Isentropic Flow for k =1.4

Table 1.3: Isentropic Flow for k=1.4

M TT0

0

AA

PP0

APAP0

FF

0.0 1.00000 1.00000 5.8E+5 1.00000 5.8E+5 2.4E+50.05 0.99950 0.99875 11.59 0.99825 11.57 4.8380.1 0.99800 0.99502 5.822 0.99303 5.781 2.4430.20 0.99206 0.98028 2.964 0.97250 2.882 1.2680.25 0.98765 0.96942 2.403 0.95745 2.300 1.0420.30 0.98232 0.95638 2.035 0.93947 1.912 0.896990.35 0.97609 0.94128 1.778 0.91877 1.634 0.797380.40 0.96899 0.92427 1.590 0.89561 1.424 0.726320.45 0.96108 0.90551 1.449 0.87027 1.261 0.674230.50 0.95238 0.88517 1.340 0.84302 1.130 0.635350.55 0.94295 0.86342 1.255 0.81417 1.022 0.606020.60 0.93284 0.84045 1.188 0.78400 0.93155 0.583770.65 0.92208 0.81644 1.136 0.75283 0.85493 0.566920.70 0.91075 0.79158 1.094 0.72093 0.78896 0.554250.75 0.89888 0.76604 1.062 0.68857 0.73155 0.544850.80 0.88652 0.73999 1.038 0.65602 0.68110 0.538070.85 0.87374 0.71361 1.021 0.62351 0.63640 0.53338



Table 1.3: Isentropic Flow for k=1.4 (continue)

M TT0

0

AA

PP0

APAP0

FF

0.90 0.86059 0.68704 1.009 0.59126 0.59650 0.530390.95 0.84710 0.66044 1.002 0.55946 0.56066 0.528771.0 0.83333 0.63394 1.000 0.52828 0.52828 0.528281.05 0.81934 0.60765 1.002 0.49787 0.49888 0.528711.10 0.80515 0.58170 1.008 0.46835 0.47207 0.529891.15 0.79083 0.55616 1.017 0.43983 0.44751 0.531691.20 0.77640 0.53114 1.030 0.41238 0.42493 0.533991.25 0.76190 0.50670 1.047 0.38606 0.40411 0.536701.30 0.74738 0.48290 1.066 0.36091 0.38484 0.539741.35 0.73287 0.45980 1.089 0.33697 0.36697 0.543051.40 0.71839 0.43742 1.115 0.31424 0.35036 0.546551.45 0.70398 0.41581 1.144 0.29272 0.33486 0.550221.50 0.68966 0.39498 1.176 0.27240 0.32039 0.554011.55 0.67545 0.37495 1.212 0.25326 0.30685 0.557881.60 0.66138 0.35573 1.250 0.23527 0.29414 0.561821.65 0.64746 0.33731 1.292 0.21839 0.28221 0.565781.70 0.63371 0.31969 1.338 0.20259 0.27099 0.569761.75 0.62016 0.30287 1.386 0.18782 0.26042 0.573731.80 0.60680 0.28682 1.439 0.17404 0.25044 0.577681.85 0.59365 0.27153 1.495 0.16119 0.24102 0.581611.90 0.58072 0.25699 1.555 0.14924 0.23211 0.585491.95 0.56802 0.24317 1.619 0.13813 0.22367 0.589322.00 0.55556 0.23005 1.688 0.12780 0.21567 0.593092.25 0.49689 0.17404 2.096 0.086482 0.18130 0.610952.50 0.44444 0.13169 2.637 0.058528 0.15432 0.626932.75 0.39801 0.099939 3.338 0.039777 0.13276 0.640993.00 0.35714 0.076226 4.235 0.027224 0.11528 0.653263.25 0.32129 0.058510 5.369 0.018798 0.10093 0.663933.50 0.28986 0.045233 6.790 0.013111 0.089018 0.673203.75 0.26230 0.035235 8.552 0.00924 0.079035 0.681274.00 0.23810 0.02766210.72 0.00659 0.070595 0.688304.25 0.21680 0.02188613.36 0.00474 0.063401 0.694444.50 0.19802 0.01744916.56 0.00346 0.057227 0.69983



Table 1.3: Isentropic Flow for k=1.4 (continue)

M TT0

0

AA

PP0

APAP0

FF

4.75 0.18141 0.01401620.41 0.00254 0.051891 0.704585.00 0.16667 0.01134025.00 0.00189 0.047251 0.708765.25 0.15355 0.00924 30.45 0.00142 0.043194 0.712485.50 0.14184 0.00758 36.87 0.00107 0.039628 0.715785.75 0.13136 0.00625 44.40 0.000822 0.036477 0.718726.00 0.12195 0.00519 53.18 0.000633 0.033682 0.721366.25 0.11348 0.00434 63.37 0.000492 0.031191 0.723726.50 0.10582 0.00364 75.13 0.000385 0.028962 0.725866.75 0.098888 0.00308 88.66 0.000304 0.026960 0.727797.00 0.092593 0.00261 1.0E+2 0.000242 0.025156 0.729537.25 0.086862 0.00222 1.2E+2 0.000193 0.023525 0.731127.50 0.081633 0.00190 1.4E+2 0.000155 0.022046 0.732577.75 0.076849 0.00164 1.6E+2 0.000126 0.020700 0.733898.00 0.072464 0.00141 1.9E+2 0.000102 0.019473 0.735108.25 0.068435 0.00123 2.2E+2 8.38E5 0.018350 0.736208.50 0.064725 0.00107 2.5E+2 6.90E5 0.017321 0.737238.75 0.061303 0.000930 2.9E+2 5.70E5 0.016375 0.738179.00 0.058140 0.000815 3.3E+2 4.74E5 0.015504 0.739039.25 0.055210 0.000716 3.7E+2 3.95E5 0.014700 0.739849.50 0.052493 0.000631 4.2E+2 3.31E5 0.013957 0.740589.75 0.049969 0.000558 4.8E+2 2.79E5 0.013268 0.7412710.0 0.047619 0.000495 5.4E+2 2.36E5 0.012628 0.7419220.0 0.012346 1.69E5 1.5E+4 0.0 0.00322 0.7515130.0 0.00552 2.27E6 1.1E+5 0.0 0.00143 0.7533540.0 0.00312 0.0 4.8E+5 0.0 0.000808 0.7540150.0 0.00200 0.0 1.5E+6 0.0 0.000517 0.75431

1.1.4 Isentropic Flow k=1.67

Table 1.4: Isentropic Flow k=1.67

M TT0

0

AA

PP0

APAP0

FF

0.E+ 1.00000 1.00000 5.6E+5 1.00000 5.6E+5 2.1E+5




M TT0

0

AA

PP0

APAP0

FF

0.050 0.99916 0.99875 11.26 0.99792 11.24 4.2280.10 0.99666 0.99502 5.661 0.99170 5.614 2.1380.20 0.98678 0.98033 2.887 0.96737 2.793 1.1160.25 0.97949 0.96955 2.344 0.94966 2.226 0.920750.30 0.97073 0.95663 1.989 0.92864 1.847 0.795610.35 0.96058 0.94174 1.741 0.90462 1.575 0.710390.40 0.94913 0.92503 1.560 0.87797 1.370 0.649990.45 0.93647 0.90668 1.424 0.84908 1.209 0.606050.50 0.92272 0.88688 1.320 0.81835 1.080 0.573520.55 0.90799 0.86583 1.239 0.78616 0.97421 0.549200.60 0.89238 0.84371 1.176 0.75291 0.88531 0.530920.65 0.87601 0.82072 1.126 0.71896 0.80968 0.517220.70 0.85900 0.79704 1.087 0.68465 0.74451 0.507020.75 0.84144 0.77285 1.058 0.65031 0.68774 0.499550.80 0.82345 0.74832 1.035 0.61620 0.63783 0.494210.85 0.80513 0.72360 1.019 0.58259 0.59359 0.490560.90 0.78657 0.69884 1.008 0.54969 0.55411 0.488260.95 0.76785 0.67417 1.002 0.51766 0.51867 0.487041.0 0.74906 0.64970 1.000 0.48667 0.48667 0.486671.05 0.73028 0.62554 1.002 0.45682 0.45765 0.486991.10 0.71157 0.60176 1.007 0.42820 0.43121 0.487851.15 0.69298 0.57846 1.015 0.40086 0.40704 0.489151.20 0.67458 0.55568 1.027 0.37485 0.38487 0.490781.25 0.65641 0.53349 1.041 0.35019 0.36446 0.492691.30 0.63851 0.51192 1.057 0.32687 0.34563 0.494801.35 0.62091 0.49101 1.077 0.30487 0.32821 0.497061.40 0.60365 0.47077 1.098 0.28418 0.31206 0.499441.45 0.58674 0.45123 1.122 0.26475 0.29705 0.501891.50 0.57021 0.43238 1.148 0.24655 0.28307 0.504391.55 0.55407 0.41424 1.177 0.22952 0.27004 0.506921.60 0.53833 0.39681 1.207 0.21361 0.25786 0.509451.65 0.52300 0.38006 1.240 0.19877 0.24646 0.511981.70 0.50809 0.36400 1.275 0.18495 0.23577 0.51449




M TT0

0

AA

PP0

APAP0

FF

1.75 0.49360 0.34862 1.312 0.17208 0.22575 0.516971.80 0.47952 0.33389 1.351 0.16011 0.21632 0.519411.85 0.46587 0.31979 1.393 0.14898 0.20746 0.521801.90 0.45262 0.30632 1.436 0.13865 0.19911 0.524151.95 0.43979 0.29344 1.482 0.12905 0.19123 0.526442.00 0.42735 0.28115 1.530 0.12015 0.18380 0.528672.25 0.37093 0.22759 1.803 0.084419 0.15221 0.538962.50 0.32323 0.18532 2.135 0.059903 0.12788 0.547792.75 0.28301 0.15198 2.529 0.043013 0.10878 0.555273.00 0.24907 0.12560 2.990 0.031282 0.093543 0.561613.25 0.22034 0.10460 3.524 0.023048 0.081215 0.566973.50 0.19593 0.087791 4.134 0.017201 0.071115 0.571523.75 0.17510 0.074231 4.827 0.012998 0.062746 0.575404.00 0.15723 0.063214 5.608 0.00994 0.055742 0.578724.25 0.14183 0.054195 6.483 0.00769 0.049827 0.581584.50 0.12847 0.046759 7.456 0.00601 0.044789 0.584054.75 0.11684 0.040585 8.533 0.00474 0.040465 0.586215.00 0.10667 0.035424 9.721 0.00378 0.036730 0.588095.25 0.097719 0.03108211.02 0.00304 0.033481 0.589745.50 0.089817 0.02740612.45 0.00246 0.030640 0.591205.75 0.082809 0.02427714.00 0.00201 0.028141 0.592496.00 0.076570 0.02159815.68 0.00165 0.025933 0.593646.25 0.070993 0.01929317.50 0.00137 0.023972 0.594676.50 0.065990 0.01729919.47 0.00114 0.022223 0.595596.75 0.061488 0.01556821.58 0.000957 0.020657 0.596417.00 0.057422 0.01405623.85 0.000807 0.019249 0.597167.25 0.053739 0.01273226.28 0.000684 0.017980 0.597847.50 0.050394 0.01156828.87 0.000583 0.016831 0.598457.75 0.047346 0.01053931.64 0.000499 0.015788 0.599018.00 0.044563 0.00963 34.58 0.000429 0.014838 0.599528.25 0.042015 0.00882 37.71 0.000370 0.013971 0.599988.50 0.039677 0.00810 41.02 0.000321 0.013177 0.600418.75 0.037526 0.00745 44.53 0.000280 0.012449 0.60081


1.2. NAUGHTY PROFESSOR TABLES (NPT) FOR ISENTROPIC FLOW 17


M TT0

0

AA

PP0

APAP0

FF

9.00 0.035543 0.00687 48.24 0.000244 0.011779 0.601179.25 0.033712 0.00635 52.15 0.000214 0.011161 0.601509.50 0.032017 0.00588 56.28 0.000188 0.010591 0.601819.75 0.030445 0.00545 60.62 0.000166 0.010063 0.6021010.0 0.028986 0.00507 65.18 0.000147 0.00957 0.6023720.0 0.00741 0.000661 4.9E+2 4.90E6 0.00242 0.6063130.0 0.00331 0.000198 1.6E+3 0.0 0.00108 0.6070540.0 0.00186 8.42E5 3.9E+3 0.0 0.000607 0.6073250.0 0.00119 4.33E5 7.5E+3 0.0 0.000388 0.60744

1.2 Naughty Professor Tables (NPT) for

Isentropic Flow

1.2.1 NPT for Isentropic Flow k=1.2

Table 1.5: Naughty Professor for Isentropic flow k=1.2

M Fn RT0P

(P0A

PA

)2 RT0P2

(mA

)2 1R0P

(mA

)2 1R02T

(mA

)2

1.0E6 0.0 1 0 0 0 00.05 0.060083 1 0.00713 2.15E5 0.00301 0.003010.1 0.12066 1.001 0.02856 0.000347 0.012206 0.0121450.2 0.24533 1.004 0.11458 0.00575 0.051371 0.0503550.25 0.31046 1.006 0.17943 0.014412 0.08338 0.0808220.3 0.37818 1.009 0.25909 0.03088 0.12577 0.120260.35 0.44909 1.012 0.35379 0.05946 0.1808 0.170130.4 0.52379 1.016 0.4638 0.10604 0.25147 0.232290.45 0.60295 1.02 0.58946 0.17858 0.34168 0.309090.5 0.68728 1.025 0.73111 0.28778 0.45649 0.403470.55 0.77755 1.03 0.88918 0.44798 0.60246 0.519060.6 0.8746 1.036 1.064 0.6783 0.78813 0.660390.65 0.97935 1.042 1.256 1.004 1.025 0.833050.7 1.093 1.049 1.467 1.459 1.326 1.044



Table 1.5: Naughty Professor for Isentropic flow k=1.2(continue)

M Fn RT0P

(P0A

PA

)2 RT0P2

(mA

)2 1R0P

(mA

)2 1R02T

(mA

)2

0.75 1.216 1.056 1.695 2.089 1.711 1.3020.8 1.35 1.064 1.943 2.952 2.205 1.6170.85 1.497 1.072 2.21 4.128 2.838 2.0020.9 1.658 1.081 2.498 5.72 3.653 2.4750.95 1.834 1.09 2.807 7.865 4.705 3.0551 2.027 1.1 3.138 10.75 6.065 3.7661.05 2.24 1.11 3.492 14.6 7.829 4.6411.1 2.474 1.121 3.87 19.74 10.12 5.7181.15 2.733 1.132 4.272 26.58 13.11 7.0451.2 3.018 1.144 4.7 35.67 17.01 8.6831.25 3.333 1.156 5.155 47.73 22.12 10.711.3 3.682 1.169 5.637 63.69 28.83 13.211.35 4.068 1.182 6.147 84.79 37.66 16.311.4 4.496 1.196 6.688 1.1E+2 49.3 20.151.45 4.97 1.21 7.26 1.5E+2 64.68 24.911.5 5.496 1.225 7.864 2.E + 2 85.05 30.831.55 6.079 1.24 8.501 2.6E+2 1.1E+2 38.191.6 6.726 1.256 9.174 3.5E+2 1.5E+2 47.351.65 7.444 1.272 9.882 4.6E+2 2.E + 2 58.751.7 8.242 1.289 10.63 6.E + 2 2.6E+2 72.961.75 9.128 1.306 11.41 7.9E+2 3.4E+2 90.691.8 10.11 1.324 12.24 1.E + 3 4.6E+2 1.1E+21.85 11.21 1.342 13.11 1.4E+3 6.1E+2 1.4E+21.9 12.42 1.361 14.02 1.8E+3 8.2E+2 1.7E+21.95 13.77 1.38 14.97 2.4E+3 1.1E+3 2.2E+22 15.27 1.4 15.98 3.1E+3 1.5E+3 2.7E+22.25 25.69 1.506 21.76 1.2E+4 6.4E+3 8.3E+22.5 43.33 1.625 28.98 4.5E+4 2.9E+4 2.5E+32.75 73.07 1.756 37.89 1.7E+5 1.3E+5 7.8E+33 1.2E+2 1.9 48.79 6.1E+5 5.9E+5 2.4E+43.25 2.1E+2 2.056 61.97 2.2E+6 2.7E+6 7.2E+43.5 3.4E+2 2.225 77.77 7.6E+6 1.2E+7 2.2E+5



Table 1.5: Naughty Professor for Isentropic flow k=1.2(continue)

M Fn RT0P

(P0A

PA

)2 RT0P2

(mA

)2 1R0P

(mA

)2 1R02T

(mA

)2

3.75 5.6E+2 2.406 96.54 2.6E+7 5.1E+7 6.4E+54 9.2E+2 2.6 1.2E+2 8.4E+7 2.2E+8 1.8E+64.25 1.5E+3 2.806 1.4E+2 2.7E+8 9.E + 8 5.2E+64.5 2.4E+3 3.025 1.7E+2 8.2E+8 3.6E+9 1.4E+74.75 3.8E+3 3.256 2.1E+2 2.5E+9 1.4E+10 3.8E+75 5.9E+3 3.5 2.5E+2 7.2E+9 5.3E+10 1.E + 85.25 9.1E+3 3.756 3.E + 2 2.1E+10 2.E+11 2.6E+85.5 1.4E+4 4.025 3.5E+2 5.7E+10 6.9E+11 6.6E+85.75 2.1E+4 4.306 4.1E+2 1.5E+11 2.4E+12 1.6E+96 3.2E+4 4.6 4.7E+2 4.E+11 8.E+12 3.9E+96.25 4.7E+4 4.906 5.5E+2 1.E+12 2.6E+13 9.1E+96.5 6.9E+4 5.225 6.3E+2 2.5E+12 8.2E+13 2.1E+106.75 1.E + 5 5.556 7.2E+2 6.2E+12 2.5E+14 4.7E+107 1.5E+5 5.9 8.2E+2 1.5E+13 7.5E+14 1.E+117.25 2.1E+5 6.256 9.4E+2 3.4E+13 2.2E+15 2.3E+117.5 3E + 5 6.625 1.1E+3 7.7E+13 6.2E+15 4.8E+117.75 4.2E+5 7.006 1.2E+3 1.7E+14 1.7E+16 1.E+128 5.8E+5 7.4 1.4E+3 3.8E+14 4.6E+16 2.1E+128.258E + 5 7.806 1.5E+3 8.1E+14 1.2E+17 4.2E+128.5 1.1E+6 8.225 1.7E+3 1.7E+15 3.1E+17 8.3E+128.75 1.5E+6 8.656 1.9E+3 3.6E+15 7.9E+17 1.6E+139 2.E + 6 9.1 2.1E+3 7.2E+15 2.E+18 3.1E+139.25 2.7E+6 9.556 2.3E+3 1.5E+16 4.7E+18 6.E+139.5 3.7E+6 10.02 2.6E+3 2.9E+16 1.1E+19 1.1E+149.75 4.9E+6 10.51 2.8E+3 5.6E+16 2.6E+19 2.1E+1410 6.4E+6 0.11E+2 3.1E+3 1.1E+17 6.1E+19 3.8E+1420 1.8E+10 0.41E+2 4.7E+4 1.2E+25 1.3E+30 1.1E+2230 2.1E+12 0.91E+2 2.3E+5 8.9E+29 2.2E+36 3.5E+2640 6.6E+13 1.6E+2 7.3E+5 2.7E+33 6.3E+40 5.8E+2950 9.5E+14 2.5E+2 1.8E+6 1.3E+36 1.9E+44 1.9E+32




Table 1.6: NPT for Isentropic Flow k=1.3

M Fn RT0P

(P0A

PA

)2 RT0P2

(mA

)2 1R0P

(mA

)2 1R02T

(mA

)2

1.0E6 1.300E61 0 0 0 00.05 0.065094 1 0.0073 2.38E5 0.00326 0.003260.1 0.13075 1.002 0.029242 0.000385 0.013236 0.013170.2 0.26603 1.006 0.11749 0.0064 0.05587 0.0547670.25 0.33684 1.009 0.1842 0.016076 0.090877 0.0880940.3 0.41057 1.014 0.26633 0.034534 0.13743 0.131420.35 0.48789 1.018 0.36425 0.066696 0.19814 0.186470.4 0.56949 1.024 0.47838 0.11934 0.27648 0.255460.45 0.6561 1.03 0.60921 0.20173 0.37697 0.341190.5 0.74852 1.038 0.75732 0.32639 0.50552 0.447140.55 0.84758 1.045 0.92331 0.51023 0.66978 0.577690.6 0.95422 1.054 1.108 0.77598 0.8797 0.738240.65 1.069 1.063 1.312 1.154 1.148 0.935520.7 1.194 1.074 1.536 1.685 1.492 1.1780.75 1.33 1.084 1.781 2.423 1.933 1.4760.8 1.478 1.096 2.048 3.441 2.499 1.8410.85 1.639 1.108 2.338 4.833 3.229 2.2910.9 1.816 1.122 2.652 6.728 4.169 2.8450.95 2.009 1.135 2.992 9.291 5.383 3.5261 2.221 1.15 3.358 12.75 6.955 4.3651.05 2.454 1.165 3.751 17.38 8.993 5.41.1 2.71 1.181 4.174 23.58 11.64 6.6761.15 2.992 1.198 4.627 31.86 15.08 8.251.2 3.301 1.216 5.113 42.87 19.57 10.21.25 3.643 1.234 5.631 57.47 25.42 12.61.3 4.018 1.254 6.185 76.82 33.06 15.571.35 4.432 1.273 6.776 1.E+2 43.06 19.241.4 4.888 1.294 7.405 1.4E+2 56.16 23.781.45 5.391 1.315 8.075 1.8E+2 73.33 29.411.5 5.945 1.338 8.787 2.4E+2 95.86 36.361.55 6.556 1.36 9.543 3.2E+2 1.3E+2 44.981.6 7.229 1.384 10.34 4.2E+2 1.6E+2 55.641.65 7.971 1.408 11.2 5.5E+2 2.2E+2 68.83



Table 1.6: NPT for Isentropic Flow k=1.3 (continue)

M Fn RT0P

(P0A

PA

)2 RT0P2

(mA

)2 1R0P

(mA

)2 1R02T

(mA

)2

1.7 8.789 1.434 12.1 7.2E+2 2.8E+2 85.171.75 9.689 1.459 13.05 9.4E+2 3.7E+2 1.1E+21.8 10.68 1.486 14.06 1.2E+3 4.9E+2 1.3E+21.85 11.77 1.513 15.12 1.6E+3 6.4E+2 1.6E+21.9 12.98 1.542 16.25 2.1E+3 8.4E+2 2.E+21.95 14.3 1.57 17.44 2.7E+3 1.1E+3 2.5E+22 15.76 1.6 18.69 3.6E+3 1.5E+3 3.1E+22.25 25.51 1.759 26.01 1.3E+4 5.8E+3 8.8E+22.5 41.02 1.938 35.36 4.6E+4 2.3E+4 2.5E+32.75 65.39 2.134 47.13 1.5E+5 8.8E+4 7.E+33 1.E + 2 2.35 61.75 5.1E+5 3.3E+5 1.9E+43.25 1.6E+2 2.584 79.7 1.6E+6 1.2E+6 5.1E+43.5 2.5E+2 2.838 1.E + 2 4.8E+6 4.3E+6 1.3E+53.75 3.8E+2 3.109 1.3E+2 1.4E+7 1.5E+7 3.4E+54 5.7E+2 3.4 1.6E+2 3.9E+7 5.E + 7 8.4E+54.25 8.4E+2 3.709 2.E + 2 1.1E+8 1.6E+8 2.E+64.5 1.2E+3 4.037 2.4E+2 2.8E+8 4.9E+8 4.7E+64.75 1.8E+3 4.384 2.9E+2 7.1E+8 1.5E+9 1.1E+75 2.6E+3 4.75 3.5E+2 1.7E+9 4.3E+9 2.4E+75.25 3.6E+3 5.134 4.1E+2 4.1E+9 1.2E+10 5.2E+75.5 5.1E+3 5.538 4.9E+2 9.6E+9 3.3E+10 1.1E+85.75 7.E + 3 5.959 5.8E+2 2.2E+10 8.6E+10 2.2E+86 9.6E+3 6.4 6.7E+2 4.8E+10 2.2E+11 4.5E+86.25 1.3E+4 6.859 7.8E+2 1.E+11 5.5E+11 9.E+86.5 1.8E+4 7.338 9.1E+2 2.1E+11 1.3E+12 1.7E+96.75 2.3E+4 7.834 1.E + 3 4.4E+11 3.2E+12 3.3E+97 3.1E+4 8.35 1.2E+3 8.9E+11 7.3E+12 6.2E+97.25 4.1E+4 8.884 1.4E+3 1.7E+12 1.7E+13 1.1E+107.5 5.3E+4 9.438 1.5E+3 3.4E+12 3.7E+13 2.1E+107.75 6.9E+4 10.01 1.8E+3 6.4E+12 7.9E+13 3.7E+108 8.9E+4 10.6 2.E + 3 1.2E+13 1.7E+14 6.4E+108.25 1.1E+5 11.21 2.2E+3 2.2E+13 3.5E+14 1.1E+118.5 1.4E+5 11.84 2.5E+3 4.E+13 7.1E+14 1.9E+11



Table 1.6: NPT for Isentropic Flow k=1.3 (continue)

M Fn RT0P

(P0A

PA

)2 RT0P2

(mA

)2 1R0P

(mA

)2 1R02T

(mA

)2

8.75 1.8E+5 12.48 2.8E+3 7.1E+13 1.4E+15 3.2E+119 2.3E+5 13.15 3.1E+3 1.2E+14 2.8E+15 5.2E+119.25 2.8E+5 13.83 3.5E+3 2.1E+14 5.5E+15 8.6E+119.5 3.5E+5 14.54 3.8E+3 3.7E+14 1.E+16 1.4E+129.75 4.4E+5 15.26 4.2E+3 6.2E+14 2.E+16 2.2E+1210 5.4E+5 16. 4.7E+3 1.E+15 3.7E+16 3.5E+1220 1.8E+8 61. 7.1E+4 1.8E+21 1.4E+24 1.5E+1830 5.9E+9 1.4E+2 3.6E+5 9.5E+24 4.7E+28 3.6E+2140 7.E+10 2.4E+2 1.1E+6 4.3E+27 8.E+31 9.2E+2350 4.8E+11 3.8E+2 2.7E+6 4.9E+29 2.6E+34 6.8E+25


Table 1.7: NPT for Isentropic flow

M Fn RT0P

(P0A

PA

)2 RT0P2

(mA

)2 1R0P

(mA

)2 1R02T

(mA

)2

1.E6 1.4E6 1. 0. 0. 0. 0.0.05 0.070106 1.001 0.00747 2.62E5 0.00352 0.003510.1 0.14084 1.002 0.02992 0.000424 0.014268 0.0141970.2 0.28677 1.008 0.12039 0.00707 0.060404 0.0592120.25 0.36329 1.012 0.18896 0.017813 0.09846 0.0954490.3 0.44309 1.018 0.27358 0.038365 0.14927 0.142760.35 0.5269 1.024 0.37474 0.074314 0.21584 0.203160.4 0.6155 1.032 0.49305 0.13342 0.30214 0.279260.45 0.70969 1.04 0.62915 0.22634 0.41338 0.374320.5 0.81034 1.05 0.78382 0.36764 0.55637 0.492490.55 0.91838 1.06 0.95791 0.57709 0.73995 0.638890.6 1.035 1.072 1.152 0.88142 0.97562 0.819960.65 1.161 1.085 1.368 1.317 1.278 1.0440.7 1.297 1.098 1.607 1.931 1.667 1.320.75 1.446 1.113 1.869 2.79 2.168 1.6610.8 1.607 1.128 2.156 3.979 2.813 2.0820.85 1.784 1.145 2.469 5.613 3.646 2.602



Table 1.7: ?? (continue)

M Fn RT0P

(P0A

PA

)2 RT0P2

(mA

)2 1R0P

(mA

)2 1R02T

(mA

)2

0.9 1.977 1.162 2.81 7.846 4.721 3.2440.95 2.188 1.181 3.181 10.88 6.112 4.0371 2.419 1.2 3.583 14.98 7.913 5.0161.05 2.673 1.22 4.018 20.5 10.25 6.2271.1 2.95 1.242 4.487 27.9 13.28 7.7231.15 3.255 1.264 4.993 37.8 17.21 9.5711.2 3.59 1.288 5.538 50.97 22.32 11.861.25 3.957 1.312 6.124 68.48 28.97 14.681.3 4.36 1.338 6.752 91.66 37.61 18.161.35 4.802 1.365 7.426 1.2E+2 48.87 22.471.4 5.287 1.392 8.147 1.6E+2 63.53 27.791.45 5.819 1.421 8.918 2.2E+2 82.61 34.351.5 6.402 1.45 9.742 2.9E+2 1.1E+2 42.451.55 7.042 1.481 10.62 3.8E+2 1.4E+2 52.441.6 7.743 1.512 11.56 4.9E+2 1.8E+2 64.751.65 8.511 1.545 12.56 6.5E+2 2.4E+2 79.911.7 9.352 1.578 13.62 8.5E+2 3.1E+2 98.581.75 10.27 1.613 14.75 1.1E+3 4.E+2 1.2E+21.8 11.28 1.648 15.94 1.4E+3 5.2E+2 1.5E+21.85 12.38 1.685 17.21 1.9E+3 6.8E+2 1.8E+21.9 13.58 1.722 18.56 2.4E+3 8.8E+2 2.3E+21.95 14.9 1.761 19.99 3.2E+3 1.1E+3 2.8E+22 16.33 1.8 21.5 4.1E+3 1.5E+3 3.4E+22.25 25.68 2.012 30.42 1.4E+4 5.4E+3 9.5E+22.5 39.87 2.25 41.99 4.8E+4 1.9E+4 2.6E+32.75 61.06 2.512 56.74 1.5E+5 6.7E+4 6.7E+33 92.2 2.8 75.25 4.6E+5 2.2E+5 1.7E+43.25 1.4E+2 3.112 98.17 1.3E+6 7.2E+5 4.2E+43.5 2.E + 2 3.45 1.3E+2 3.6E+6 2.2E+6 1.E+53.75 2.9E+2 3.812 1.6E+2 9.7E+6 6.5E+6 2.3E+54 4.1E+2 4.2 2.E+2 2.5E+7 1.9E+7 5.2E+54.25 5.8E+2 4.612 2.5E+2 6.1E+7 5.1E+7 1.1E+64.5 8.1E+2 5.05 3.1E+2 1.4E+8 1.4E+8 2.4E+6




M Fn RT0P

(P0A

PA

)2 RT0P2

(mA

)2 1R0P

(mA

)2 1R02T

(mA

)2

4.75 1.1E+3 5.512 3.7E+2 3.3E+8 3.5E+8 4.9E+65 1.5E+3 6. 4.5E+2 7.3E+8 8.6E+8 9.8E+65.25 2.E + 3 6.512 5.4E+2 1.6E+9 2.1E+9 1.9E+75.5 2.7E+3 7.05 6.4E+2 3.3E+9 4.8E+9 3.7E+75.75 3.6E+3 7.612 7.5E+2 6.8E+9 1.1E+10 6.9E+76 4.6E+3 8.2 8.8E+2 1.4E+10 2.4E+10 1.3E+86.25 6.E + 3 8.812 1.E+3 2.6E+10 5.2E+10 2.3E+86.5 7.7E+3 9.45 1.2E+3 5.E+10 1.1E+11 4.E+86.75 9.8E+3 10.11 1.4E+3 9.4E+10 2.2E+11 6.9E+87 1.2E+4 10.8 1.6E+3 1.7E+11 4.5E+11 1.2E+97.25 1.5E+4 11.51 1.8E+3 3.1E+11 8.9E+11 2.E+97.5 1.9E+4 12.25 2.1E+3 5.5E+11 1.7E+12 3.3E+97.75 2.4E+4 13.01 2.3E+3 9.5E+11 3.2E+12 5.3E+98 2.9E+4 13.8 2.6E+3 1.6E+12 6.E+12 8.5E+98.25 3.6E+4 14.61 3.E+3 2.8E+12 1.1E+13 1.4E+108.5 4.4E+4 15.45 3.3E+3 4.6E+12 2.E+13 2.1E+108.75 5.3E+4 16.31 3.7E+3 7.5E+12 3.5E+13 3.3E+109 6.4E+4 17.2 4.2E+3 1.2E+13 6.2E+13 5.1E+109.25 7.7E+4 18.11 4.6E+3 2.E+13 1.1E+14 7.7E+109.5 9.2E+4 19.05 5.1E+3 3.1E+13 1.8E+14 1.2E+119.75 1.1E+5 20.01 5.7E+3 4.9E+13 3.1E+14 1.7E+1110 1.3E+5 21 6.3E+3 7.5E+13 5.1E+14 2.5E+1120 1.5E+7 81 9.7E+4 1.5E+19 7.6E+20 1.3E+1630 2.5E+8 1.8E+2 4.9E+5 2.2E+22 3.5E+24 8.E+1840 1.9E+9 3.2E+2 1.5E+6 3.8E+24 1.5E+27 7.9E+2050 8.8E+9 5.E + 2 3.7E+6 2.1E+26 1.6E+29 2.8E+22


Table 1.8: NPT for Isentropic Flow

M Fn RT0P

(P0A

PA

)2 RT0P2

(mA

)2 1R0P

(mA

)2 1R02T

(mA

)2

1.E6 1.67E6 1 0 0 0 0



Table 1.8: NPT for Isentropic Flow (continue)

M Fn RT0P

(P0A

PA

)2 RT0P2

(mA

)2 1R0P

(mA

)2 1R02T

(mA

)2

0.05 0.08364 1.001 0.00791 3.31E5 0.0042 0.004190.1 0.16812 1.003 0.031733 0.000537 0.017066 0.0169810.2 0.34298 1.013 0.1282 0.00903 0.072815 0.0713830.25 0.4351 1.021 0.2018 0.022877 0.11937 0.115730.3 0.53155 1.03 0.29322 0.049609 0.18219 0.174290.35 0.63327 1.041 0.40332 0.096853 0.26546 0.249990.4 0.74124 1.054 0.53315 0.17541 0.37473 0.346640.45 0.8565 1.068 0.68388 0.30041 0.51735 0.469070.5 0.98013 1.084 0.85688 0.49292 0.70293 0.623420.55 1.113 1.101 1.054 0.78198 0.94403 0.817370.6 1.257 1.121 1.276 1.208 1.257 1.0610.65 1.413 1.142 1.525 1.824 1.663 1.3650.7 1.582 1.164 1.804 2.705 2.19 1.7460.75 1.767 1.188 2.114 3.952 2.874 2.2210.8 1.967 1.214 2.458 5.697 3.761 2.8150.85 2.186 1.242 2.838 8.123 4.913 3.5550.9 2.425 1.271 3.257 11.47 6.406 4.4770.95 2.686 1.302 3.717 16.05 8.343 5.6241 2.97 1.335 4.222 22.3 10.85 7.0511.05 3.28 1.369 4.775 30.76 14.1 8.8231.1 3.619 1.405 5.378 42.18 18.31 11.021.15 3.988 1.443 6.036 57.49 23.76 13.741.2 4.391 1.482 6.751 77.94 30.8 17.111.25 4.83 1.523 7.528 1.1E+2 39.88 21.281.3 5.307 1.566 8.371 1.4E+2 51.6 26.421.35 5.827 1.611 9.283 1.9E+2 66.69 32.751.4 6.392 1.657 10.27 2.5E+2 86.1 40.531.45 7.006 1.704 11.33 3.3E+2 1.1E+2 50.091.5 7.672 1.754 12.48 4.4E+2 1.4E+2 61.821.55 8.395 1.805 13.71 5.8E+2 1.8E+2 76.161.6 9.178 1.858 15.04 7.6E+2 2.4E+2 93.691.65 10.03 1.912 16.46 9.9E+2 3.E+2 1.2E+21.7 10.94 1.968 17.99 1.3E+3 3.9E+2 1.4E+2




M Fn RT0P

(P0A

PA

)2 RT0P2

(mA

)2 1R0P

(mA

)2 1R02T

(mA

)2

1.75 11.93 2.026 19.62 1.7E+3 5.E+2 1.7E+21.8 13 2.085 21.37 2.2E+3 6.3E+2 2.1E+21.85 14.15 2.147 23.23 2.8E+3 8.1E+2 2.6E+21.9 15.4 2.209 25.22 3.6E+3 1.E+3 3.1E+21.95 16.73 2.274 27.35 4.6E+3 1.3E+3 3.8E+22 18.17 2.34 29.6 5.9E+3 1.6E+3 4.6E+22.25 27.11 2.696 43.16 1.9E+4 5.2E+3 1.2E+32.5 39.62 3.094 61.15 5.7E+4 1.6E+4 2.9E+32.75 56.8 3.533 84.51 1.6E+5 4.5E+4 6.8E+33 79.93 4.015 1.1E+2 4.4E+5 1.2E+5 1.5E+43.25 1.1E+2 4.538 1.5E+2 1.1E+6 3.2E+5 3.3E+43.5 1.5E+2 5.104 2.E+2 2.7E+6 7.9E+5 6.9E+43.75 2.E + 2 5.711 2.5E+2 6.2E+6 1.9E+6 1.4E+54 2.7E+2 6.36 3.2E+2 1.4E+7 4.3E+6 2.7E+54.25 3.5E+2 7.051 4.E+2 2.9E+7 9.4E+6 5.1E+54.5 4.5E+2 7.784 5.E+2 6.E+7 2.E+7 9.4E+54.75 5.7E+2 8.558 6.1E+2 1.2E+8 4.1E+7 1.7E+65 7.2E+2 9.375 7.4E+2 2.3E+8 8.3E+7 2.9E+65.25 9.E + 2 10.23 8.9E+2 4.3E+8 1.6E+8 5.E+65.5 1.1E+3 11.13 1.1E+3 8.E+8 3.E+8 8.3E+65.75 1.4E+3 12.08 1.3E+3 1.4E+9 5.6E+8 1.4E+76 1.7E+3 13.06 1.5E+3 2.5E+9 1.E+9 2.2E+76.25 2.E + 3 14.09 1.7E+3 4.3E+9 1.8E+9 3.5E+76.5 2.4E+3 15.15 2.E+3 7.2E+9 3.1E+9 5.4E+76.75 2.9E+3 16.26 2.3E+3 1.2E+10 5.3E+9 8.3E+77 3.5E+3 17.41 2.7E+3 1.9E+10 8.9E+9 1.3E+87.25 4.1E+3 18.61 3.1E+3 3.1E+10 1.5E+10 1.9E+87.5 4.8E+3 19.84 3.5E+3 4.9E+10 2.4E+10 2.8E+87.75 5.6E+3 21.12 4.E+3 7.7E+10 3.8E+10 4.E+88 6.6E+3 22.44 4.5E+3 1.2E+11 6.E+10 5.8E+88.25 7.6E+3 23.8 5.1E+3 1.8E+11 9.4E+10 8.3E+88.5 8.8E+3 25.2 5.8E+3 2.7E+11 1.4E+11 1.2E+98.75 1.E + 4 26.65 6.5E+3 4.E+11 2.2E+11 1.6E+9




M Fn RT0P

(P0A

PA

)2 RT0P2

(mA

)2 1R0P

(mA

)2 1R02T

(mA

)2

9 1.2E+4 28.13 7.2E+3 5.8E+11 3.3E+11 2.3E+99.25 1.3E+4 29.66 8.E+3 8.4E+11 4.9E+11 3.1E+99.5 1.5E+4 31.23 8.9E+3 1.2E+12 7.2E+11 4.3E+99.75 1.7E+4 32.85 9.9E+3 1.7E+12 1.1E+12 5.8E+910 1.9E+4 34.5 1.1E+4 2.4E+12 1.5E+12 7.7E+920 5.9E+5 1.4E+2 1.7E+5 3.5E+16 4.2E+16 2.8E+1330 4.4E+6 3.E+2 8.6E+5 1.E+19 1.8E+19 3.5E+1540 1.8E+7 5.4E+2 2.7E+6 5.5E+20 1.3E+21 1.1E+1750 5.6E+7 8.4E+2 6.6E+6 1.2E+22 3.6E+22 1.6E+18


Chapter 2

Isothermal Nozzle

2.1 Isothermal Nozzle for k=1.2

Table 2.1: Isothermal Nozzle for k=1.2

M T0T0

P0P0

AA

PP

APAP0

FF

1.E6 0.90909 1.029 5.5E + 5 1.822 1.E + 6 4.5E+50.05 0.90932 1.029 10.99 1.819 20 9.1180.1 0.91 1.029 5.521 1.811 10 4.60.2 0.91273 1.028 2.811 1.779 5 2.3820.25 0.91477 1.028 2.279 1.755 4 1.9550.3 0.91727 1.028 1.931 1.726 3.333 1.6790.35 0.92023 1.028 1.688 1.693 2.857 1.490.4 0.92364 1.028 1.51 1.655 2.5 1.3550.45 0.9275 1.027 1.377 1.614 2.222 1.2560.5 0.93182 1.027 1.275 1.568 2 1.1820.55 0.93659 1.026 1.196 1.52 1.818 1.1260.6 0.94182 1.025 1.135 1.468 1.667 1.0850.65 0.9475 1.023 1.088 1.414 1.538 1.0540.7 0.95364 1.021 1.052 1.358 1.429 1.0310.75 0.96023 1.019 1.026 1.3 1.333 1.0150.8 0.96727 1.016 1.007 1.241 1.25 1.0050.85 0.97477 1.013 0.99603 1.181 1.176 0.99840.9 0.98273 1.01 0.9914 1.121 1.111 0.99596

29

30 CHAPTER 2. ISOTHERMAL NOZZLE

Table 2.1: Isothermal Nozzle for k=1.2 (continue)

M T0T0

P0P0

AA

PP

APAP0

FF

0.95 0.99114 1.005 0.99282 1.06 1.053 0.996651 1 1 1 1 1 11.05 1.009 0.99417 1.013 0.94035 0.95238 1.0061.1 1.019 0.98754 1.031 0.88161 0.90909 1.0131.15 1.029 0.98008 1.055 0.82407 0.86957 1.0231.2 1.04 0.97173 1.085 0.76797 0.83333 1.0331.25 1.051 0.96245 1.121 0.71355 0.8 1.0451.3 1.063 0.95221 1.164 0.661 0.76923 1.0591.35 1.075 0.94097 1.213 0.61049 0.74074 1.0731.4 1.087 0.9287 1.271 0.56214 0.71429 1.0881.45 1.1 0.9154 1.336 0.51608 0.68966 1.1041.5 1.114 0.90103 1.411 0.47237 0.66667 1.1211.55 1.127 0.88561 1.497 0.43106 0.64516 1.1391.6 1.142 0.86912 1.594 0.39219 0.625 1.1571.65 1.157 0.8516 1.704 0.35576 0.60606 1.1751.7 1.172 0.83305 1.828 0.32174 0.58824 1.1951.75 1.188 0.81351 1.97 0.29011 0.57143 1.2141.8 1.204 0.79301 2.13 0.2608 0.55556 1.2341.85 1.22 0.77161 2.312 0.23375 0.54054 1.2551.9 1.237 0.74935 2.52 0.20888 0.52632 1.2761.95 1.255 0.72631 2.756 0.18609 0.51282 1.2972 1.273 0.70256 3.025 0.1653 0.5 1.3182.25 1.369 0.57601 5.086 0.087379 0.44444 1.4292.5 1.477 0.44539 9.334 0.042852 0.4 1.5452.75 1.597 0.32294 18.65 0.019497 0.36364 1.6653 1.727 0.21855 40.5 0.00823 0.33333 1.7883.25 1.869 0.13751 95.47 0.00322 0.30769 1.9133.5 2.023 0.080193 2.4E + 2 0.00117 0.28571 2.0393.75 2.187 0.043242 6.8E + 2 0.000395 0.26667 2.1674 2.364 0.02152 2.E + 3 0.000123 0.25 2.2954.25 2.551 0.00987 6.6E + 3 3.58E5 0.23529 2.4254.5 2.75 0.00417 2.3E + 4 9.64E6 0.22222 2.5564.75 2.96 0.00162 8.7E + 4 2.41E6 0.21053 2.687


2.1. ISOTHERMAL NOZZLE FOR K=1.2 31


M T0T0

P0P0

AA

PP

APAP0

FF

5 3.182 0.000578 3.6E + 5 0 0 2.8185.25 3.415 0.00019 1.6E + 6 0 0 2.955.5 3.659 5.73E5 7.6E + 6 0 0 3.0835.75 3.915 1.59E5 3.9E + 7 0 0 3.2156 4.182 4.06E6 2.2E + 8 0 0 3.3486.25 4.46 0 1.3E + 9 0 0 3.4826.5 4.75 0 8.6E + 9 0 0 3.6156.75 5.051 0 6.1E+10 0 0 3.7497 5.364 0 4.6E+11 0 0 3.8837.25 5.687 0 3.8E+12 0 0 4.0177.5 6.023 0 3.3E+13 0 0 4.1527.75 6.369 0 3.2E+14 0 0 4.2868 6.727 0 3.3E+15 0 0 4.428.25 7.097 0 3.6E+16 0 0 4.5558.5 7.477 0 4.3E+17 0 0 4.698.75 7.869 0 5.6E+18 0 0 4.8259 8.273 0 7.8E+19 0 0 4.969.25 8.687 0 1.2E+21 0 0 5.0959.5 9.114 0 1.9E+22 0 0 5.239.75 9.551 0 3.3E+23 0 0 5.36510 10 0 6.3E+24 0 0 5.520 37.27 0 4.7E+102 0 0 10.9330 82.73 0 6.E+232 0 0 16.3840 1.5E+2 0 0 0 21.8350 2.3E+2 0 0 0 27.28

Table 2.2: Isothermal Table

M T0T0

P0P0

AA

PP

APAP0

FF

0.00 0.52828 1.064 5.0E + 5 2.014 1.0E+6 4.2E+50.05 0.52921 1.064 9.949 2.010 20.00 8.3620.1 0.53199 1.064 5.001 2.000 10.00 4.2250.2 0.54322 1.064 2.553 1.958 5.000 2.200




M T0T0

P0P0

AA

PP

APAP0

FF

0.3 0.56232 1.063 1.763 1.891 3.333 1.5640.4 0.58985 1.062 1.389 1.800 2.500 1.2750.5 0.62665 1.059 1.183 1.690 2.000 1.1250.6 0.67383 1.055 1.065 1.565 1.667 1.0440.7 0.73278 1.047 0.99967 1.429 1.429 1.0040.8 0.80528 1.036 0.97156 1.287 1.250 0.987500.9 0.89348 1.021 0.97274 1.142 1.111 0.987961.00 1.000 1.000 1.000 1.000 1.000 1.0001.10 1.128 0.97376 1.053 0.86329 0.90909 1.0201.20 1.281 0.94147 1.134 0.73492 0.83333 1.0471.30 1.464 0.90302 1.247 0.61693 0.76923 1.0791.40 1.681 0.85853 1.399 0.51069 0.71429 1.1141.50 1.939 0.80844 1.599 0.41686 0.66667 1.1531.60 2.245 0.75344 1.863 0.33554 0.62500 1.1941.70 2.608 0.69449 2.209 0.26634 0.58824 1.2371.80 3.035 0.63276 2.665 0.20846 0.55556 1.2811.90 3.540 0.56954 3.271 0.16090 0.52632 1.3282.00 4.134 0.50618 4.083 0.12246 0.50000 1.3752.50 9.026 0.22881 15.78 0.025349 0.40000 1.6253.000 19.41 0.071758 90.14 0.00370 0.33333 1.8893.500 40.29 0.015317 7.5E + 2 0.000380 0.28571 2.1614.000 80.21 0.00221 9.1E + 3 2.75E5 0.25000 2.4384.500 1.5E + 2 0.000215 1.6E + 5 1.41E6 0.22222 2.7185.000 2.8E + 2 1.41E5 4.0E + 6 0.0 0.20000 3.0005.500 4.9E + 2 0.0 1.4E + 8 0.0 0.18182 3.2846.000 8.3E + 2 0.0 7.3E + 9 0.0 0.16667 3.5696.500 1.4E + 3 0.0 5.3E+11 0.0 0.15385 3.8567.000 2.2E + 3 0.0 5.6E+13 0.0 0.14286 4.1437.500 3.4E + 3 0.0 8.3E+15 0.0 0.13333 4.4318.000 5.2E + 3 0.0 1.8E+18 0.0 0.12500 4.7198.500 7.7E + 3 0.0 5.4E+20 0.0 0.11765 5.0079.000 1.1E + 4 0.0 2.3E+23 0.0 0.11111 5.2969.500 1.6E + 4 0.0 1.4E+26 0.0 0.10526 5.586




M T0T0

P0P0

AA

PP

APAP0

FF

10.00 2.2E + 4 0.0 1.2E+29 0.0 0.1000005.875


Table 2.3: Isothermal Nozzle for K=1.3

M T0T0

P0P0

AA

PP

APAP0

FF

1.0E6 0.86957 1.045 5.2E + 5 1.916 1.E + 6 4.3E+50.05 0.86989 1.045 10.46 1.912 20 8.7240.1 0.87087 1.045 5.255 1.903 10 4.4040.2 0.87478 1.045 2.679 1.866 5 2.2870.25 0.87772 1.045 2.175 1.839 4 1.880.3 0.8813 1.045 1.845 1.807 3.333 1.6190.35 0.88554 1.045 1.615 1.769 2.857 1.440.4 0.89043 1.044 1.448 1.726 2.5 1.3130.45 0.89598 1.043 1.323 1.679 2.222 1.2210.5 0.90217 1.042 1.228 1.628 2 1.1520.55 0.90902 1.041 1.155 1.574 1.818 1.1010.6 0.91652 1.039 1.099 1.516 1.667 1.0640.65 0.92467 1.037 1.057 1.456 1.538 1.0360.7 0.93348 1.034 1.025 1.393 1.429 1.0170.75 0.94293 1.03 1.003 1.329 1.333 1.0040.8 0.95304 1.026 0.9892 1.264 1.25 0.995650.85 0.9638 1.021 0.9823 1.198 1.176 0.991940.9 0.97522 1.015 0.98202 1.131 1.111 0.991790.95 0.98728 1.008 0.98799 1.065 1.053 0.994621 1 1 1 1 1 11.05 1.013 0.99097 1.018 0.93555 0.95238 1.0081.1 1.027 0.98079 1.042 0.87241 0.90909 1.0171.15 1.042 0.96941 1.072 0.81089 0.86957 1.0281.2 1.057 0.95678 1.109 0.75126 0.83333 1.0411.25 1.073 0.94288 1.153 0.69376 0.8 1.0541.3 1.09 0.92768 1.205 0.63859 0.76923 1.069



Table 2.3: Isothermal Nozzle for K=1.3 (continue)

M T0T0

P0P0

AA

PP

APAP0

FF

1.35 1.107 0.91118 1.264 0.58589 0.74074 1.0851.4 1.125 0.89336 1.333 0.5358 0.71429 1.1021.45 1.144 0.87424 1.412 0.4884 0.68966 1.1191.5 1.163 0.85386 1.502 0.44375 0.66667 1.1381.55 1.183 0.83224 1.605 0.40187 0.64516 1.1571.6 1.203 0.80945 1.723 0.36277 0.625 1.1761.65 1.225 0.78555 1.857 0.3264 0.60606 1.1961.7 1.247 0.76062 2.009 0.29273 0.58824 1.2171.75 1.269 0.73475 2.184 0.26168 0.57143 1.2381.8 1.292 0.70804 2.383 0.23317 0.55556 1.2591.85 1.316 0.6806 2.61 0.20709 0.54054 1.2811.9 1.34 0.65256 2.871 0.18332 0.52632 1.3031.95 1.366 0.62403 3.17 0.16176 0.51282 1.3252 1.391 0.59514 3.514 0.14227 0.5 1.3482.25 1.53 0.45018 6.232 0.071317 0.44444 1.4652.5 1.685 0.31598 12.14 0.032959 0.4 1.5872.75 1.856 0.20478 25.89 0.014043 0.36364 1.7123 2.043 0.12207 60.42 0.00552 0.33333 1.8413.25 2.247 0.066748 1.5E + 2 0.002 0.30769 1.9713.5 2.467 0.033413 4.3E + 2 0.000667 0.28571 2.1023.75 2.704 0.015292 1.3E + 3 0.000205 0.26667 2.2364 2.957 0.00639 4.3E + 3 5.83E5 0.25 2.374.25 3.226 0.00244 1.5E + 4 1.53E5 0.23529 2.5044.5 3.511 0.00085 6.E + 4 3.68E6 0.22222 2.644.75 3.813 0.00027 2.6E + 5 0 0 2.7765 4.13 7.84E5 1.2E + 6 0 0 2.9135.25 4.465 2.08E5 6.E + 6 0 0 3.055.5 4.815 5.02E6 3.3E + 7 0 0 3.1885.75 5.182 0 2.E + 8 0 0 3.3266 5.565 0 1.3E + 9 0 0 3.4646.25 5.965 0 8.9E + 9 0 0 3.6026.5 6.38 0 6.8E+10 0 0 3.7416.75 6.813 0 5.6E+11 0 0 3.88



Table 2.3: Isothermal Nozzle for K=1.3 (continue)

M T0T0

P0P0

AA

PP

APAP0

FF

7 7.261 0 5.1E+12 0 0 4.0197.25 7.726 0 5.E + 13 0 0 4.1587.5 8.207 0 5.3E+14 0 0 4.2977.75 8.704 0 6.1E+15 0 0 4.4378 9.217 0 7.6E+16 0 0 4.5768.25 9.747 0 1.E + 18 0 0 4.7168.5 10.29 0 1.5E+19 0 0 4.8558.75 10.86 0 2.4E+20 0 0 4.9959 11.43 0 4.3E+21 0 0 5.1359.25 12.03 0 8.E + 22 0 0 5.2759.5 12.64 0 1.6E+24 0 0 5.4159.75 13.27 0 3.7E+25 0 0 5.55510 13.91 0 8.8E+26 0 0 5.69620 53.04 0 2.2E+111 0 0 11.3330 1.2E+2 0 2.E+252 0 0 16.9740 2.1E+2 0 0 0 22.6250 3.3E+2 0 0 0 28.27



M T0T0

P0P0

AA

PP

APAP0

FF

1.0E6 0.83333 1.064 5.E + 5 2.014 1.E + 6 4.2E+50.05 0.83375 1.064 9.949 2.01 20 8.3620.1 0.835 1.064 5.001 2 10 4.2250.2 0.84 1.064 2.553 1.958 5 2.20.25 0.84375 1.064 2.075 1.928 4 1.8120.3 0.84833 1.063 1.763 1.891 3.333 1.5640.35 0.85375 1.063 1.546 1.848 2.857 1.3950.4 0.86 1.062 1.389 1.8 2.5 1.2750.45 0.86708 1.061 1.272 1.748 2.222 1.188




M T0T0

P0P0

AA

PP

APAP0

FF

0.5 0.875 1.059 1.183 1.69 2 1.1250.55 0.88375 1.057 1.116 1.629 1.818 1.0780.6 0.89333 1.055 1.065 1.565 1.667 1.0440.65 0.90375 1.051 1.027 1.498 1.538 1.020.7 0.915 1.047 0.99967 1.429 1.429 1.0040.75 0.92708 1.042 0.9816 1.358 1.333 0.993060.8 0.94 1.036 0.97156 1.287 1.25 0.98750.85 0.95375 1.029 0.96877 1.214 1.176 0.986030.9 0.96833 1.021 0.97274 1.142 1.111 0.987960.95 0.98375 1.011 0.98319 1.071 1.053 0.992761 1 1 1 1 1 11.05 1.017 0.98761 1.023 0.93076 0.95238 1.0091.1 1.035 0.97376 1.053 0.86329 0.90909 1.021.15 1.054 0.95838 1.09 0.79792 0.86957 1.0331.2 1.073 0.94147 1.134 0.73492 0.83333 1.0471.25 1.094 0.92302 1.186 0.67452 0.8 1.0631.3 1.115 0.90302 1.247 0.61693 0.76923 1.0791.35 1.137 0.88151 1.317 0.56228 0.74074 1.0961.4 1.16 0.85853 1.399 0.51069 0.71429 1.1141.45 1.184 0.83415 1.492 0.4622 0.68966 1.1331.5 1.208 0.80844 1.599 0.41686 0.66667 1.1531.55 1.234 0.7815 1.722 0.37465 0.64516 1.1731.6 1.26 0.75344 1.863 0.33554 0.625 1.1941.65 1.287 0.72439 2.024 0.29947 0.60606 1.2151.7 1.315 0.69449 2.209 0.26634 0.58824 1.2371.75 1.344 0.6639 2.421 0.23604 0.57143 1.2591.8 1.373 0.63276 2.665 0.20846 0.55556 1.2811.85 1.404 0.60126 2.946 0.18346 0.54054 1.3041.9 1.435 0.56954 3.271 0.1609 0.52632 1.3281.95 1.467 0.53779 3.647 0.14061 0.51282 1.3512 1.5 0.50618 4.083 0.12246 0.5 1.3752.25 1.677 0.35556 7.636 0.058207 0.44444 1.4982.5 1.875 0.22881 15.78 0.025349 0.4 1.625




M T0T0

P0P0

AA

PP

APAP0

FF

2.75 2.094 0.13434 35.95 0.010115 0.36364 1.7563 2.333 0.07175890.14 0.0037 0.33333 1.8893.25 2.594 0.034809 2.5E + 2 0.00124 0.30769 2.0243.5 2.875 0.015317 7.5E + 2 0.00038 0.28571 2.1613.75 3.177 0.00611 2.5E + 3 0.000107 0.26667 2.2994 3.5 0.00221 9.1E + 3 2.75E5 0.25 2.4384.25 3.844 0.000724 3.6E + 4 6.5E 6 0.23529 2.5774.5 4.208 0.000215 1.6E + 5 1.41E6 0.22222 2.7184.75 4.594 5.79E5 7.6E + 5 0 0 2.8595 5 1.41E5 4.E + 6 0 0 35.25 5.427 3.13E6 2.3E + 7 0 0 3.1425.5 5.875 0 1.4E + 8 0 0 3.2845.75 6.344 0 9.7E + 8 0 0 3.4276 6.833 0 7.3E + 9 0 0 3.5696.25 7.344 0 6.E + 10 0 0 3.7126.5 7.875 0 5.3E+11 0 0 3.8566.75 8.427 0 5.2E+12 0 0 3.9997 9 0 5.6E+13 0 0 4.1437.25 9.594 0 6.5E+14 0 0 4.2877.5 10.21 0 8.3E+15 0 0 4.4317.75 10.84 0 1.2E+17 0 0 4.5758 11.5 0 1.8E+18 0 0 4.7198.25 12.18 0 3.E + 19 0 0 4.8638.5 12.87 0 5.4E+20 0 0 5.0078.75 13.59 0 1.1E+22 0 0 5.1529 14.33 0 2.3E+23 0 0 5.2969.25 15.09 0 5.5E+24 0 0 5.4419.5 15.87 0 1.4E+26 0 0 5.5869.75 16.68 0 4.E + 27 0 0 5.7310 17.5 0 1.2E+29 0 0 5.87520 67.5 0 9.9E+119 0 0 11.6930 1.5E+2 0 6.7E+271 0 0 17.5140 2.7E+2 0 0 0 23.34




M T0T0

P0P0

AA

PP

APAP0

FF

50 4.2E+2 0 0 0 29.18



M T0T0

P0P0

AA

PP

APAP0

FF

1.E6 0.74906 1.122 4.3E + 5 2.305 1.E + 6 3.7E+50.05 0.74969 1.122 8.696 2.3 20 7.5220.1 0.75157 1.122 4.375 2.286 10 3.8080.2 0.7591 1.121 2.243 2.229 5 1.9980.25 0.76475 1.121 1.828 2.188 4 1.6540.3 0.77165 1.12 1.559 2.138 3.333 1.4360.35 0.7798 1.119 1.373 2.081 2.857 1.2890.4 0.78921 1.118 1.24 2.017 2.5 1.1870.45 0.79988 1.116 1.142 1.946 2.222 1.1140.5 0.8118 1.112 1.069 1.871 2 1.0620.55 0.82497 1.108 1.016 1.79 1.818 1.0250.6 0.8394 1.103 0.9767 1.706 1.667 0.99950.65 0.85508 1.096 0.94987 1.62 1.538 0.982760.7 0.87202 1.088 0.93316 1.531 1.429 0.972870.75 0.89022 1.078 0.92531 1.441 1.333 0.968480.8 0.90966 1.067 0.92547 1.351 1.25 0.968540.85 0.93037 1.053 0.93315 1.261 1.176 0.972270.9 0.95232 1.038 0.94811 1.172 1.111 0.979070.95 0.97553 1.02 0.97033 1.085 1.053 0.988441 1 1 1 1 1 11.05 1.026 0.97796 1.037 0.91797 0.95238 1.0131.1 1.053 0.95376 1.083 0.83916 0.90909 1.0281.15 1.081 0.92745 1.138 0.76392 0.86957 1.0451.2 1.11 0.89911 1.203 0.69253 0.83333 1.0631.25 1.141 0.86886 1.28 0.6252 0.8 1.081




M T0T0

P0P0

AA

PP

APAP0

FF

1.3 1.173 0.83684 1.369 0.56206 0.76923 1.1011.35 1.206 0.80324 1.472 0.50319 0.74074 1.1221.4 1.241 0.76826 1.592 0.44861 0.71429 1.1431.45 1.277 0.73213 1.732 0.39828 0.68966 1.1651.5 1.314 0.69508 1.893 0.35213 0.66667 1.1881.55 1.352 0.65738 2.081 0.31003 0.64516 1.2111.6 1.391 0.61929 2.299 0.27182 0.625 1.2351.65 1.432 0.58108 2.554 0.23733 0.60606 1.2591.7 1.474 0.543 2.851 0.20636 0.58824 1.2841.75 1.518 0.50533 3.198 0.17867 0.57143 1.3091.8 1.562 0.4683 3.606 0.15406 0.55556 1.3341.85 1.608 0.43213 4.086 0.13229 0.54054 1.361.9 1.655 0.39705 4.653 0.11312 0.52632 1.3861.95 1.703 0.36323 5.324 0.096319 0.51282 1.4122 1.753 0.33083 6.122 0.081676 0.5 1.4382.25 2.019 0.1939 13.21 0.033635 0.44444 1.5742.5 2.317 0.10138 32.06 0.012478 0.4 1.7132.75 2.647 0.047189 87.19 0.00417 0.36364 1.8563 3.007 0.019537 2.7E + 2 0.00126 0.33333 2.0013.25 3.4 0.00719 9.E + 2 0.000341 0.30769 2.1483.5 3.823 0.00236 3.4E + 3 8.32E5 0.28571 2.2963.75 4.278 0.000686 1.5E + 4 1.83E5 0.26667 2.4454 4.764 0.000178 6.9E + 4 3.63E6 0.25 2.5964.25 5.282 4.11E5 3.6E + 5 0 0 2.7464.5 5.831 8.47E6 2.1E + 6 0 0 2.8984.75 6.411 1.56E6 1.4E + 7 0 0 3.055 7.022 0 1.E + 8 0 0 3.2025.25 7.665 0 8.2E + 8 0 0 3.3555.5 8.34 0 7.4E + 9 0 0 3.5085.75 9.046 0 7.4E+10 0 0 3.6626 9.783 0 8.2E+11 0 0 3.8156.25 10.55 0 1.E + 13 0 0 3.9696.5 11.35 0 1.4E+14 0 0 4.123




M T0T0

P0P0

AA

PP

APAP0

FF

6.75 12.18 0 2.1E+15 0 0 4.2777 13.04 0 3.6E+16 0 0 4.4327.25 13.94 0 6.9E+17 0 0 4.5867.5 14.86 0 1.4E+19 0 0 4.7417.75 15.82 0 3.4E+20 0 0 4.8968 16.81 0 8.8E+21 0 0 5.0518.25 17.83 0 2.5E+23 0 0 5.2068.5 18.88 0 8.1E+24 0 0 5.3618.75 19.96 0 2.9E+26 0 0 5.5169 21.07 0 1.1E+28 0 0 5.6719.25 22.22 0 5.E + 29 0 0 5.8269.5 23.4 0 2.4E+31 0 0 5.9819.75 24.6 0 1.3E+33 0 0 6.13710 25.84 0 8.E + 34 0 0 6.29220 1.E+2 0 2.5E+143 0 0 12.5330 2.3E+2 0 0 0 18.7840 4.E+2 0 0 0 25.0350 6.3E+2 0 0 0 31.28


Chapter 3

Normal Shock

3.1 Normal Shock Standard tables

3.1.1 Normal Shock Standard Table for k=1.2

Table 3.1: Normal Shock Standard Table for k=1.2

Mx MyTy

Tx

y

x

Py

Px

P0y

P0x

1.0000 1.0000 1.0000 1.0000 1.0000 1.00001.0100 0.99012 1.0036 1.0182 1.0219 1.000001.0200 0.98046 1.0072 1.0366 1.0441 0.999991.0300 0.97103 1.0108 1.0551 1.0664 0.999971.0400 0.96181 1.0143 1.0736 1.0890 0.999921.0500 0.95279 1.0178 1.0923 1.1118 0.999851.0600 0.94397 1.0213 1.1111 1.1348 0.999741.0700 0.93535 1.0248 1.1300 1.1581 0.999601.0800 0.92691 1.0283 1.1490 1.1815 0.999411.0900 0.91865 1.0317 1.1681 1.2052 0.999171.1000 0.91057 1.0352 1.1873 1.2291 0.998881.2000 0.83827 1.0689 1.3846 1.4800 0.992351.2500 0.80710 1.0855 1.4865 1.6136 0.986141.3000 0.77867 1.1022 1.5902 1.7527 0.977731.3500 0.75265 1.1189 1.6957 1.8973 0.967071.4000 0.72875 1.1357 1.8027 2.0473 0.95417

41

42 CHAPTER 3. NORMAL SHOCK

Table 3.1: Normal Shock Standard Table for k=1.2 (con-tinue)

Mx MyTy

Tx

y

x

Py

Px

P0y

P0x

1.4500 0.70674 1.1527 1.9110 2.2027 0.939111.5000 0.68641 1.1699 2.0204 2.3636 0.922001.5500 0.66757 1.1873 2.1308 2.5300 0.902981.6000 0.65009 1.2051 2.2420 2.7018 0.882221.6500 0.63381 1.2231 2.3539 2.8791 0.859911.7000 0.61864 1.2415 2.4663 3.0618 0.836241.7500 0.60447 1.2602 2.5789 3.2500 0.811411.8000 0.59121 1.2793 2.6918 3.4436 0.785621.8500 0.57877 1.2987 2.8048 3.6427 0.759071.9000 0.56710 1.3186 2.9177 3.8473 0.731961.9500 0.55612 1.3388 3.0304 4.0573 0.704462.0000 0.54578 1.3595 3.1429 4.2727 0.676742.1000 0.52682 1.4021 3.3664 4.7200 0.621292.2000 0.50989 1.4464 3.5876 5.1891 0.566722.3000 0.49469 1.4925 3.8058 5.6800 0.513932.4000 0.48100 1.5404 4.0203 6.1927 0.463602.5000 0.46861 1.5901 4.2308 6.7273 0.416222.6000 0.45737 1.6417 4.4368 7.2836 0.372092.7000 0.44714 1.6951 4.6379 7.8618 0.331392.8000 0.43779 1.7505 4.8341 8.4618 0.294152.9000 0.42924 1.8077 5.0250 9.0836 0.260323.0000 0.42139 1.8669 5.2105 9.7273 0.229793.5000 0.39038 2.1916 6.0562 13.2727 0.119784.0000 0.36895 2.5651 6.7692 17.3636 0.060964.5000 0.35355 2.9877 7.3636 22.0000 0.030935.0000 0.34214 3.4595 7.8571 27.1818 0.015865.5000 0.33345 3.9807 8.2671 32.9091 0.008276 0.32669 4.551 8.609 39.18 0.004416.5 0.32134 5.172 8.895 46 0.00247 0.31703 5.841 9.136 53.36 0.001347.5 0.31352 6.561 9.34 61.27 0.0007688 0.31061 7.329 9.514 69.73 0.00045


3.1. NORMAL SHOCK STANDARD TABLES 43


Mx MyTy

Tx

y

x

Py

Px

P0y

P0x

8.5 0.30818 8.148 9.663 78.73 0.0002699 0.30613 9.016 9.791 88.27 0.0001649.5 0.30439 9.933 9.903 98.36 0.00010210 0.30289 10.9 10 1.1E+2 6.5E 520 0.29229 40.65 10.73 4.4E+2 025 0.29099 62.97 10.83 6.8E+2 030 0.29029 90.24 10.88 9.8E+2 035 0.28986 1.2E+2 10.91 1.3E+3 040 0.28958 1.6E+2 10.93 1.7E+3 045 0.28939 2.E + 2 10.95 2.2E+3 050 0.28926 2.5E+2 10.96 2.7E+3 055 0.28916 3.E + 2 10.96 3.3E+3 060 0.28908 3.6E+2 10.97 3.9E+3 065 0.28902 4.2E+2 10.97 4.6E+3 070 0.28897 4.9E+2 10.98 5.3E+3 0


Table 3.2: Standard Normal Shock for k=1.3

Mx MyTy

Tx

y

x

Py

Px

P0y

P0x

1.0000 1.0000 1.0000 1.0000 1.0000 1.00001.0100 0.99012 1.0052 1.0174 1.0227 1.000001.0200 0.98049 1.0104 1.0349 1.0457 0.999991.0300 0.97109 1.0155 1.0525 1.0688 0.999971.0400 0.96192 1.0206 1.0702 1.0922 0.999921.0500 0.95297 1.0257 1.0880 1.1159 0.999851.0600 0.94422 1.0307 1.1058 1.1397 0.999751.0700 0.93568 1.0357 1.1237 1.1638 0.999601.0800 0.92733 1.0407 1.1416 1.1881 0.999421.0900 0.91918 1.0457 1.1596 1.2126 0.999191.1000 0.91120 1.0506 1.1777 1.2374 0.99891



Table 3.2: Standard Normal Shock for k=1.3 (continue)

Mx MyTy

Tx

y

x

Py

Px

P0y

P0x

1.2000 0.84033 1.0995 1.3618 1.4974 0.992581.2500 0.81003 1.1238 1.4557 1.6359 0.986611.3000 0.78253 1.1480 1.5505 1.7800 0.978581.3500 0.75749 1.1725 1.6459 1.9298 0.968451.4000 0.73459 1.1971 1.7419 2.0852 0.956271.4500 0.71358 1.2220 1.8382 2.2463 0.942111.5000 0.69425 1.2473 1.9346 2.4130 0.926101.5500 0.67642 1.2730 2.0310 2.5854 0.908381.6000 0.65992 1.2991 2.1272 2.7635 0.889111.6500 0.64463 1.3257 2.2230 2.9472 0.868471.7000 0.63041 1.3529 2.3185 3.1365 0.846641.7500 0.61718 1.3805 2.4133 3.3315 0.823801.8000 0.60484 1.4087 2.5074 3.5322 0.800141.8500 0.59330 1.4375 2.6007 3.7385 0.775821.9000 0.58251 1.4668 2.6932 3.9504 0.751021.9500 0.57238 1.4968 2.7846 4.1680 0.725892.0000 0.56288 1.5274 2.8750 4.3913 0.700572.1000 0.54553 1.5905 3.0524 4.8548 0.649922.2000 0.53011 1.6562 3.2248 5.3409 0.599982.3000 0.51635 1.7245 3.3920 5.8496 0.551502.4000 0.50400 1.7956 3.5536 6.3809 0.505042.5000 0.49290 1.8694 3.7097 6.9348 0.460982.6000 0.48286 1.9459 3.8600 7.5113 0.419582.7000 0.47377 2.0253 4.0045 8.1104 0.380992.8000 0.46550 2.1075 4.1434 8.7322 0.345252.9000 0.45796 2.1925 4.2766 9.3765 0.312333.0000 0.45107 2.2804 4.4043 10.0435 0.282163.5000 0.42411 2.7630 4.9648 13.7174 0.167754.0000 0.40577 3.3181 5.4118 17.9565 0.099334.5000 0.39275 3.9462 5.7678 22.7609 0.059395.0000 0.38319 4.6476 6.0526 28.1304 0.036135.5000 0.37597 5.4225 6.2822 34.0652 0.022436.0000 0.37039 6.2710 6.4687 40.5652 0.01422



Table 3.2: Standard Normal Shock for k=1.3 (continue)

Mx MyTy

Tx

y

x

Py

Px

P0y

P0x

6.5000 0.36600 7.1930 6.6218 47.6304 0.009227 0.36248 8.189 6.749 55.26 0.00617.5 0.35962 9.258 6.854 63.46 0.004118 0.35726 10.4 6.943 72.22 0.002838.5 0.35529 11.62 7.019 81.54 0.001989 0.35364 12.91 7.084 91.43 0.00149.5 0.35223 14.27 7.139 1.E + 2 0.0010110 0.35103 15.71 7.187 1.1E+2 0.0007420 0.34255 59.94 7.541 4.5E+2 8.95E625 0.34152 93.12 7.586 7.1E+2 2.07E630 0.34096 1.3E+2 7.61 1.E + 3 035 0.34062 1.8E+2 7.625 1.4E+3 040 0.3404 2.4E+2 7.635 1.8E+3 045 0.34025 3.E + 2 7.642 2.3E+3 050 0.34014 3.7E+2 7.646 2.8E+3 055 0.34006 4.5E+2 7.65 3.4E+3 060 0.34 5.3E+2 7.652 4.1E+3 065 0.33996 6.2E+2 7.655 4.8E+3 070 0.33992 7.2E+2 7.656 5.5E+3 0


Table 3.3: Standard Shock Standard Table for k=1.4

Mx MyTy

Tx

y

x

Py

Px

P0y

P0x

1.0000 1.0000 1.0000 1.0000 1.0000 1.00001.0100 0.99013 1.0066 1.0167 1.0235 1.000001.0200 0.98052 1.0132 1.0334 1.0471 0.999991.0300 0.97115 1.0198 1.0502 1.0711 0.999971.0400 0.96203 1.0263 1.0671 1.0952 0.999921.0500 0.95313 1.0328 1.0840 1.1196 0.999851.0600 0.94445 1.0393 1.1009 1.1442 0.999751.0700 0.93598 1.0458 1.1179 1.1691 0.99961




Mx MyTy

Tx

y

x

Py

Px

P0y

P0x

1.0800 0.92771 1.0522 1.1349 1.1941 0.999431.0900 0.91965 1.0586 1.1520 1.2195 0.999201.1000 0.91177 1.0649 1.1691 1.2450 0.998931.2000 0.84217 1.1280 1.3416 1.5133 0.992801.2500 0.81264 1.1594 1.4286 1.6562 0.987061.3000 0.78596 1.1909 1.5157 1.8050 0.979371.3500 0.76175 1.2226 1.6028 1.9596 0.969741.4000 0.73971 1.2547 1.6897 2.1200 0.958191.4500 0.71956 1.2872 1.7761 2.2863 0.944841.5000 0.70109 1.3202 1.8621 2.4583 0.929791.5500 0.68410 1.3538 1.9473 2.6363 0.913191.6000 0.66844 1.3880 2.0317 2.8200 0.895201.6500 0.65396 1.4228 2.1152 3.0096 0.875991.7000 0.64054 1.4583 2.1977 3.2050 0.855721.7500 0.62809 1.4946 2.2791 3.4063 0.834571.8000 0.61650 1.5316 2.3592 3.6133 0.812681.8500 0.60570 1.5693 2.4381 3.8263 0.790231.9000 0.59562 1.6079 2.5157 4.0450 0.767361.9500 0.58618 1.6473 2.5919 4.2696 0.744202.0000 0.57735 1.6875 2.6667 4.5000 0.720872.1000 0.56128 1.7705 2.8119 4.9783 0.674202.2000 0.54706 1.8569 2.9512 5.4800 0.628142.3000 0.53441 1.9468 3.0845 6.0050 0.583292.4000 0.52312 2.0403 3.2119 6.5533 0.540142.5000 0.51299 2.1375 3.3333 7.1250 0.499012.6000 0.50387 2.2383 3.4490 7.7200 0.460122.7000 0.49563 2.3429 3.5590 8.3383 0.423592.8000 0.48817 2.4512 3.6636 8.9800 0.389462.9000 0.48138 2.5632 3.7629 9.6450 0.357733.0000 0.47519 2.6790 3.8571 10.3333 0.328343.5000 0.45115 3.3151 4.2609 14.1250 0.212954.0000 0.43496 4.0469 4.5714 18.5000 0.13876




Mx MyTy

Tx

y

x

Py

Px

P0y

P0x

4.5000 0.42355 4.8751 4.8119 23.4583 0.091705.0000 0.41523 5.8000 5.0000 29.0000 0.061725.5000 0.40897 6.8218 5.1489 35.1250 0.042366.0000 0.40416 7.9406 5.2683 41.8333 0.029656.5000 0.40038 9.1564 5.3651 49.1250 0.021157.0000 0.39736 10.4694 5.4444 57.0000 0.015357.5000 0.39491 11.8795 5.5102 65.4583 0.011338.0000 0.39289 13.3867 5.5652 74.5000 0.008498.5 0.39121 14.99 5.612 84.12 0.006459 0.3898 16.69 5.651 94.33 0.004969.5 0.3886 18.49 5.685 1.1E+2 0.0038710 0.38758 20.39 5.714 1.2E+2 0.0030420 0.38039 78.72 5.926 4.7E+2 0.00010825 0.37952 1.2E+2 5.952 7.3E+2 3.59E530 0.37904 1.8E+2 5.967 1.E + 3 1.45E535 0.37876 2.4E+2 5.976 1.4E+3 6.76E640 0.37857 3.1E+2 5.981 1.9E+3 3.48E645 0.37844 3.9E+2 5.985 2.4E+3 1.93E650 0.37835 4.9E+2 5.988 2.9E+3 055 0.37829 5.9E+2 5.99 3.5E+3 060 0.37823 7.E + 2 5.992 4.2E+3 065 0.37819 8.2E+2 5.993 4.9E+3 070 0.37816 9.5E+2 5.994 5.7E+3 0

3.1.4 Normal shock Standard Table for k=1.67

Table 3.4: Standard Normal Shock Table k=1.67

Mx MyTy

Tx

y

x

Py

Px

P0y

P0x

1.0000 1.00000 1.0000 1.0000 1.0000 1.00001.0100 0.99015 1.0100 1.0150 1.0251 1.000001.0200 0.98058 1.0200 1.0300 1.0505 0.99999



Table 3.4: Standard Normal Shock Table k=1.67 (con-tinue)

Mx MyTy

Tx

y

x

Py

Px

P0y

P0x

1.0300 0.97129 1.0299 1.0449 1.0762 0.999971.0400 0.96227 1.0398 1.0599 1.1021 0.999931.0500 0.95349 1.0497 1.0749 1.1282 0.999861.0600 0.94496 1.0595 1.0898 1.1546 0.999761.0700 0.93666 1.0693 1.1047 1.1813 0.999631.0800 0.92858 1.0790 1.1196 1.2082 0.999461.0900 0.92072 1.0888 1.1345 1.2353 0.999251.1000 0.91307 1.0985 1.1494 1.2627 0.998991.2000 0.84629 1.1956 1.2968 1.5504 0.993351.2500 0.81843 1.2442 1.3692 1.7037 0.988161.3000 0.79351 1.2933 1.4406 1.8631 0.981301.3500 0.77111 1.3430 1.5107 2.0289 0.972771.4000 0.75088 1.3934 1.5795 2.2009 0.962661.4500 0.73253 1.4446 1.6469 2.3792 0.951071.5000 0.71583 1.4968 1.7128 2.5637 0.938111.5500 0.70059 1.5500 1.7771 2.7544 0.923931.6000 0.68662 1.6042 1.8398 2.9515 0.908651.6500 0.67379 1.6596 1.9009 3.1547 0.892441.7000 0.66198 1.7162 1.9603 3.3643 0.875421.7500 0.65107 1.7740 2.0180 3.5801 0.857731.8000 0.64098 1.8331 2.0741 3.8021 0.839501.8500 0.63162 1.8935 2.1286 4.0304 0.820851.9000 0.62292 1.9552 2.1813 4.2649 0.801891.9500 0.61483 2.0183 2.2325 4.5057 0.782712.0000 0.60728 2.0827 2.2821 4.7528 0.763422.1000 0.59364 2.2158 2.3765 5.2657 0.724812.2000 0.58167 2.3545 2.4649 5.8036 0.686612.3000 0.57111 2.4991 2.5475 6.3665 0.649262.4000 0.56174 2.6495 2.6248 6.9545 0.613062.5000 0.55339 2.8059 2.6970 7.5674 0.578252.6000 0.54591 2.9683 2.7644 8.2054 0.544972.7000 0.53920 3.1366 2.8273 8.8684 0.51332



Table 3.4: Standard Normal Shock Table k=1.67 (con-tinue)

Mx MyTy

Tx

y

x

Py

Px

P0y

P0x

2.8000 0.53315 3.3111 2.8862 9.5564 0.483332.9000 0.52768 3.4917 2.9411 10.2694 0.455013.0000 0.52271 3.6783 2.9925 11.0075 0.428343.5000 0.50362 4.7041 3.2043 15.0730 0.317714.0000 0.49096 5.8848 3.3585 19.7640 0.238394.5000 0.48215 7.2214 3.4731 25.0805 0.181635.0000 0.47578 8.7142 3.5600 31.0225 0.140655.5000 0.47103 10.3635 3.6271 37.5899 0.110636.0000 0.46739 12.1694 3.6799 44.7828 0.088316.5000 0.46454 14.1321 3.7221 52.6011 0.071467.0000 0.46227 16.2516 3.7562 61.0449 0.058547.5000 0.46043 18.5279 3.7843 70.1142 0.048508.0000 0.45893 20.9611 3.8075 79.8090 0.040598.5000 0.45768 23.5511 3.8270 90.1292 0.034289.0000 0.45663 26.2981 3.8434 101.07 0.029209.5000 0.45574 29.2019 3.8575 112.65 0.0250710.0000 0.45497 32.2627 3.8696 124.84 0.0216720.0000 0.44966 126.44 3.9556 500.12 0.0028825 0.44902 2.E + 2 3.966 7.8E+2 0.0014930 0.44867 2.8E+2 3.972 1.1E+3 0.00086835 0.44846 3.9E+2 3.975 1.5E+3 0.00054940 0.44833 5.0E+2 3.978 2.E + 3 0.00036945 0.44823 6.4E+2 3.979 2.5E+3 0.0002650 0.44817 7.9E+2 3.98 3.1E+3 0.0001955 0.44812 9.5E+2 3.981 3.8E+3 0.00014360 0.44808 1.1E+3 3.982 4.5E+3 0.0001165 0.44805 1.3E+3 3.982 5.3E+3 8.69E570 0.44803 1.5E+3 3.983 6.1E+3 6.97E5



3.2 Open Valve maximum values

k Mx My My Ty

Tx

1.30 1073.25 0.33968 2.2645 169842.291.40 985.85 0.37797 1.8898 188982.961.50 922.23 0.40825 1.6330 204124.861.60 873.09 0.43301 1.4434 216507.051.70 833.61 0.45374 1.2964 226871.991.80 801.02 0.47141 1.1785 235702.931.90 773.54 0.48667 1.0815 243332.792.00 750.00 0.50000 1.00000 250000.642.10 729.56 0.51177 0.93048 255883.782.20 711.62 0.52223 0.87039 261117.092.30 695.74 0.53161 0.81786 265805.362.40 681.56 0.54006 0.77151 270031.442.50 668.81 0.54772 0.73029 273861.85

Table of maximum values of the shock-chocking phenomenon.

3.3 Shock Reflecting from a Suddenly Closed

Valve

3.3.1 Reflecting Shock (closed Valve) k =1.2

Table 3.5: Isothermal Flow k=1.2

M 4fLD

PP

P0P0

T0T0

0.010008323.31 91.2871 56.4759 91.2871 0.923090.020002074.69 45.6435 28.2430 45.6435 0.923110.03000 918.10 30.4290 18.8343 30.4290 0.923160.04000 513.58 22.8218 14.1317 22.8218 0.923220.05000 326.52 18.2574 11.3114 18.2574 0.923310.06000 225.04 15.2145 9.4324 15.2145 0.923410.07000 163.93 13.0410 8.0912 13.0410 0.923530.08000 124.34 11.4109 7.0862 11.4109 0.92367


3.3. SHOCK REFLECTING FROM A SUDDENLY CLOSED VALVE 51

Table 3.5: Isothermal Flow k=1.2 (continue)

M 4fLD

PP

P0P0

T0T0

0.09000 97.2471 10.1430 6.3053 10.1430 0.923820.10000 77.9105 9.1287 5.6812 9.1287 0.924000.11000 63.6383 8.2988 5.1712 8.2988 0.924190.12000 52.8122 7.6073 4.7468 7.6073 0.924410.13000 44.4115 7.0221 4.3883 7.0221 0.924640.14000 37.7671 6.5205 4.0814 6.5205 0.924890.15000 32.4251 6.0858 3.8159 6.0858 0.925150.16000 28.0692 5.7054 3.5841 5.7054 0.925440.17000 24.4735 5.3698 3.3799 5.3698 0.925740.18000 21.4729 5.0715 3.1988 5.0715 0.926070.19000 18.9449 4.8046 3.0372 4.8046 0.926410.20000 16.7968 4.5644 2.8921 4.5644 0.926770.21000 14.9575 4.3470 2.7611 4.3470 0.927150.22000 13.3717 4.1494 2.6424 4.1494 0.927540.23000 11.9960 3.9690 2.5343 3.9690 0.927960.24000 10.7957 3.8036 2.4355 3.8036 0.928390.25000 9.7431 3.6515 2.3449 3.6515 0.928850.26000 8.8156 3.5110 2.2616 3.5110 0.929320.27000 7.9948 3.3810 2.1847 3.3810 0.929810.28000 7.2656 3.2603 2.1136 3.2603 0.930310.29000 6.6154 3.1478 2.0477 3.1478 0.930840.30000 6.0336 3.0429 1.9864 3.0429 0.931380.31000 5.5115 2.9447 1.9293 2.9447 0.931950.32000 5.0415 2.8527 1.8760 2.8527 0.932530.33000 4.6173 2.7663 1.8262 2.7663 0.933130.34000 4.2335 2.6849 1.7795 2.6849 0.933750.35000 3.8854 2.6082 1.7358 2.6082 0.934380.36000 3.5691 2.5358 1.6947 2.5358 0.935040.37000 3.2810 2.4672 1.6560 2.4672 0.935710.38000 3.0182 2.4023 1.6196 2.4023 0.936410.39000 2.7780 2.3407 1.5853 2.3407 0.937120.40000 2.5581 2.2822 1.5529 2.2822 0.937850.41000 2.3565 2.2265 1.5223 2.2265 0.93859




M 4fLD

PP

P0P0

T0T0

0.42000 2.1714 2.1735 1.4933 2.1735 0.939360.43000 2.0013 2.1230 1.4659 2.1230 0.940140.44000 1.8448 2.0747 1.4400 2.0747 0.940950.45000 1.7005 2.0286 1.4153 2.0286 0.941770.46000 1.5675 1.9845 1.3920 1.9845 0.942610.47000 1.4447 1.9423 1.3699 1.9423 0.943470.48000 1.3313 1.9018 1.3488 1.9018 0.944340.49000 1.2264 1.8630 1.3288 1.8630 0.945240.50000 1.1294 1.8257 1.3098 1.8257 0.946150.51000 1.0395 1.7899 1.2917 1.7899 0.947090.52000 0.95632 1.7555 1.2746 1.7555 0.948040.53000 0.87922 1.7224 1.2582 1.7224 0.949010.54000 0.80775 1.6905 1.2426 1.6905 0.949990.55000 0.74147 1.6598 1.2278 1.6598 0.951000.56000 0.68000 1.6301 1.2137 1.6301 0.952020.57000 0.62298 1.6015 1.2003 1.6015 0.953070.58000 0.57008 1.5739 1.1875 1.5739 0.954130.59000 0.52100 1.5472 1.1753 1.5472 0.955210.60000 0.47549 1.5215 1.1637 1.5215 0.956310.61000 0.43327 1.4965 1.1527 1.4965 0.957420.62000 0.39413 1.4724 1.1422 1.4724 0.958560.63000 0.35786 1.4490 1.1322 1.4490 0.959710.64000 0.32425 1.4264 1.1227 1.4264 0.960890.65000 0.29314 1.4044 1.1137 1.4044 0.962080.66000 0.26436 1.3831 1.1051 1.3831 0.963290.67000 0.23776 1.3625 1.0969 1.3625 0.964510.68000 0.21319 1.3425 1.0892 1.3425 0.965760.69000 0.19053 1.3230 1.0819 1.3230 0.967020.70000 0.16965 1.3041 1.0750 1.3041 0.968310.71000 0.15045 1.2857 1.0684 1.2857 0.969610.72000 0.13282 1.2679 1.0622 1.2679 0.970930.73000 0.11667 1.2505 1.0563 1.2505 0.972270.74000 0.10190 1.2336 1.0508 1.2336 0.97362




M 4fLD

PP

P0P0

T0T0

0.75000 0.08844 1.2172 1.0456 1.2172 0.975000.76000 0.07620 1.2011 1.0407 1.2011 0.976390.77000 0.06511 1.1855 1.0362 1.1855 0.977810.78000 0.05511 1.1703 1.0319 1.1703 0.979240.79000 0.04613 1.1555 1.0279 1.1555 0.980690.80000 0.03812 1.1411 1.0242 1.1411 0.982150.81000 0.03101 1.1270 1.0208 1.1270 0.983640.82000 0.02476 1.1133 1.0176 1.1133 0.985140.83000 0.01932 1.0998 1.0147 1.0998 0.986670.84000 0.01464 1.0868 1.0121 1.0868 0.988210.85000 0.01069 1.0740 1.0097 1.0740 0.989770.86000 0.00741 1.061 1.008 1.061 0.991350.87 0.00478 1.049 1.006 1.049 0.992940.88 0.00276 1.037 1.004 1.037 0.994560.89 0.00131 1.026 1.002 1.026 0.996190.9 0.000407 1.014 1.001 1.014 0.997850.91 1.99E5 1.003 1 1.003 0.999520.91032 1.57E5 1.003 1 1.003 0.999570.91064 1.2E5 1.002 1 1.002 0.999620.91096 8.82E6 1.002 1 1.002 0.999680.91128 6.12E6 1.002 1 1.002 0.999730.91159 3.92E6 1.001 1 1.001 0.999790.91191 2.2E6 1.001 1 1.001 0.999840.91223 0 1.001 1 1.001 0.999890.91255 0 1 1 1 0.999950.91287 0 1 1 1 1




Table 3.6: Table for shock reflecting from a suddenlyclosed end (k=1.3)

Mx My Mx

My Ty

Tx

Py

Px

P0y

P0x

1.0058 0.99428 0.01 0 1.003 1.013 11.012 0.9886 0.02 0 1.006 1.026 11.017 0.98297 0.03 0 1.009 1.04 0.999991.023 0.9774 0.04 0 1.012 1.053 0.999981.029 0.97187 0.05 0 1.015 1.067 0.999971.035 0.96639 0.06 0 1.018 1.081 0.999951.041 0.96096 0.07 0 1.021 1.095 0.999921.047 0.95558 0.08 0 1.024 1.109 0.999871.053 0.95024 0.09 0 1.027 1.123 0.999821.059 0.94495 0.1 0 1.03 1.138 0.999761.122 0.89458 0.2 0 1.061 1.292 0.99811.196 0.84308 0.3125 0 1.097 1.486 0.9931.274 0.79661 0.425 0 1.135 1.704 0.983041.356 0.75476 0.5375 0 1.175 1.947 0.967161.441 0.7171 0.65 0 1.218 2.218 0.944711.53 0.68326 0.7625 0 1.263 2.517 0.915541.623 0.65288 0.875 0 1.311 2.846 0.879951.718 0.6256 0.9875 0 1.363 3.205 0.838621.816 0.60112 1.1 0 1.418 3.597 0.792541.905 0.58147 1.2 0 1.47 3.972 0.748541.996 0.56362 1.3 0 1.525 4.373 0.70262.089 0.54738 1.4 0 1.583 4.802 0.655592.183 0.5326 1.5 0 1.645 5.257 0.608352.279 0.51913 1.6 0 1.71 5.74 0.561622.376 0.50686 1.7 0 1.778 6.251 0.516032.474 0.49566 1.8 0 1.85 6.79 0.472112.574 0.48542 1.9 0 1.925 7.357 0.430262.674 0.47605 2 0 2.004 7.952 0.390762.775 0.46747 2.1 0 2.087 8.577 0.35382.878 0.4596 2.2 0 2.173 9.23 0.319492.981 0.45236 2.3 0 2.263 9.912 0.287833.084 0.44571 2.4 0 2.357 10.62 0.2588



Table 3.6: Reflection shock suddenly closed valve k=1.3(continue)

Mx My Mx

My Ty

Tx

Py

Px

P0y

P0x

3.189 0.43959 2.5 0 2.454 11.36 0.232313.294 0.43393 2.6 0 2.555 12.13 0.208243.399 0.42871 2.7 0 2.66 12.93 0.186463.505 0.42388 2.8 0 2.768 13.76 0.166823.612 0.41941 2.9 0 2.881 14.62 0.14915


Table 3.7: Table for Shock Reflecting from a suddenlyclosed end (k=1.4)

Mx My Mx

My Ty

Tx

Py

Px

P0y

P0x

1.0060 0.99403 0.01 0 1.004 1.014 11.012 0.98812 0.02 0 1.008 1.028 11.018 0.98227 0.03 0 1.012 1.043 0.999991.024 0.97647 0.04 0 1.016 1.057 0.999981.03 0.97074 0.05 0 1.02 1.072 0.999971.037 0.96506 0.06 0 1.024 1.087 0.999941.043 0.95944 0.07 0 1.028 1.102 0.999911.049 0.95387 0.08 0 1.032 1.118 0.999861.055 0.94836 0.09 0 1.036 1.133 0.99981.062 0.94291 0.1 0 1.04 1.149 0.999731.127 0.89128 0.2 0 1.082 1.316 0.99791.205 0.83912 0.3125 0 1.131 1.527 0.992321.287 0.79264 0.425 0 1.183 1.766 0.981561.373 0.75127 0.5375 0 1.237 2.033 0.964611.463 0.71447 0.65 0 1.296 2.332 0.940981.557 0.68177 0.7625 0 1.359 2.662 0.910691.654 0.65273 0.875 0 1.426 3.027 0.874231.755 0.62693 0.9875 0 1.498 3.426 0.832471.858 0.60401 1.1 0 1.576 3.862 0.786521.952 0.58578 1.2 0 1.649 4.28 0.74316




Mx My Mx

My Ty

Tx

Py

Px

P0y

P0x

2.048 0.56935 1.3 0 1.727 4.728 0.698342.146 0.55453 1.4 0 1.81 5.206 0.65292.245 0.54114 1.5 0 1.897 5.715 0.607612.346 0.52904 1.6 0 1.99 6.256 0.563122.448 0.51808 1.7 0 2.087 6.827 0.519962.552 0.50814 1.8 0 2.189 7.431 0.478552.656 0.49912 1.9 0 2.297 8.066 0.439212.762 0.49092 2.0 0 2.41 8.734 0.402132.869 0.48344 2.1 0 2.528 9.434 0.367442.976 0.47662 2.2 0 2.651 10.17 0.335183.084 0.47039 2.3 0 2.779 10.93 0.305343.193 0.46469 2.4 0 2.913 11.73 0.277873.303 0.45946 2.5 0 3.053 12.56 0.252673.413 0.45466 2.6 0 3.198 13.42 0.229623.524 0.45024 2.7 0 3.348 14.32 0.208613.635 0.44617 2.8 0 3.503 15.25 0.189493.747 0.44241 2.9 0 3.664 16.21 0.17212


Table 3.8: Table for Shock Reflecting from a suddenlyclosed end (k=1.67)

Mx My Mx

My Ty

Tx

Py

Px

P0y

P0x

1.0067 0.99337 0.01 0 1.007 1.017 11.013 0.98683 0.02 0 1.013 1.034 11.02 0.98037 0.03 0 1.02 1.051 0.999991.027 0.974 0.04 0 1.027 1.069 0.999981.034 0.96771 0.05 0 1.034 1.086 0.999951.041 0.96151 0.06 0 1.041 1.104 0.999921.048 0.95539 0.07 0 1.048 1.122 0.999881.055 0.94935 0.08 0 1.054 1.141 0.99982



Table 3.8: Reflecting shock suddenly closed valvek=1.67 (continue)

Mx My Mx

My Ty

Tx

Py

Px

P0y

P0x

1.062 0.94338 0.09 0 1.061 1.16 0.999741.069 0.9375 0.1 0 1.068 1.179 0.999651.142 0.88274 0.2 0 1.14 1.382 0.997321.23 0.82913 0.3125 0 1.225 1.642 0.990431.323 0.78285 0.425 0 1.316 1.939 0.977551.421 0.74288 0.5375 0 1.415 2.276 0.957921.524 0.70836 0.65 0 1.522 2.654 0.931461.631 0.67853 0.7625 0 1.638 3.077 0.898691.742 0.65273 0.875 0 1.765 3.546 0.860551.857 0.63039 0.9875 0 1.902 4.062 0.818271.975 0.61101 1.1 0 2.05 4.628 0.773132.082 0.59593 1.2 0 2.192 5.173 0.731652.192 0.5826 1.3 0 2.343 5.758 0.689742.303 0.57079 1.4 0 2.504 6.385 0.648092.416 0.5603 1.5 0 2.675 7.053 0.607272.531 0.55098 1.6 0 2.856 7.763 0.567732.647 0.54265 1.7 0 3.047 8.516 0.529812.765 0.53522 1.8 0 3.249 9.311 0.493722.883 0.52855 1.9 0 3.461 10.15 0.459623.003 0.52256 2 0 3.684 11.03 0.427563.124 0.51717 2.1 0 3.918 11.95 0.397563.245 0.51231 2.2 0 4.162 12.92 0.36963.367 0.50791 2.3 0 4.417 13.93 0.34363.49 0.50391 2.4 0 4.683 14.99 0.31953.614 0.50028 2.5 0 4.96 16.09 0.297183.738 0.49698 2.6 0 5.248 17.23 0.276553.863 0.49396 2.7 0 5.547 18.42 0.257493.989 0.4912 2.8 0 5.856 19.65 0.23994.115 0.48867 2.9 0 6.177 20.93 0.22368



3.4 Shock propagating from suddenly open

valve

3.4.1 Shock from suddenly open valve k =1.2

Table 3.9: Shock from suddenly open valve k=1.2 orderMy

Mx My Mx

My Ty

Tx

Py

Px

P0y

P0x

916.67 0.28868 0 2.887 8.3E+4 9.2E+5 033.95 0.28993 0 2.872 1.2E+2 1.3E+3 023.99 0.29119 0 2.857 58.07 6.3E+2 019.57 0.29245 0 2.843 38.97 4.2E+2 016.93 0.29371 0 2.828 29.41 3.1E+2 015.13 0.29497 0 2.814 23.68 2.5E+2 1.41E613.8 0.29623 0 2.8 19.86 2.1E+2 3.38E612.76 0.29748 0 2.785 17.13 1.8E+2 7.02E611.92 0.29874 0 2.771 15.08 1.6E+2 1.32E511.23 0.3 0 2.758 13.49 1.4E+2 2.28E58.118 0.31 0 2.651 7.518 71.8 0.0003986.645 0.32 0 2.55 5.36 48.08 0.002035.74 0.33 0 2.455 4.249 35.85 0.00615.111 0.34 0 2.365 3.571 28.41 0.0136954.641 0.35 0 2.279 3.116 23.4 0.0255914.271 0.36 0 2.198 2.788 19.81 0.0421553.971 0.37 0 2.121 2.542 17.11 0.0633973.721 0.38 0 2.047 2.35 15.01 0.0890353.508 0.39 0 1.976 2.197 13.33 0.118593.323 0.4 0 1.909 2.071 11.96 0.151453.162 0.41 0 1.845 1.967 10.81 0.186963.019 0.42 0 1.783 1.878 9.85 0.224462.891 0.43 0 1.723 1.802 9.025 0.263312.776 0.44 0 1.666 1.737 8.313 0.302932.671 0.45 0 1.611 1.679 7.692 0.342812.576 0.46 0 1.558 1.629 7.147 0.38249


3.4. SHOCK PROPAGATING FROM SUDDENLY OPEN VALVE 59

Table 3.9: Shock from suddenly open valve k=1.2 (con-tinue)

Mx My Mx

My Ty

Tx

Py

Px

P0y

P0x

2.488 0.47 0 1.507 1.584 6.663 0.421612.408 0.48 0 1.458 1.544 6.233 0.459852.333 0.49 0 1.41 1.508 5.847 0.496972.264 0.5 0 1.364 1.476 5.5 0.532762.199 0.51 0 1.319 1.446 5.186 0.56712.139 0.52 0 1.276 1.419 4.9 0.599862.082 0.53 0 1.233 1.394 4.64 0.6312.029 0.54 0 1.193 1.372 4.401 0.660481.979 0.55 0 1.153 1.351 4.183 0.688281.932 0.56 0 1.114 1.331 3.981 0.714411.887 0.57 0 1.077 1.314 3.795 0.73891.845 0.58 0 1.04 1.297 3.622 0.76181.805 0.59 0 1.004 1.281 3.462 0.783151.766 0.6 0 0.9697 1.266 3.313 0.8031.73 0.61 0 0.93577 1.253 3.174 0.821421.695 0.62 0 0.90264 1.24 3.045 0.838471.662 0.63 0 0.87027 1.228 2.923 0.854231.631 0.64 0 0.83864 1.216 2.81 0.868751.6 0.65 0 0.80769 1.205 2.703 0.882111.571 0.66 0 0.77741 1.195 2.602 0.894381.543 0.67 0 0.74776 1.185 2.508 0.905621.517 0.68 0 0.71872 1.176 2.418 0.915891.491 0.69 0 0.69025 1.167 2.334 0.925271.466 0.7 0 0.66234 1.158 2.254 0.93381.442 0.71 0 0.63496 1.15 2.179 0.941561.419 0.72 0 0.60808 1.142 2.107 0.948581.397 0.73 0 0.58169 1.135 2.039 0.954931.376 0.74 0 0.55577 1.128 1.974 0.960651.355 0.75 0 0.5303 1.121 1.913 0.965791.335 0.76 0 0.50526 1.114 1.855 0.970411.316 0.77 0 0.48064 1.108 1.799 0.974521.298 0.78 0 0.45641 1.101 1.746 0.97819



Table 3.9: Shock from suddenly open valve k=1.2 (con-tinue)

Mx My Mx

My Ty

Tx

Py

Px

P0y

P0x

1.28 0.79 0 0.43257 1.095 1.695 0.981441.262 0.8 0 0.40909 1.09 1.647 0.984311.245 0.81 0 0.38597 1.084 1.6 0.986841.229 0.82 0 0.36319 1.078 1.556 0.989041.213 0.83 0 0.34074 1.073 1.514 0.990961.197 0.84 0 0.31861 1.068 1.473 0.992621.182 0.85 0 0.29679 1.063 1.434 0.994051.168 0.86 0 0.27526 1.058 1.397 0.995261.154 0.87 0 0.25402 1.053 1.361 0.996281.14 0.88 0 0.23306 1.049 1.326 0.997131.126 0.89 0 0.21236 1.044 1.293 0.997841.113 0.9 0 0.19192 1.04 1.261 0.998411.101 0.91 0 0.17173 1.035 1.231 0.998861.088 0.92 0 0.15178 1.031 1.201 0.999211.076 0.93 0 0.13206 1.027 1.173 0.999481.065 0.94 0 0.11257 1.023 1.145 0.999681.053 0.95 0 0.093301 1.019 1.119 0.999821.042 0.96 0 0.074242 1.015 1.094 0.999911.031 0.97 0 0.055389 1.011 1.069 0.999961.02 0.98 0 0.036735 1.007 1.045 0.999991.01 0.99 0 0.018274 1.004 1.022 11 1 0 0 1 1 1



Mx My Mx

My Ty

Tx

Py

Px

P0y

P0x

884.62 0.33968 0 2.265 1.2E+5 8.8E+5 013.05 0.34639 0 2.209 26.07 1.9E+2 0.000149.186 0.35309 0 2.156 13.41 95.26 0.00124



Table 3.10: Shock from suddenly open valve k=1.3 orderMy (continue)

Mx My Mx

My Ty

Tx

Py

Px

P0y

P0x

7.467 0.35979 0 2.104 9.185 62.9 0.004226.438 0.36649 0 2.054 7.075 46.73 0.009715.734 0.37319 0 2.006 5.81 37.03 0.0180825.212 0.37989 0 1.959 4.966 30.57 0.0294524.804 0.3866 0 1.913 4.365 25.96 0.0437814.475 0.3933 0 1.869 3.913 22.51 0.0609034.202 0.4 0 1.826 3.563 19.83 0.0805733.868 0.41 0 1.764 3.164 16.78 0.114023.597 0.42 0 1.705 2.865 14.5 0.151443.372 0.43 0 1.648 2.633 12.73 0.191793.181 0.44 0 1.594 2.447 11.31 0.234093.016 0.45 0 1.541 2.295 10.15 0.277492.872 0.46 0 1.49 2.168 9.194 0.321252.744 0.47 0 1.441 2.061 8.384 0.364762.63 0.48 0 1.394 1.97 7.691 0.407532.528 0.49 0 1.349 1.89 7.093 0.449172.435 0.5 0 1.304 1.821 6.571 0.489392.35 0.51 0 1.262 1.76 6.113 0.527952.272 0.52 0 1.22 1.705 5.707 0.564732.201 0.53 0 1.18 1.657 5.345 0.599612.135 0.54 0 1.141 1.613 5.02 0.632552.073 0.55 0 1.103 1.573 4.728 0.663532.016 0.56 0 1.066 1.537 4.463 0.692571.962 0.57 0 1.03 1.504 4.222 0.71971.912 0.58 0 0.9949 1.474 4.003 0.744971.865 0.59 0 0.9608 1.446 3.801 0.768451.821 0.6 0 0.92754 1.42 3.616 0.79021.779 0.61 0 0.89508 1.397 3.446 0.810321.739 0.62 0 0.86339 1.374 3.288 0.828881.702 0.63 0 0.83244 1.354 3.142 0.845961.666 0.64 0 0.80217 1.334 3.007 0.861651.632 0.65 0 0.77258 1.316 2.88 0.87604




Mx My Mx

My Ty

Tx

Py

Px

P0y

P0x

1.6 0.66 0 0.74361 1.299 2.763 0.889211.569 0.67 0 0.71525 1.283 2.652 0.901231.54 0.68 0 0.68747 1.268 2.549 0.912191.512 0.69 0 0.66024 1.253 2.452 0.922151.485 0.7 0 0.63354 1.24 2.361 0.931191.459 0.71 0 0.60735 1.227 2.276 0.939381.434 0.72 0 0.58164 1.214 2.195 0.946781.411 0.73 0 0.5564 1.202 2.119 0.953441.388 0.74 0 0.53161 1.191 2.047 0.959431.366 0.75 0 0.50725 1.18 1.978 0.964811.345 0.76 0 0.4833 1.17 1.914 0.969611.324 0.77 0 0.45974 1.16 1.853 0.973891.305 0.78 0 0.43657 1.15 1.794 0.977681.286 0.79 0 0.41376 1.141 1.739 0.981041.268 0.8 0 0.3913 1.132 1.686 0.9841.25 0.81 0 0.36919 1.124 1.636 0.98661.233 0.82 0 0.3474 1.116 1.588 0.988871.216 0.83 0 0.32593 1.108 1.542 0.990831.201 0.84 0 0.30476 1.1 1.499 0.992531.185 0.85 0 0.28389 1.092 1.457 0.993981.17 0.86 0 0.2633 1.085 1.417 0.995211.156 0.87 0 0.24298 1.078 1.379 0.996251.141 0.88 0 0.22292 1.071 1.342 0.997111.128 0.89 0 0.20313 1.064 1.307 0.997821.114 0.9 0 0.18357 1.058 1.274 0.99841.102 0.91 0 0.16426 1.051 1.241 0.998861.089 0.92 0 0.14518 1.045 1.21 0.999211.077 0.93 0 0.12632 1.039 1.18 0.999481.065 0.94 0 0.10768 1.033 1.152 0.999681.053 0.95 0 0.089245 1.027 1.124 0.999821.042 0.96 0 0.071014 1.022 1.097 0.999911.031 0.97 0 0.052981 1.016 1.072 0.99996




Mx My Mx

My Ty

Tx

Py

Px

P0y

P0x

1.021 0.98 0 0.035138 1.011 1.047 0.999991.01 0.99 0 0.017479 1.005 1.023 11 1 0 0 1 1 1



Mx My Mx

My Ty

Tx

Py

Px

P0y

P0x

857.14 0.37797 0 1.89 1.4E+5 8.6E+5 019.89 0.38041 0 1.874 77.87 4.6E+2 0.00011114.05 0.38286 0 1.858 39.31 2.3E+2 0.00060411.45 0.38531 0 1.8

table gas dynamics

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