The version of these tables is 1.1.

The version of these tables (this file) is a function of addtional information.

Change Log

Version 1.1

• Add table for moving shock

• Add the ”naughty professor” table for isentropic flow.

These Tables were created by Potto and later where translated by using latex2html versions 1.7.

These Gas Dynamics tables are more extensive than regular tables from other sources. In fact some of the table haven’t appear in any other source since they are the innovative ideas. To how to use these tables please see the corresponding chapter in the book.

2

Chapter 1 Isentropic Flow

Table 1.1: Isentropic Table k = 1.4

M \frac{T}{T_{0}} \frac{ρ}{ρ_{0}} \frac{A}{A^{⋆}} \frac{P}{P_{0}} \frac{A×P}{A^{∗}×P_{0}} \frac{F}{F^{∗}}
0.000 1.00000 1.00000 5.8E+5 1.0000  5.8E + 5 2.4E+5
0.050 0.99950 0.99875 11.59  0.99825 11.57  4.838
0.100 0.99800 0.99502 5.822  0.99303 5.781  2.443
0.200 0.99206 0.98028 2.964  0.97250 2.882  1.268
0.300 0.98232 0.95638 2.035  0.93947 1.912  0.89699
0.400 0.96899 0.92427 1.590  0.89561 1.424  0.72632
0.500 0.95238 0.88517 1.340  0.84302 1.130  0.63535
0.600 0.93284 0.84045 1.188  0.78400 0.93155 0.58377
0.700 0.91075 0.79158 1.094  0.72093 0.78896 0.55425
0.800 0.88652 0.73999 1.038  0.65602 0.68110 0.53807
0.900 0.86059 0.68704 1.009  0.59126 0.59650 0.53039
1.00 0.83333 0.63394 1.000  0.52828 0.52828 0.52828
1.100 0.80515 0.58170 1.008  0.46835 0.47207 0.52989
1.200 0.77640 0.53114 1.030  0.41238 0.42493 0.53399
1.300 0.74738 0.48290 1.066  0.36091 0.38484 0.53974
1.400 0.71839 0.43742 1.115  0.31424 0.35036 0.54655
1.500 0.68966 0.39498 1.176  0.27240 0.32039 0.55401
1.600 0.66138 0.35573 1.250  0.23527 0.29414 0.56182
1.700 0.63371 0.31969 1.338  0.20259 0.27099 0.56976
1.800 0.60680 0.28682 1.439  0.17404 0.25044 0.57768

1.900 0.58072 0.25699 1.555  0.14924 0.23211 0.58549^{2.000 0.55556 0.23005 1.688  0.12780 0.21567 0.59309}^{2.500 0.44444 0.13169 2.637  0.058528 0.15432 0.62693}^{3.000 0.35714 0.076226 4.235  0.027224 0.11528 0.65326}^{3.500 0.28986 0.045233 6.790  0.013111 0.089018 0.67320}^{4.000 0.23810 0.027662 10.72  0.00659 0.070595 0.68830}^{4.500 0.19802 0.017449 16.56  0.00346 0.057227 0.69983}^{5.000 0.16667 0.011340 25.00  0.00189 0.047251 0.70876}^{5.500 0.14184 0.00758 36.87  0.00107 0.039628 0.71578}^{6.000 0.12195 0.00519 53.18  0.000633 0.033682 0.72136}^{6.500 0.10582 0.00364 75.13  0.000385 0.028962 0.72586}^{7.000 0.092593 0.00261 1.0E+2 0.000242 0.025156 0.72953}^{7.500 0.081633 0.00190 1.4E+2 0.000155 0.022046 0.73257}^{8.000 0.072464 0.00141 1.9E+2 0.000102 0.019473 0.73510}^{8.500 0.064725 0.00107 2.5E+2 6.90E−5 0.017321 0.73723}^{9.000 0.058140 0.000815 3.3E+2 4.74E−5 0.015504 0.73903}^{9.500 0.052493 0.000631 4.2E+2 3.31E−5 0.013957 0.74058} 10.00 0.047619 0.000495 5.4E+2 2.36E−5 0.012628 0.74192

Table 1.2: Isothermal Table

M  \frac{T_{0}}{T_{0}^{⋆}}  \frac{P_{0}}{P_{0}^{⋆}}  \frac{A}{A^{⋆}}  \frac{P}{P^{⋆}}  \frac{A×P}{A^{∗}×P_{0}}  \frac{F}{F^{∗}}
0.00  0.52828 1.064  5.0E + 5 2.014  1.0E+6 4.2E+5
0.05  0.52921 1.064  9.949  2.010  20.00  8.362
0.1  0.53199 1.064  5.001  2.000  10.00  4.225
0.2  0.54322 1.064  2.553  1.958  5.000 2.200
0.3  0.56232 1.063  1.763  1.891  3.333 1.564
0.4  0.58985 1.062  1.389  1.800  2.500 1.275
0.5  0.62665 1.059  1.183  1.690  2.000 1.125
0.6  0.67383 1.055  1.065  1.565  1.667 1.044
0.7  0.73278 1.047  0.99967 1.429  1.429 1.004
0.8  0.80528 1.036  0.97156 1.287  1.250 0.98750
0.9  0.89348 1.021  0.97274 1.142  1.111 0.98796
1.00  1.000  1.000  1.000  1.000  1.000 1.000
1.10  1.128  0.97376 1.053  0.86329 0.90909 1.020

Table 1.2: Isothermal Table

M  \frac{T_{0}}{T_{0}^{⋆}}  \frac{P_{0}}{P_{0}^{⋆}}  \frac{A}{A^{⋆}}  \frac{P}{P^{⋆}}  \frac{A×P}{A^{∗}×P_{0}}  \frac{F}{F^{∗}}
1.20  1.281  0.94147 1.134  0.73492 0.83333 1.047
1.30  1.464  0.90302 1.247  0.61693 0.76923 1.079
1.40  1.681  0.85853 1.399  0.51069 0.71429 1.114
1.50  1.939  0.80844 1.599  0.41686 0.66667 1.153
1.60  2.245  0.75344 1.863  0.33554 0.62500 1.194
1.70  2.608  0.69449 2.209  0.26634 0.58824 1.237
1.80  3.035  0.63276 2.665  0.20846 0.55556 1.281
1.90  3.540  0.56954 3.271  0.16090 0.52632 1.328
2.00  4.134  0.50618 4.083  0.12246 0.50000 1.375
2.50  9.026  0.22881 15.78  0.025349 0.40000 1.625
3.000 19.41  0.071758 90.14  0.00370 0.33333 1.889
3.500 40.29  0.015317 7.5E + 2 0.000380 0.28571 2.161
4.000 80.21  0.00221 9.1E + 3 2.75E−5 0.25000 2.438
4.500 1.5E + 2 0.000215 1.6E + 5 1.41E−6 0.22222 2.718
5.000 2.8E + 2 1.41E−5 4.0E + 6 0.0  0.20000 3.000
5.500 4.9E + 2 0.0  1.4E + 8 0.0  0.18182 3.284
6.000 8.3E + 2 0.0  7.3E + 9 0.0  0.16667 3.569
6.500 1.4E + 3 0.0  5.3E+11 0.0  0.15385 3.856
7.000 2.2E + 3 0.0  5.6E+13 0.0  0.14286 4.143
7.500 3.4E + 3 0.0  8.3E+15 0.0  0.13333 4.431
8.000 5.2E + 3 0.0  1.8E+18 0.0  0.12500 4.719
8.500 7.7E + 3 0.0  5.4E+20 0.0  0.11765 5.007
9.000 1.1E + 4 0.0  2.3E+23 0.0  0.11111 5.296
9.500 1.6E + 4 0.0  1.4E+26 0.0  0.10526 5.586
10.00  2.2E + 4 0.0  1.2E+29 0.0  0.1000005.875

This table is very useful in the naughty’s professor questions. Table 1.3: Fliegner’s number and other paramters as function of Mach number

M  Fn  ρ̂  ^{(\frac{P_{0}A^{∗}}{AP} )}2 \frac{RT_{0}}{P^{2}} ^{(\frac{ṁ}{A})}2 \frac{1}{Rρ_{0}P} ^{(\frac{ṁ}{A})}2 \frac{1}{Rρ_{0}^{2}T} ^{(\frac{ṁ}{A})}2
0.00  1.4E−6 1.000 0.0  0.0  0.0  0.0
0.0500010.0701061.000 0.00747 2.62E−5 0.00352  0.00351

7 8 CHAPTER 1. ISENTROPIC FLOW

\begin{matrix}0.91000 & 2.018 & 1.703 & 2.882 & 8.381 & 4.972 & 3.389 \\ 0.92000 & 2.059 & 1.736 & 2.955 & 8.949 & 5.235 & 3.541 \\ 0.93000 & 2.101 & 1.771 & 3.029 & 9.554 & 5.513 & 3.699 \\ 0.94000 & 2.144 & 1.806 & 3.105 & 10.20 & 5.805 & 3.865 \\ 0.95000 & 2.188 & 1.843 & 3.181 & 10.88 & 6.112 & 4.037 \\ 0.96000 & 2.233 & 1.881 & 3.259 & 11.60 & 6.436 & 4.217 \\ 0.97000 & 2.278 & 1.920 & 3.338 & 12.37 & 6.777 & 4.404 \\ 0.98000 & 2.324 & 1.961 & 3.419 & 13.19 & 7.136 & 4.600 \\ 0.99000 & 2.371 & 2.003 & 3.500 & 14.06 & 7.515 & 4.804 \\ 1.000 & 2.419 & 2.046 & 3.583 & 14.98 & 7.913 & 5.016 \end{matrix}

Chapter 2 Normal Shock

k  M_{x}  M_{y}  M_{y}′  \frac{T_{y}}{T_{x}}
1.30 1073.25 0.33968 2.2645  169842.29
1.40  985.85 0.37797 1.8898  188982.96
1.50  922.23 0.40825 1.6330  204124.86
1.60  873.09 0.43301 1.4434  216507.05
1.70  833.61 0.45374 1.2964  226871.99
1.80  801.02 0.47141 1.1785  235702.93
1.90  773.54 0.48667 1.0815  243332.79
2.00  750.00 0.50000 1.00000  250000.64
2.10  729.56 0.51177 0.93048  255883.78
2.20  711.62 0.52223 0.87039  261117.09
2.30  695.74 0.53161 0.81786  265805.36
2.40  681.56 0.54006 0.77151  270031.44
2.50  668.81 0.54772 0.73029  273861.85

Table of maximum values of the shock-chocking phenomenon.

Table 2.1: The shock wave Table for k = 1.4

M_{x}  M_{y}  \frac{T_{y}}{T_{x}}  \frac{ρ_{y}}{ρ_{x}}  \frac{P_{y}}{P_{x}}  \frac{P_{0y}}{P_{0x}}
1.00 1.00000  1.00000  1.00000  1.00000  1.00000
1.05 0.95313  1.03284  1.08398  1.11958  0.99985
1.10 0.91177  1.06494  1.16908  1.24500  0.99893

1.15 0.87502  1.09658  1.25504  1.37625  0.99669^{1.20 0.84217  1.12799  1.34161  1.51333  0.99280}^{1.25 0.81264  1.15938  1.42857  1.65625  0.98706}^{1.30 0.78596  1.19087  1.51570  1.80500  0.97937}^{1.35 0.76175  1.22261  1.60278  1.95958  0.96974}^{1.40 0.73971  1.25469  1.68966  2.12000  0.95819}^{1.45 0.71956  1.28720  1.77614  2.28625  0.94484}^{1.50 0.70109  1.32022  1.86207  2.45833  0.92979}^{1.55 0.68410  1.35379  1.94732  2.63625  0.91319}^{1.60 0.66844  1.38797  2.03175  2.82000  0.89520}^{1.65 0.65396  1.42280  2.11525  3.00958  0.87599}^{1.70 0.64054  1.45833  2.19772  3.20500  0.85572}^{1.75 0.62809  1.49458  2.27907  3.40625  0.83457}^{1.80 0.61650  1.53158  2.35922  3.61333  0.81268}^{1.85 0.60570  1.56935  2.43811  3.82625  0.79023}^{1.90 0.59562  1.60792  2.51568  4.04500  0.76736}^{1.95 0.58618  1.64729  2.59188  4.26958  0.74420}^{2.00 0.57735  1.68750  2.66667  4.50000  0.72087}^{2.05 0.56906  1.72855  2.74002  4.73625  0.69751}^{2.10 0.56128  1.77045  2.81190  4.97833  0.67420}^{2.15 0.55395  1.81322  2.88231  5.22625  0.65105}^{2.20 0.54706  1.85686  2.95122  5.48000  0.62814}^{2.25 0.54055  1.90138  3.01863  5.73958  0.60553}^{2.30 0.53441  1.94680  3.08455  6.00500  0.58329}^{2.35 0.52861  1.99311  3.14897  6.27625  0.56148}^{2.40 0.52312  2.04033  3.21190  6.55333  0.54014}^{2.45 0.51792  2.08846  3.27335  6.83625  0.51931}^{2.50 0.51299  2.13750  3.33333  7.12500  0.49901}^{2.75 0.49181  2.39657  3.61194  8.65625  0.40623}^{3.00 0.47519  2.67901  3.85714 10.33333  0.32834}^{3.25 0.46192  2.98511  4.07229 12.15625  0.26451}^{3.50 0.45115  3.31505  4.26087 14.12500  0.21295}^{3.75 0.44231  3.66894  4.42623 16.23958  0.17166}^{4.00 0.43496  4.04688  4.57143 18.50000  0.13876}^{4.25 0.42878  4.44891  4.69919 20.90625  0.11256} 4.50 0.42355  4.87509  4.81188 23.45833  0.09170

4.75 0.41908  5.32544  4.91156 26.15625  0.07505^{5.00 0.41523  5.80000  5.00000 29.00000  0.06172}^{5.25 0.41189  6.29878  5.07869 31.98958  0.05100}^{5.50 0.40897  6.82180  5.14894 35.12500  0.04236}^{5.75 0.40642  7.36906  5.21182 38.40625  0.03536}^{6.00 0.40416  7.94059  5.26829 41.83333  0.02965}^{6.25 0.40216  8.53637  5.31915 45.40625  0.02498}^{6.50 0.40038  9.15643  5.36508 49.12500  0.02115}^{6.75 0.39879  9.80077  5.40667 52.98958  0.01798}^{7.00 0.39736 10.46939  5.44444 57.00000  0.01535}^{7.25 0.39607 11.16229  5.47883 61.15625  0.01316}^{7.50 0.39491 11.87948  5.51020 65.45833  0.01133}^{7.75 0.39385 12.62095  5.53890 69.90625  0.00979}^{8.00 0.39289 13.38672  5.56522 74.50000  0.00849}^{8.25 0.39201 14.17678  5.58939 79.23958  0.00739}^{8.50 0.39121 14.99113  5.61165 84.12500  0.00645}^{8.75 0.39048 15.82978  5.63218 89.15625  0.00565}^{9.00 0.38980 16.69273  5.65116 94.33333  0.00496}^{9.25 0.38918 17.57997  5.66874 99.65625  0.00437}^{9.50 0.38860 18.49152  5.68504 105.12500  0.00387}^{9.75 0.38807 19.42736  5.70019 110.73958  0.00343} 10.00 0.38758 20.38750  5.71429 116.50000  0.00304

Table 2.2: Table for Shock Reflecting from suddenly closed end (k=1.4)

M_{x}  M_{y}  M_{x}′  M_{y}′  \frac{T_{y}}{T_{x}}  \frac{P_{y}}{P_{x}}  P_{0}_{y} P_{0}_{x}
1.006 0.99403 0.01 0.0 1.004  1.014  1.00000
1.012 0.98812 0.02 0.0 1.008  1.028  1.00000
1.018 0.98227 0.03 0.0 1.012  1.043  0.99999
1.024 0.97647 0.04 0.0 1.016  1.057  0.99998
1.030 0.97074 0.05 0.0 1.020  1.072  0.99997
1.037 0.96506 0.06 0.0 1.024  1.087  0.99994
1.043 0.95944 0.07 0.0 1.028  1.102  0.99991
1.049 0.95387 0.08 0.0 1.032  1.118  0.99986

12 CHAPTER 2. NORMAL SHOCK Table 2.2: Table for Shock Reflecting from suddenly closed end (k=1.4)(continue)

M_{x}  M_{y}  M_{x}′  M_{y}′  \frac{T_{y}}{T_{x}}  \frac{P_{y}}{P_{x}}  P_{0}_{y} P_{0}_{x}
1.055 0.94836 0.09 0.0 1.036  1.133  0.99980
1.062 0.94291 0.100 0.0 1.040  1.149  0.99973
1.127 0.89128 0.200 0.0 1.082  1.316  0.99790
1.196 0.84463 0.300 0.0 1.126  1.502  0.99317
1.268 0.80251 0.400 0.0 1.171  1.710  0.98446
1.344 0.76452 0.500 0.0 1.219  1.941  0.97099
1.423 0.73029 0.600 0.0 1.269  2.195  0.95231
1.505 0.69946 0.700 0.0 1.323  2.475  0.92832
1.589 0.67171 0.800 0.0 1.381  2.780  0.89918
1.676 0.64673 0.900 0.0 1.442  3.112  0.86537
1.766 0.62425 1.000 0.0 1.506  3.473  0.82755
1.858 0.60401 1.100 0.0 1.576  3.862  0.78652
1.952 0.58578 1.200 0.0 1.649  4.280  0.74316
2.048 0.56935 1.300 0.0 1.727  4.728  0.69834
2.146 0.55453 1.400 0.0 1.810  5.206  0.65290
2.245 0.54114 1.500 0.0 1.897  5.715  0.60761
2.346 0.52904 1.600 0.0 1.990  6.256  0.56312
2.448 0.51808 1.700 0.0 2.087  6.827  0.51996
2.552 0.50814 1.800 0.0 2.189  7.431  0.47855
2.656 0.49912 1.900 0.0 2.297  8.066  0.43921
2.762 0.49092 2.000 0.0 2.410  8.734  0.40213
3.859 0.43894 3.000 0.0 3.831  17.21  0.15637
5.000 0.41523 4.000 0.0 5.800  29.00  0.061716
6.162 0.40284 5.000 0.0 8.325  44.14  0.026517
7.336 0.39566 6.000 0.0 11.41  62.62  0.012492
8.517 0.39116 7.000 0.0 15.05  84.47  0.00639
9.703 0.38817 8.000 0.0 19.25  1.1E+2 0.00350
10.89 0.38608 9.000 0.0 24.01  1.4E+2 0.00204
12.08 0.38457 10.00 0.0 29.33  1.7E+2 0.00125

Table 2.3: Table for Shock Propagating From suddenly open valve (k=1.4)

M_{x}  M_{y}  M_{x}′  M_{y}′  \frac{T_{y}}{T_{x}}  \frac{P_{y}}{P_{x}}  P_{0}_{y} P_{0}_{x}
1.006 0.99402 0.0 0.01  1.004  1.014  1.00000
1.012 0.98807 0.0 0.02  1.008  1.028  1.00000
1.018 0.98216 0.0 0.03  1.012  1.043  0.99999
1.024 0.97629 0.0 0.04  1.016  1.058  0.99998
1.031 0.97045 0.0 0.05  1.020  1.073  0.99996
1.037 0.96465 0.0 0.06  1.024  1.088  0.99994
1.044 0.95888 0.0 0.07  1.029  1.104  0.99990
1.050 0.95315 0.0 0.08  1.033  1.120  0.99985
1.057 0.94746 0.0 0.09  1.037  1.136  0.99979
1.063 0.94180 0.0 0.10  1.041  1.152  0.99971
1.133 0.88717 0.0 0.20  1.086  1.331  0.99763
1.210 0.83607 0.0 0.30  1.134  1.541  0.99181
1.295 0.78840 0.0 0.40  1.188  1.791  0.98019
1.390 0.74403 0.0 0.50  1.248  2.087  0.96069
1.495 0.70283 0.0 0.60  1.317  2.441  0.93133
1.613 0.66462 0.0 0.70  1.397  2.868  0.89039
1.745 0.62923 0.0 0.80  1.491  3.387  0.83661
1.896 0.59649 0.0 0.90  1.604  4.025  0.76940
2.068 0.56619 0.0 1.00  1.744  4.823  0.68907
2.269 0.53817 0.0 1.100 1.919  5.840  0.59699
2.508 0.51223 0.0 1.200 2.145  7.171  0.49586
2.799 0.48823 0.0 1.300 2.450  8.975  0.38974
3.167 0.46599 0.0 1.400 2.881 11.54  0.28412
3.658 0.44536 0.0 1.500 3.536 15.45  0.18575
4.368 0.42622 0.0 1.600 4.646 22.09  0.10216
5.551 0.40843 0.0 1.700 6.931 35.78  0.040812
8.293 0.39187 0.0 1.800 14.32  80.07  0.00721
8.821 0.39028 0.0 1.810 16.07  90.61  0.00544
9.457 0.38870 0.0 1.820 18.33  1.0E + 2 0.00395
10.24 0.38713 0.0 1.830 21.35  1.2E + 2 0.00272
11.25 0.38557 0.0 1.840 25.57  1.5E + 2 0.00175
12.62 0.38402 0.0 1.850 31.92  1.9E + 2 0.00101

Table 2.3: Table for Shock Propagating from suddenly open valve (k=1.4)

M_{x}  M_{y}  M_{x}′  M_{y}′  \frac{T_{y}}{T_{x}}  \frac{P_{y}}{P_{x}}  P_{0}_{y} P_{0}_{x}
14.62 0.38248 0.0 1.860 42.53  2.5E + 2 0.000497
17.99 0.38096 0.0 1.870 63.84  3.8E + 2 0.000181
25.62 0.37944 0.0 1.880 1.3E+2 7.7E + 2 3.18E−5
61.31 0.37822 0.0 1.888 7.3E+2 4.4E + 3 0.0
62.95 0.37821 0.0 1.888 7.7E+2 4.6E + 3 0.0
64.74 0.37820 0.0 1.888 8.2E+2 4.9E + 3 0.0
66.69 0.37818 0.0 1.888 8.7E+2 5.2E + 3 0.0
68.83 0.37817 0.0 1.888 9.2E+2 5.5E + 3 0.0
71.18 0.37816 0.0 1.889 9.9E+2 5.9E + 3 0.0
73.80 0.37814 0.0 1.889 1.1E+3 6.4E + 3 0.0
76.72 0.37813 0.0 1.889 1.1E+3 6.9E + 3 0.0
80.02 0.37812 0.0 1.889 1.2E+3 7.5E + 3 0.0
83.79 0.37810 0.0 1.889 1.4E+3 8.2E + 3 0.0

Table 2.4: Table for Shock Propagating from suddenly open valve (k=1.3)

M_{x}  M_{y}  M_{x}′  M_{y}′  \frac{T_{y}}{T_{x}}  \frac{P_{y}}{P_{x}}  P_{0}_{y} P_{0}_{x}
1.0058 0.99427 0.0 0.010 1.003  1.013 1.00000
1.012 0.98857 0.0 0.020 1.006  1.026 1.00000
1.017 0.98290 0.0 0.030 1.009  1.040 0.99999
1.023 0.97726 0.0 0.040 1.012  1.054 0.99998
1.029 0.97166 0.0 0.050 1.015  1.067 0.99997
1.035 0.96610 0.0 0.060 1.018  1.081 0.99995
1.042 0.96056 0.0 0.070 1.021  1.096 0.99991
1.048 0.95506 0.0 0.080 1.024  1.110 0.99987
1.054 0.94959 0.0 0.090 1.028  1.125 0.99981
1.060 0.94415 0.0 0.100 1.031  1.140 0.99975
1.126 0.89159 0.0 0.200 1.063  1.302 0.99792
1.197 0.84227 0.0 0.300 1.098  1.489 0.99288
1.275 0.79611 0.0 0.400 1.136  1.706 0.98290
1.359 0.75301 0.0 0.500 1.177  1.959 0.96631

Table 2.4: Table for Shock Propagating from suddenly open valve (k=1.3)

M_{x} M_{y} M_{x}′ M_{y}′ \frac{T_{y}}{T_{x}} \frac{P_{y}}{P_{x}} P_{0}_{y} P_{0}_{x}
1.452 0.71284 0.0 0.600 1.223  2.252 0.94156
1.553 0.67546 0.0 0.700 1.274  2.595 0.90734
1.663 0.64073 0.0 0.800 1.333  2.997 0.86274
1.785 0.60847 0.0 0.900 1.400  3.471 0.80734
1.919 0.57853 0.0 1.00 1.478  4.034 0.74136
2.069 0.55074 0.0 1.100 1.570  4.707 0.66575
2.236 0.52495 0.0 1.200 1.681  5.522 0.58223
2.426 0.50100 0.0 1.300 1.815  6.523 0.49333
2.644 0.47875 0.0 1.400 1.980  7.772 0.40226
2.898 0.45807 0.0 1.500 2.191  9.367 0.31281
3.202 0.43882 0.0 1.600 2.467 11.46  0.22904
3.576 0.42089 0.0 1.700 2.842 14.32  0.15495
4.053 0.40418 0.0 1.800 3.381 18.44  0.093988
4.109 0.40257 0.0 1.810 3.448 18.95  0.088718
4.166 0.40097 0.0 1.820 3.519 19.49  0.083607
4.225 0.39938 0.0 1.830 3.592 20.05  0.078654
4.286 0.39780 0.0 1.840 3.669 20.64  0.073863
4.349 0.39624 0.0 1.850 3.749 21.25  0.069233
4.415 0.39468 0.0 1.860 3.834 21.90  0.064766
4.482 0.39314 0.0 1.870 3.923 22.58  0.060462
4.553 0.39160 0.0 1.880 4.016 23.30  0.056322
4.611 0.39037 0.0 1.888 4.096 23.91  0.053088
4.612 0.39035 0.0 1.888 4.097 23.91  0.053053
4.613 0.39034 0.0 1.888 4.098 23.92  0.053018
4.613 0.39033 0.0 1.888 4.099 23.93  0.052984
4.614 0.39031 0.0 1.888 4.099 23.93  0.052949
4.615 0.39030 0.0 1.889 4.100 23.94  0.052914
4.615 0.39029 0.0 1.889 4.101 23.95  0.052879
4.616 0.39027 0.0 1.889 4.102 23.95  0.052844
4.616 0.39026 0.0 1.889 4.103 23.96  0.052809
4.617 0.39025 0.0 1.889 4.104 23.97  0.052775

16 CHAPTER 2. NORMAL SHOCK

Chapter 3 Isothermal Flow

Table 3.1: The Isothermal Flow basic parameters

M  \frac{4fL}{D}  \frac{P}{P^{∗}}  \frac{P_{0}}{P_{0}^{∗}}  \frac{ρ}{ρ^{∗}}  \frac{T_{0}}{T_{0}^{∗}}
0.03000 785.97  28.1718 17.6651 28.1718  0.87516
0.04000 439.33  21.1289 13.2553 21.1289  0.87528
0.05000 279.06  16.9031 10.6109 16.9031  0.87544
0.06000 192.12  14.0859  8.8493 14.0859  0.87563
0.07000 139.79  12.0736  7.5920 12.0736  0.87586
0.08000 105.89  10.5644  6.6500 10.5644  0.87612
0.09000 82.7040  9.3906  5.9181  9.3906  0.87642
0.10000 66.1599  8.4515  5.3334  8.4515  0.87675
0.20000 13.9747  4.2258  2.7230  4.2258  0.88200
0.25000 7.9925  3.3806  2.2126  3.3806  0.88594
0.30000 4.8650  2.8172  1.8791  2.8172  0.89075
0.35000 3.0677  2.4147  1.6470  2.4147  0.89644
0.40000 1.9682  2.1129  1.4784  2.1129  0.90300
0.45000 1.2668  1.8781  1.3524  1.8781  0.91044
0.50000 0.80732 1.6903  1.2565  1.6903  0.91875
0.55000 0.50207 1.5366  1.1827  1.5366  0.92794
0.60000 0.29895 1.4086  1.1259  1.4086  0.93800
0.65000 0.16552 1.3002  1.0823  1.3002  0.94894
0.70000 0.08085 1.2074  1.0495  1.2074  0.96075
0.75000 0.03095 1.1269  1.0255  1.1269  0.97344

Table 3.1: The Isothermal Flow basic parameters (continue)

M  \frac{4fL}{D}  \frac{P}{P^{∗}}  \frac{P_{0}}{P_{0}^{∗}}  \frac{ρ}{ρ^{∗}}  \frac{T_{0}}{T_{0}^{∗}}
0.80000 0.00626 1.056  1.009  1.056  0.98700
0.81000 0.00371 1.043  1.007  1.043  0.98982
0.81879 0.00205 1.032  1.005  1.032  0.99232
0.82758 0.000896 1.021  1.003  1.021  0.99485
0.83637 0.000220 1.011  1.001  1.011  0.99741
0.84515 0.0  1.000  1.000  1.000  1.000

To produce this table rum program with:\\
variableName =  machV;
int isRange = yes;
whatInfo = infoStandard ;

Table 3.2: The flow parameters for unchoked flow

M_{1}  M_{2}  ^{^{\frac{4fL_{max}}{D}} |}^{1}  \frac{4fL}{D}  \frac{P_{2}}{P_{1}}
0.7272 0.84095  0.05005  0.05000  0.10000
0.6934 0.83997  0.08978  0.08971  0.10000
0.6684 0.84018  0.12949  0.12942  0.10000
0.6483 0.83920  0.16922  0.16912  0.10000
0.5914 0.83889  0.32807  0.32795  0.10000
0.5807 0.83827  0.36780  0.36766  0.10000
0.5708 0.83740  0.40754  0.40737  0.10000

Chapter 4 Fanno Flow

Table 4.1: Fanno Flow Standard basic Table

M \frac{4fL}{D} \frac{P}{P^{∗}} \frac{P_{0}}{P_{0}^{∗}} \frac{ρ}{ρ^{∗}} \frac{U}{U^{∗}} \frac{T}{T^{∗}}
0.030 787.08  36.5116 19.3005 30.4318 0.03286 1.1998
0.040 440.35  27.3817 14.4815 22.8254 0.04381 1.1996
0.050 280.02  21.9034 11.5914 18.2620 0.05476 1.1994
0.060 193.03  18.2508 9.6659 15.2200 0.06570 1.1991
0.070 140.66  15.6416 8.2915 13.0474 0.07664 1.1988
0.080 106.72  13.6843 7.2616 11.4182 0.08758 1.1985
0.090 83.4961 12.1618 6.4613 10.1512 0.09851 1.1981
0.100 66.9216 10.9435 5.8218 9.1378 0.10944 1.1976
0.200 14.5333  5.4554 2.9635 4.5826 0.21822 1.1905
0.250  8.4834  4.3546 2.4027 3.6742 0.27217 1.1852
0.300  5.2993  3.6191 2.0351 3.0702 0.32572 1.1788
0.350  3.4525  3.0922 1.7780 2.6400 0.37879 1.1713
0.400  2.3085  2.6958 1.5901 2.3184 0.43133 1.1628
0.450  1.5664  2.3865 1.4487 2.0693 0.48326 1.1533
0.500  1.0691  2.1381 1.3398 1.8708 0.53452 1.1429
0.550  0.72805 1.9341 1.2549 1.7092 0.58506 1.1315
0.600  0.49082 1.7634 1.1882 1.5753 0.63481 1.1194
0.650  0.32459 1.6183 1.1356 1.4626 0.68374 1.1065
0.700  0.20814 1.4935 1.0944 1.3665 0.73179 1.0929
0.750  0.12728 1.3848 1.0624 1.2838 0.77894 1.0787

\begin{matrix}0.800 & 0.07229 & 1.2893 & 1.0382 & 1.2119 & 0.82514 & 1.0638 \\ 0.850 & 0.03633 & 1.2047 & 1.0207 & 1.1489 & 0.87037 & 1.0485 \\ 0.900 & 0.01451 & 1.1291 & 1.0089 & 1.0934 & 0.91460 & 1.0327 \\ 0.950 & 0.00328 & 1.061 & 1.002 & 1.044 & 0.95781 & 1.017 \\ 1.000 & 0.0 & 1.00000 & 1.00000 & 1.00000 & 1.000 & 1.00000 \\ 2.000 & 0.30500 & 0.40825 & 1.688 & 0.61237 & 1.633 & 0.66667 \\ 3.000 & 0.52216 & 0.21822 & 4.235 & 0.50918 & 1.964 & 0.42857 \\ 4.000 & 0.63306 & 0.13363 & 10.72 & 0.46771 & 2.138 & 0.28571 \\ 5.000 & 0.69380 & 0.089443 & 25.00 & 0.44721 & 2.236 & 0.20000 \\ 6.000 & 0.72988 & 0.063758 & 53.18 & 0.43568 & 2.295 & 0.14634 \\ 7.000 & 0.75280 & 0.047619 & 1.0E+2 & 0.42857 & 2.333 & 0.11111 \\ 8.000 & 0.76819 & 0.036860 & 1.9E+2 & 0.42390 & 2.359 & 0.086957 \\ 9.000 & 0.77899 & 0.029348 & 3.3E+2 & 0.42066 & 2.377 & 0.069767 \\ 10.00 & 0.78683 & 0.023905 & 5.4E+2 & 0.41833 & 2.390 & 0.057143 \\ 20.00 & 0.81265 & 0.00609 & 1.5E+4 & 0.41079 & 2.434 & 0.014815 \\ 25.00 & 0.81582 & 0.00390 & 4.6E+4 & 0.40988 & 2.440 & 0.00952 \\ 30.00 & 0.81755 & 0.00271 & 1.1E+5 & 0.40938 & 2.443 & 0.00663 \\ 35.00 & 0.81860 & 0.00200 & 2.5E+5 & 0.40908 & 2.445 & 0.00488 \\ 40.00 & 0.81928 & 0.00153 & 4.8E+5 & 0.40889 & 2.446 & 0.00374 \\ 45.00 & 0.81975 & 0.00121 & 8.6E+5 & 0.40875 & 2.446 & 0.00296 \\ 50.00 & 0.82008 & 0.000979 & 1.5E+6 & 0.40866 & 2.447 & 0.00240 \\ 55.00 & 0.82033 & 0.000809 & 2.3E+6 & 0.40859 & 2.447 & 0.00198 \\ 60.00 & 0.82052 & 0.000680 & 3.6E+6 & 0.40853 & 2.448 & 0.00166 \\ 65.00 & 0.82066 & 0.000579 & 5.4E+6 & 0.40849 & 2.448 & 0.00142 \\ 70.00 & 0.82078 & 0.000500 & 7.8E+6 & 0.40846 & 2.448 & 0.00122 \end{matrix}

Chapter 5 Rayleigh Flow

Table 5.1: Rayleigh Flow k=1.4

M  \frac{T}{T^{∗}}  \frac{T_{0}}{T_{0}^{∗}}  \frac{P}{P^{∗}}  \frac{P_{0}}{P_{0}^{∗}}  \frac{ρ^{∗}}{ρ}
0.03  0.00517  0.00431 2.397  1.267  0.00216
0.040 0.00917  0.00765 2.395  1.266  0.00383
0.050 0.014300 0.011922 2.392  1.266  0.00598
0.060 0.020529 0.017119 2.388  1.265  0.00860
0.070 0.027841 0.023223 2.384  1.264  0.011680
0.080 0.036212 0.030215 2.379  1.262  0.015224
0.090 0.045616 0.038075 2.373  1.261  0.019222
0.100 0.056020 0.046777 2.367  1.259  0.023669
0.20  0.20661  0.17355 2.273  1.235  0.090909
0.25  0.30440  0.25684 2.207  1.218  0.13793
0.30  0.40887  0.34686 2.131  1.199  0.19183
0.35  0.51413  0.43894 2.049  1.178  0.25096
0.40  0.61515  0.52903 1.961  1.157  0.31373
0.45  0.70804  0.61393 1.870  1.135  0.37865
0.50  0.79012  0.69136 1.778  1.114  0.44444
0.55  0.85987  0.75991 1.686  1.094  0.51001
0.60  0.91670  0.81892 1.596  1.075  0.57447
0.65  0.96081  0.86833 1.508  1.058  0.63713
0.70  0.99290  0.90850 1.423  1.043  0.69751
0.75  1.014  0.94009 1.343  1.030  0.75524

22 CHAPTER 5. RAYLEIGH FLOW

Table 5.1: Rayleigh Flow k=1.4 (continue)

M  \frac{T}{T^{∗}}  \frac{T_{0}}{T_{0}^{∗}}  \frac{P}{P^{∗}}  \frac{P_{0}}{P_{0}^{∗}}  \frac{ρ^{∗}}{ρ}
0.80  1.025  0.96395 1.266  1.019  0.81013
0.85  1.029  0.98097 1.193  1.011  0.86204
0.90  1.025  0.99207 1.125  1.005  0.91097
0.95  1.015  0.99814 1.060  1.001  0.95693
1.0  1.00  1.00  1.00  1.00  1.000
1.1  0.96031  0.99392 0.89087  1.005  1.078
1.2  0.91185  0.97872 0.79576  1.019  1.146
1.3  0.85917  0.95798 0.71301  1.044  1.205
1.4  0.80539  0.93425 0.64103  1.078  1.256
1.5  0.75250  0.90928 0.57831  1.122  1.301
1.6  0.70174  0.88419 0.52356  1.176  1.340
1.7  0.65377  0.85971 0.47562  1.240  1.375
1.8  0.60894  0.83628 0.43353  1.316  1.405
1.9  0.56734  0.81414 0.39643  1.403  1.431
2.0  0.52893  0.79339 0.36364  1.503  1.455
2.1  0.49356  0.77406 0.33454  1.616  1.475
2.2  0.46106  0.75613 0.30864  1.743  1.494
2.3  0.43122  0.73954 0.28551  1.886  1.510
2.4  0.40384  0.72421 0.26478  2.045  1.525
2.5  0.37870  0.71006 0.24615  2.222  1.538
2.6  0.35561  0.69700 0.22936  2.418  1.550
2.7  0.33439  0.68494 0.21417  2.634  1.561
2.8  0.31486  0.67380 0.20040  2.873  1.571
2.9  0.29687  0.66350 0.18788  3.136  1.580
3.0  0.28028  0.65398 0.17647  3.424  1.588
3.5  0.21419  0.61580 0.13223  5.328  1.620
4.0  0.16831  0.58909 0.10256  8.227  1.641
4.5  0.13540  0.56982 0.081772 12.50  1.656
5.0  0.11111  0.55556 0.066667 18.63  1.667
5.5  0.092719 0.54473 0.055363 27.21  1.675
6.0  0.078487 0.53633 0.046693 38.95  1.681
6.5  0.067263 0.52970 0.039900 54.68  1.686
7.0  0.058264 0.52438 0.034483 75.41  1.690

Table 5.1: Rayleigh Flow k=1.4 (continue)

M \frac{T}{T^{∗}} \frac{T_{0}}{T_{0}^{∗}} \frac{P}{P^{∗}} \frac{P_{0}}{P_{0}^{∗}} \frac{ρ^{∗}}{ρ}
7.5  0.050943 0.52004 0.030094 1.0E+2 1.693
8.0  0.044910 0.51647 0.026490 1.4E+2 1.695
8.5  0.039883 0.51349 0.023495 1.8E+2 1.698
9.0  0.035650 0.51098 0.020979 2.3E+2 1.699
9.5  0.032053 0.50885 0.018846 3.0E+2 1.701
10.0  0.028972 0.50702 0.017021 3.8E+2 1.702
20.0  0.00732  0.49415 0.00428  1.1E+4 1.711
25.0  0.00469  0.49259 0.00274  3.2E+4 1.712
30.0  0.00326  0.49174 0.00190  8.0E+4 1.713
35.0  0.00240  0.49122 0.00140  1.7E+5 1.713
40.0  0.00184  0.49089 0.00107  3.4E+5 1.714
45.0  0.00145  0.49066 0.000846 6.0E+5 1.714
50.0  0.00117  0.49050 0.000686 1.0E+6 1.714
55.0  0.000971 0.49037 0.000567 1.6E+6 1.714
60.0  0.000816 0.49028 0.000476 2.5E+6 1.714
65.0  0.000695 0.49021 0.000406 3.8E+6 1.714
70.0  0.000600 0.49015 0.000350 5.5E+6 1.714

24 CHAPTER 5. RAYLEIGH FLOW

Chapter 6 Prandtl-Meyer Function

Table 6.1: ??

M  ν  \frac{P}{P_{0}}  \frac{T}{T_{0}}  \frac{ρ}{ρ_{0}}  μ
1.0000  0.0  0.52828 0.83333 0.63394 45.00
1.100  1.336  0.46835 0.80515 0.58170 47.73
1.200  3.558  0.41238 0.77640 0.53114 50.19
1.300  6.170  0.36091 0.74738 0.48290 52.43
1.400  8.987  0.31424 0.71839 0.43742 54.46
1.500  11.91  0.27240 0.68966 0.39498 56.31
1.600  14.86  0.23527 0.66138 0.35573 57.99
1.700  17.81  0.20259 0.63371 0.31969 59.53
1.800  20.73  0.17404 0.60680 0.28682 60.95
1.900  23.59  0.14924 0.58072 0.25699 62.24
2.000  26.38  0.12780 0.55556 0.23005 63.43
3.000  49.76  0.027224 0.35714 0.076226 71.57
4.000  65.78  0.00659 0.23810 0.027662 75.96
5.000  76.92  0.00189 0.16667 0.011340 78.69
6.000  84.96  0.000633 0.12195 0.00519 80.54
7.000  90.97  0.000242 0.092593 0.00261 81.87
8.000  95.62  0.000102 0.072464 0.00141 82.87
9.000  99.32  4.74E−05 0.058140 0.000815 83.66
10.00  1.0E+02 2.36E−05 0.047619 0.000495 84.29