11.9.3: Rayleigh Flow Tables and Figures
- Page ID
- 835
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Several observations can be made in regards to the stagnation temperature. The maximum temperature is not at Mach equal to one. Yet the maximum enetropy accurs at Mach equal to one.
\(M\) | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 | 0.10 | 0.20 | 0.25 | 0.30 | 0.35 | 0.40 | 0.45 | 0.50 | 0.55 | 0.60 | 0.65 | 0.70 | 0.75 | 0.80 | 0.85 | 0.90 | 0.95 | 1.0 | 1.1 | 1.2 | 1.3 | 1.4 | 1.5 | 1.6 | 1.7 | 1.8 | 1.9 | 2.0 | 2.1 | 2.2 | 2.3 | 2.4 | 2.5 | 2.6 | 2.7 | 2.8 | 2.9 | 3.0 | 3.5 | 4.0 | 4.5 | 5.0 | 5.5 | 6.0 | 6.5 | 7.0 | 7.5 | 8.0 | 8.5 | 9.0 | 9.5 | 10.0 | 20.0 | 25.0 | 30.0 | 35.0 | 40.0 | 45.0 | 50.0 | 55.0 | 60.0 | 65.0 | 70.0 |
\(\dfrac{T}{T^{\star}}\) | 0.00517 | 0.00917 | 0.014300 | 0.020529 | 0.027841 | 0.036212 | 0.045616 | 0.056020 | 0.20661 | 0.30440 | 0.40887 | 0.51413 | 0.61515 | 0.70804 | 0.79012 | 0.85987 | 0.91670 | 0.96081 | 0.99290 | 1.014 | 1.025 | 1.029 | 1.025 | 1.015 | 1.00 | 0.96031 | 0.91185 | 0.85917 | 0.80539 | 0.75250 | 0.70174 | 0.65377 | 0.60894 | 0.56734 | 0.52893 | 0.49356 | 0.46106 | 0.43122 | 0.40384 | 0.37870 | 0.35561 | 0.33439 | 0.31486 | 0.29687 | 0.28028 | 0.21419 | 0.16831 | 0.13540 | 0.11111 | 0.092719 | 0.078487 | 0.067263 | 0.058264 | 0.050943 | 0.044910 | 0.039883 | 0.035650 | 0.032053 | 0.028972 | 0.00732 | 0.00469 | 0.00326 | 0.00240 | 0.00184 | 0.00145 | 0.00117 | 0.000971 | 0.000816 | 0.000695 | 0.000600 |
\(\dfrac{T_0} (click for details) \) Callstack:
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0.00431 | 0.00765 | 0.011922 | 0.017119 | 0.023223 | 0.030215 | 0.038075 | 0.046777 | 0.17355 | 0.25684 | 0.34686 | 0.43894 | 0.52903 | 0.61393 | 0.69136 | 0.75991 | 0.81892 | 0.86833 | 0.90850 | 0.94009 | 0.96395 | 0.98097 | 0.99207 | 0.99814 | 1.00 | 0.99392 | 0.97872 | 0.95798 | 0.93425 | 0.90928 | 0.88419 | 0.85971 | 0.83628 | 0.81414 | 0.79339 | 0.77406 | 0.75613 | 0.73954 | 0.72421 | 0.71006 | 0.69700 | 0.68494 | 0.67380 | 0.66350 | 0.65398 | 0.61580 | 0.58909 | 0.56982 | 0.55556 | 0.54473 | 0.53633 | 0.52970 | 0.52438 | 0.52004 | 0.51647 | 0.51349 | 0.51098 | 0.50885 | 0.50702 | 0.49415 | 0.49259 | 0.49174 | 0.49122 | 0.49089 | 0.49066 | 0.49050 | 0.49037 | 0.49028 | 0.49021 | 0.49015 |
\(\dfrac{P} (click for details) \) Callstack:
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2.397 | 2.395 | 2.392 | 2.388 | 2.384 | 2.379 | 2.373 | 2.367 | 2.273 | 2.207 | 2.131 | 2.049 | 1.961 | 1.870 | 1.778 | 1.686 | 1.596 | 1.508 | 1.423 | 1.343 | 1.266 | 1.193 | 1.125 | 1.060 | 1.00 | 0.89087 | 0.79576 | 0.71301 | 0.64103 | 0.57831 | 0.52356 | 0.47562 | 0.43353 | 0.39643 | 0.36364 | 0.33454 | 0.30864 | 0.28551 | 0.26478 | 0.24615 | 0.22936 | 0.21417 | 0.20040 | 0.18788 | 0.17647 | 0.13223 | 0.10256 | 0.081772 | 0.066667 | 0.055363 | 0.046693 | 0.039900 | 0.034483 | 0.030094 | 0.026490 | 0.023495 | 0.020979 | 0.018846 | 0.017021 | 0.00428 | 0.00274 | 0.00190 | 0.00140 | 0.00107 | 0.000846 | 0.000686 | 0.000567 | 0.000476 | 0.000406 | 0.000350 |
\(\dfrac{P_0} (click for details) \) Callstack:
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1.267 | 1.266 | 1.266 | 1.265 | 1.264 | 1.262 | 1.261 | 1.259 | 1.235 | 1.218 | 1.199 | 1.178 | 1.157 | 1.135 | 1.114 | 1.094 | 1.075 | 1.058 | 1.043 | 1.030 | 1.019 | 1.011 | 1.005 | 1.001 | 1.00 | 1.005 | 1.019 | 1.044 | 1.078 | 1.122 | 1.176 | 1.240 | 1.316 | 1.403 | 1.503 | 1.616 | 1.743 | 1.886 | 2.045 | 2.222 | 2.418 | 2.634 | 2.873 | 3.136 | 3.424 | 5.328 | 8.227 | 12.50 | 18.63 | 27.21 | 38.95 | 54.68 | 75.41 | 1.0E+2 | 1.4E+2 | 1.8E+2 | 2.3E+2 | 3.0E+2 | 3.8E+2 | 1.1E+4 | 3.2E+4 | 8.0E+4 | 1.7E+5 | 3.4E+5 | 6.0E+5 | 1.0E+6 | 1.6E+6 | 2.5E+6 | 3.8E+6 | 5.5E+6 |
\(\dfrac (click for details) {\rho}\) Callstack:
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0.00216 | 0.00383 | 0.00598 | 0.00860 | 0.011680 | 0.015224 | 0.019222 | 0.023669 | 0.090909 | 0.13793 | 0.19183 | 0.25096 | 0.31373 | 0.37865 | 0.44444 | 0.51001 | 0.57447 | 0.63713 | 0.69751 | 0.75524 | 0.81013 | 0.86204 | 0.91097 | 0.95693 | 1.000 | 1.078 | 1.146 | 1.205 | 1.256 | 1.301 | 1.340 | 1.375 | 1.405 | 1.431 | 1.455 | 1.475 | 1.494 | 1.510 | 1.525 | 1.538 | 1.550 | 1.561 | 1.571 | 1.580 | 1.588 | 1.620 | 1.641 | 1.656 | 1.667 | 1.675 | 1.681 | 1.686 | 1.690 | 1.693 | 1.695 | 1.698 | 1.699 | 1.701 | 1.702 | 1.711 | 1.712 | 1.713 | 1.713 | 1.714 | 1.714 | 1.714 | 1.714 | 1.714 | 1.714 | 1.714 |
The data is presented in Figure 11.41.
Fig. 11.41 The basic functions of Rayleigh Flow (k=1.4).
Contributors and Attributions
Dr. Genick Bar-Meir. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or later or Potto license.