11.8: The Table for Fanno Flow
- Page ID
- 831
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)\(M\) | 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 | 1.00 | 2.00 | 3.00 | 4.00 | 5.00 | 6.00 | 7.00 | 8.00 | 9.00 | 10.00 | 20.00 | 25.00 | 30.00 | 35.00 | 40.00 | 45.00 | 50.00 | 55.00 | 60.00 | 65.00 | 70.00 |
\(\dfrac{4\,f\,L}{D}\) | 787.08 | 440.35 | 280.02 | 193.03 | 140.66 | 106.72 | 83.4961 | 66.9216 | 14.5333 | 8.4834 | 5.2993 | 3.4525 | 2.3085 | 1.5664 | 1.0691 | 0.72805 | 0.49082 | 0.32459 | 0.20814 | 0.12728 | 0.07229 | 0.03633 | 0.01451 | 0.00328 | 0.0 | 0.30500 | 0.52216 | 0.63306 | 0.69380 | 0.72988 | 0.75280 | 0.76819 | 0.77899 | 0.78683 | 0.81265 | 0.81582 | 0.81755 | 0.81860 | 0.81928 | 0.81975 | 0.82008 | 0.82033 | 0.82052 | 0.82066 | 0.82078 |
\(\dfrac{P}{P^{\star}}\) | 36.5116 | 27.3817 | 21.9034 | 18.2508 | 15.6416 | 13.6843 | 12.1618 | 10.9435 | 5.4554 | 4.3546 | 3.6191 | 3.0922 | 2.6958 | 2.3865 | 2.1381 | 1.9341 | 1.7634 | 1.6183 | 1.4935 | 1.3848 | 1.2893 | 1.2047 | 1.1291 | 1.061 | 1.00000 | 0.40825 | 0.21822 | 0.13363 | 0.089443 | 0.063758 | 0.047619 | 0.036860 | 0.029348 | 0.023905 | 0.00609 | 0.00390 | 0.00271 | 0.00200 | 0.00153 | 0.00121 | 0.000979 | 0.000809 | 0.000680 | 0.000579 | 0.000500 |
\(\dfrac{P_0} (click for details) \) Callstack:
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19.3005 | 14.4815 | 11.5914 | 9.6659 | 8.2915 | 7.2616 | 6.4613 | 5.8218 | 2.9635 | 2.4027 | 2.0351 | 1.7780 | 1.5901 | 1.4487 | 1.3398 | 1.2549 | 1.1882 | 1.1356 | 1.0944 | 1.0624 | 1.0382 | 1.0207 | 1.0089 | 1.002 | 1.000 | 1.688 | 4.235 | 10.72 | 25.00 | 53.18 | 1.0E+2 | 1.9E+2 | 3.3E+2 | 5.4E+2 | 1.5E+4 | 4.6E+4 | 1.1E+5 | 2.5E+5 | 4.8E+5 | 8.6E+5 | 1.5E+6 | 2.3E+6 | 3.6E+6 | 5.4E+6 | 7.8E+6 |
\(\dfrac{\rho} (click for details) \) Callstack:
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30.4318 | 22.8254 | 18.2620 | 15.2200 | 13.0474 | 11.4182 | 10.1512 | 9.1378 | 4.5826 | 3.6742 | 3.0702 | 2.6400 | 2.3184 | 2.0693 | 1.8708 | 1.7092 | 1.5753 | 1.4626 | 1.3665 | 1.2838 | 1.2119 | 1.1489 | 1.0934 | 1.044 | 1.000 | 0.61237 | 0.50918 | 0.46771 | 0.44721 | 0.43568 | 0.42857 | 0.42390 | 0.42066 | 0.41833 | 0.41079 | 0.40988 | 0.40938 | 0.40908 | 0.40889 | 0.40875 | 0.40866 | 0.40859 | 0.40853 | 0.40849 | 0.40846 |
\(\dfrac{U} (click for details) \) Callstack:
at (Bookshelves/Civil_Engineering/Book:_Fluid_Mechanics_(Bar-Meir)/11:_Compressible_Flow_One_Dimensional/11.8:_The_Table_for_Fanno_Flow), /content/body/table/tbody/tr[6]/td[1]/span, line 1, column 2
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0.03286 | 0.04381 | 0.05476 | 0.06570 | 0.07664 | 0.08758 | 0.09851 | 0.10944 | 0.21822 | 0.27217 | 0.32572 | 0.37879 | 0.43133 | 0.48326 | 0.53452 | 0.58506 | 0.63481 | 0.68374 | 0.73179 | 0.77894 | 0.82514 | 0.87037 | 0.91460 | 0.95781 | 1.00 | 1.633 | 1.964 | 2.138 | 2.236 | 2.295 | 2.333 | 2.359 | 2.377 | 2.390 | 2.434 | 2.440 | 2.443 | 2.445 | 2.446 | 2.446 | 2.447 | 2.447 | 2.448 | 2.448 | 2.448 |
\(\dfrac{T} (click for details) \) Callstack:
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1.1998 | 1.1996 | 1.1994 | 1.1991 | 1.1988 | 1.1985 | 1.1981 | 1.1976 | 1.1905 | 1.1852 | 1.1788 | 1.1713 | 1.1628 | 1.1533 | 1.1429 | 1.1315 | 1.1194 | 1.1065 | 1.0929 | 1.0787 | 1.0638 | 1.0485 | 1.0327 | 1.017 | 1.000 | 0.66667 | 0.42857 | 0.28571 | 0.20000 | 0.14634 | 0.11111 | 0.086957 | 0.069767 | 0.057143 | 0.014815 | 0.00952 | 0.00663 | 0.00488 | 0.00374 | 0.00296 | 0.00240 | 0.00198 | 0.00166 | 0.00142 | 0.00122 |
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.