Commit b736a93d authored by Olivier's avatar Olivier

Compilation 2019-04-13

parent a2dd1a26
No preview for this file type
No preview for this file type
No preview for this file type
No preview for this file type
No preview for this file type
No preview for this file type
No preview for this file type
No preview for this file type
No preview for this file type
No preview for this file type
No preview for this file type
No preview for this file type
No preview for this file type
No preview for this file type
No preview for this file type
No preview for this file type
No preview for this file type
No preview for this file type
No preview for this file type
No preview for this file type
No preview for this file type
No preview for this file type
[0] Config.pm:302> INFO - This is Biber 2.9 [0] Config.pm:302> INFO - This is Biber 2.9
[0] Config.pm:305> INFO - Logfile is 'fluidmech.blg' [1] Config.pm:305> INFO - Logfile is 'fluidmech.blg'
[51] biber:313> INFO - === Thu Apr 11, 2019, 22:10:17 [63] biber:313> INFO - === Sat Apr 13, 2019, 18:15:38
[86] Biber.pm:371> INFO - Reading 'fluidmech.bcf' [96] Biber.pm:371> INFO - Reading 'fluidmech.bcf'
[205] Biber.pm:857> INFO - Found 19 citekeys in bib section 0 [203] Biber.pm:857> INFO - Found 19 citekeys in bib section 0
[231] Biber.pm:3981> INFO - Processing section 0 [229] Biber.pm:3981> INFO - Processing section 0
[251] Biber.pm:4154> INFO - Looking for bibtex format file '/home/olivier/.fluidmechbib.bib' for section 0 [246] Biber.pm:4154> INFO - Looking for bibtex format file '/home/olivier/.fluidmechbib.bib' for section 0
[254] bibtex.pm:1468> INFO - LaTeX decoding ... [249] bibtex.pm:1468> INFO - LaTeX decoding ...
[316] bibtex.pm:1294> INFO - Found BibTeX data source '/home/olivier/.fluidmechbib.bib' [305] bibtex.pm:1294> INFO - Found BibTeX data source '/home/olivier/.fluidmechbib.bib'
[548] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'normalization = NFD' with 'normalization = prenormalized' [525] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'variable = shifted' with 'variable = non-ignorable'
[548] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'variable = shifted' with 'variable = non-ignorable' [526] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'normalization = NFD' with 'normalization = prenormalized'
[548] Biber.pm:3809> INFO - Sorting list 'ynt/global//global/global' of type 'entry' with template 'ynt' and locale 'en-US' [526] Biber.pm:3809> INFO - Sorting list 'ynt/global//global/global' of type 'entry' with template 'ynt' and locale 'en-US'
[548] Biber.pm:3815> INFO - No sort tailoring available for locale 'en-US' [526] Biber.pm:3815> INFO - No sort tailoring available for locale 'en-US'
[582] bbl.pm:617> INFO - Writing 'fluidmech.bbl' with encoding 'UTF-8' [560] bbl.pm:617> INFO - Writing 'fluidmech.bbl' with encoding 'UTF-8'
[592] bbl.pm:720> INFO - Output to fluidmech.bbl [574] bbl.pm:720> INFO - Output to fluidmech.bbl
This is pdfTeX, Version 3.14159265-2.6-1.40.18 (TeX Live 2017/Debian) (preloaded format=pdflatex 2018.10.12) 11 APR 2019 22:12 This is pdfTeX, Version 3.14159265-2.6-1.40.18 (TeX Live 2017/Debian) (preloaded format=pdflatex 2018.10.12) 13 APR 2019 18:18
entering extended mode entering extended mode
restricted \write18 enabled. restricted \write18 enabled.
file:line:error style messages enabled. file:line:error style messages enabled.
...@@ -2808,12 +2808,12 @@ Package: niceframe v1.1c <2009/31/08> (Marcus Ohlhaut) ...@@ -2808,12 +2808,12 @@ Package: niceframe v1.1c <2009/31/08> (Marcus Ohlhaut)
\swruledelta=\dimen361 \swruledelta=\dimen361
\swrulepiece=\dimen362 \swrulepiece=\dimen362
) )
Package hyperref Info: Option `colorlinks' set `true' on input line 291. Package hyperref Info: Option `colorlinks' set `true' on input line 292.
Package biblatex Info: Redefining '\fullcite' on input line 296. Package biblatex Info: Redefining '\fullcite' on input line 297.
................................................. .................................................
. LaTeX info: "xparse/define-command" . LaTeX info: "xparse/define-command"
. .
. Defining command \vocab with sig. 'om' on line 349. . Defining command \vocab with sig. 'om' on line 350.
................................................. .................................................
) )
(/home/olivier/computing/latex/sty/nonpublic/nonpublicsty.sty) (/home/olivier/computing/latex/sty/nonpublic/nonpublicsty.sty)
...@@ -2950,17 +2950,17 @@ Package: changepage 2009/10/20 v1.0c check page and change page layout ...@@ -2950,17 +2950,17 @@ Package: changepage 2009/10/20 v1.0c check page and change page layout
) )
Package hyperref Warning: Option `pdftex' has already been used, Package hyperref Warning: Option `pdftex' has already been used,
(hyperref) setting the option has no effect on input line 285. (hyperref) setting the option has no effect on input line 298.
Package hyperref Info: Option `pdfnewwindow' set `false' on input line 285. Package hyperref Info: Option `pdfnewwindow' set `false' on input line 298.
Package hyperref Info: Option `colorlinks' set `true' on input line 285. Package hyperref Info: Option `colorlinks' set `true' on input line 298.
Package hyperref Warning: Option `bookmarks' has already been used, Package hyperref Warning: Option `bookmarks' has already been used,
(hyperref) setting the option has no effect on input line 285. (hyperref) setting the option has no effect on input line 298.
Package hyperref Info: Option `unicode' set `false' on input line 285. Package hyperref Info: Option `unicode' set `false' on input line 298.
Package hyperref Info: Option `pdftoolbar' set `true' on input line 285. Package hyperref Info: Option `pdftoolbar' set `true' on input line 298.
Package hyperref Info: Option `pdfmenubar' set `true' on input line 285. Package hyperref Info: Option `pdfmenubar' set `true' on input line 298.
) (/usr/share/texlive/texmf-dist/tex/latex/oberdiek/hypcap.sty ) (/usr/share/texlive/texmf-dist/tex/latex/oberdiek/hypcap.sty
Package: hypcap 2016/05/16 v1.12 Adjusting the anchors of captions (HO) Package: hypcap 2016/05/16 v1.12 Adjusting the anchors of captions (HO)
) )
...@@ -3387,7 +3387,7 @@ LaTeX Font Info: Font shape `T1/fxl/m/sl' will be ...@@ -3387,7 +3387,7 @@ LaTeX Font Info: Font shape `T1/fxl/m/sl' will be
LaTeX Warning: `h' float specifier changed to `ht'. LaTeX Warning: `h' float specifier changed to `ht'.
[191 [193
...@@ -3431,7 +3431,7 @@ File: images/hangar.png Graphic file (type png) ...@@ -3431,7 +3431,7 @@ File: images/hangar.png Graphic file (type png)
<use images/hangar.png> <use images/hangar.png>
Package pdftex.def Info: images/hangar.png used on input line 77. Package pdftex.def Info: images/hangar.png used on input line 77.
(pdftex.def) Requested size: 426.79135pt x 108.84332pt. (pdftex.def) Requested size: 426.79135pt x 108.84332pt.
[192 <./11/images/water_drops.png>] [194 <./11/images/water_drops.png>]
Overfull \hbox (6.88841pt too wide) in paragraph at lines 91--94 Overfull \hbox (6.88841pt too wide) in paragraph at lines 91--94
\T1/fxl/m/n/12 (-20) (a cou-ple of hints to help with the al-ge-bra: $[] [] \LS \T1/fxl/m/n/12 (-20) (a cou-ple of hints to help with the al-ge-bra: $[] [] \LS
1/libertinust1math/m/it/12 x \LS1/libertinust1math/m/n/12 d\LS1/libertinust1mat 1/libertinust1math/m/it/12 x \LS1/libertinust1math/m/n/12 d\LS1/libertinust1mat
...@@ -3459,7 +3459,7 @@ LaTeX Font Info: Font shape `T1/fxl/m/sl' will be ...@@ -3459,7 +3459,7 @@ LaTeX Font Info: Font shape `T1/fxl/m/sl' will be
(Font) scaled to size 10.95pt on input line 116. (Font) scaled to size 10.95pt on input line 116.
LaTeX Font Info: Font shape `TS1/fxl/m/sl' will be LaTeX Font Info: Font shape `TS1/fxl/m/sl' will be
(Font) scaled to size 8.0pt on input line 116. (Font) scaled to size 8.0pt on input line 116.
[193 <./11/images/hangar.png>] [194 <./11/images/cylinder_sphere_drag_munson_1. [195 <./11/images/hangar.png>] [196 <./11/images/cylinder_sphere_drag_munson_1.
png (PNG copy)> <./11/images/cylinder_sphere_drag_munson_2.png (PNG copy)>] png (PNG copy)> <./11/images/cylinder_sphere_drag_munson_2.png (PNG copy)>]
<images/rotating_sphere_munson.png, id=101, 212.7147pt x 251.4996pt> <images/rotating_sphere_munson.png, id=101, 212.7147pt x 251.4996pt>
File: images/rotating_sphere_munson.png Graphic file (type png) File: images/rotating_sphere_munson.png Graphic file (type png)
...@@ -3468,7 +3468,7 @@ Package pdftex.def Info: images/rotating_sphere_munson.png used on input line ...@@ -3468,7 +3468,7 @@ Package pdftex.def Info: images/rotating_sphere_munson.png used on input line
135. 135.
(pdftex.def) Requested size: 298.75264pt x 353.26749pt. (pdftex.def) Requested size: 298.75264pt x 353.26749pt.
[195 <./11/images/rotating_sphere_munson.png (PNG copy)>] [197 <./11/images/rotating_sphere_munson.png (PNG copy)>]
<F5_tornado_Elie_Manitoba_2007.jpg, id=116, 1606.0pt x 1204.5pt> <F5_tornado_Elie_Manitoba_2007.jpg, id=116, 1606.0pt x 1204.5pt>
File: F5_tornado_Elie_Manitoba_2007.jpg Graphic file (type jpg) File: F5_tornado_Elie_Manitoba_2007.jpg Graphic file (type jpg)
<use F5_tornado_Elie_Manitoba_2007.jpg> <use F5_tornado_Elie_Manitoba_2007.jpg>
...@@ -3482,10 +3482,10 @@ Package pdftex.def Info: RankineVortex.png used on input line 158. ...@@ -3482,10 +3482,10 @@ Package pdftex.def Info: RankineVortex.png used on input line 158.
(pdftex.def) Requested size: 213.39568pt x 131.23917pt. (pdftex.def) Requested size: 213.39568pt x 131.23917pt.
LaTeX Font Info: Font shape `T1/fxl/m/sl' will be LaTeX Font Info: Font shape `T1/fxl/m/sl' will be
(Font) scaled to size 10.0pt on input line 169. (Font) scaled to size 10.0pt on input line 169.
[196 [198
<./0/illustrations/F5_tornado_Elie_Manitoba_2007.jpg> <./11/images/RankineVort <./0/illustrations/F5_tornado_Elie_Manitoba_2007.jpg> <./11/images/RankineVort
ex.png>] [197] ex.png>] [199]
Overfull \hbox (5.58pt too wide) detected at line 267 Overfull \hbox (5.58pt too wide) detected at line 267
[] []
...@@ -3555,7 +3555,7 @@ Underfull \hbox (badness 10000) in alignment at lines 267--267 ...@@ -3555,7 +3555,7 @@ Underfull \hbox (badness 10000) in alignment at lines 267--267
[][][] [][][]
[] []
[198] [200]
LaTeX Font Info: Font shape `T1/fxl/bx/n' in size <12> not available LaTeX Font Info: Font shape `T1/fxl/bx/n' in size <12> not available
(Font) Font shape `T1/fxl/b/n' tried instead on input line 283. (Font) Font shape `T1/fxl/b/n' tried instead on input line 283.
LaTeX Font Info: Font shape `T1/fxl/b/n' will be LaTeX Font Info: Font shape `T1/fxl/b/n' will be
...@@ -3568,9 +3568,9 @@ m/it/12 U[] \LS1/libertinust1math/m/n/12 = [] []$ \T1/fxl/m/n/12 (-20) and $\LS ...@@ -3568,9 +3568,9 @@ m/it/12 U[] \LS1/libertinust1math/m/n/12 = [] []$ \T1/fxl/m/n/12 (-20) and $\LS
/12 (-20) , with Reynolds /12 (-20) , with Reynolds
[] []
[199 [201
] [200 ] [202
...@@ -3616,10 +3616,10 @@ Package logreq Info: Writing requests to 'fluidmech.run.xml'. ...@@ -3616,10 +3616,10 @@ Package logreq Info: Writing requests to 'fluidmech.run.xml'.
) )
Here is how much of TeX's memory you used: Here is how much of TeX's memory you used:
62594 strings out of 494214 62598 strings out of 494214
1148262 string characters out of 6166503 1148312 string characters out of 6166503
1747897 words of memory out of 5000000 1748140 words of memory out of 5000000
64423 multiletter control sequences out of 15000+600000 64427 multiletter control sequences out of 15000+600000
762686 words of font info for 348 fonts, out of 8000000 for 9000 762686 words of font info for 348 fonts, out of 8000000 for 9000
500 hyphenation exceptions out of 8191 500 hyphenation exceptions out of 8191
100i,14n,108p,10420b,2113s stack positions out of 5000i,500n,10000p,200000b,80000s 100i,14n,108p,10420b,2113s stack positions out of 5000i,500n,10000p,200000b,80000s
...@@ -3688,7 +3688,7 @@ public/libertinust1math/LibertinusT1Math.pfb></usr/local/share/texmf/fonts/type ...@@ -3688,7 +3688,7 @@ public/libertinust1math/LibertinusT1Math.pfb></usr/local/share/texmf/fonts/type
ibertine-legacy/fxlr.pfb></usr/local/share/texmf/fonts/type1/public/libertine-l ibertine-legacy/fxlr.pfb></usr/local/share/texmf/fonts/type1/public/libertine-l
egacy/fxlri.pfb></usr/local/share/texmf/fonts/type1/public/libertine-legacy/fxl egacy/fxlri.pfb></usr/local/share/texmf/fonts/type1/public/libertine-legacy/fxl
ro.pfb> ro.pfb>
Output written on fluidmech.pdf (10 pages, 1689577 bytes). Output written on fluidmech.pdf (10 pages, 1689579 bytes).
PDF statistics: PDF statistics:
235 PDF objects out of 1000 (max. 8388607) 235 PDF objects out of 1000 (max. 8388607)
205 compressed objects within 3 object streams 205 compressed objects within 3 object streams
......
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {9.1}Motivation}{\reset@font\mtcSfont 141}{section.9.1}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {9.1}Motivation}{\reset@font\mtcSfont 143}{section.9.1}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {9.2}Comparing influences: the weighted momentum balance}{\reset@font\mtcSfont 141}{section.9.2}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {9.2}Comparing influences: the weighted momentum balance}{\reset@font\mtcSfont 143}{section.9.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {9.2.1}Principle}{\reset@font\mtcSSfont 141}{subsection.9.2.1}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {9.2.1}Principle}{\reset@font\mtcSSfont 143}{subsection.9.2.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {9.2.2}The non-dimensional Navier-Stokes equation}{\reset@font\mtcSSfont 142}{subsection.9.2.2}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {9.2.2}The non-dimensional Navier-Stokes equation}{\reset@font\mtcSSfont 144}{subsection.9.2.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {9.2.3}The flow parameters of Navier-Stokes}{\reset@font\mtcSSfont 144}{subsection.9.2.3}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {9.2.3}The flow parameters of Navier-Stokes}{\reset@font\mtcSSfont 146}{subsection.9.2.3}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {9.2.4}Flow parameters obtained as force ratios}{\reset@font\mtcSSfont 145}{subsection.9.2.4}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {9.2.4}Flow parameters obtained as force ratios}{\reset@font\mtcSSfont 147}{subsection.9.2.4}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {9.2.5}The Reynolds number in practice}{\reset@font\mtcSSfont 145}{subsection.9.2.5}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {9.2.5}The Reynolds number in practice}{\reset@font\mtcSSfont 147}{subsection.9.2.5}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {9.3}Making models}{\reset@font\mtcSfont 147}{section.9.3}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {9.3}Making models}{\reset@font\mtcSfont 149}{section.9.3}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {9.4}Comparing results: coefficients}{\reset@font\mtcSfont 148}{section.9.4}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {9.4}Comparing results: coefficients}{\reset@font\mtcSfont 150}{section.9.4}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {9.4.1}Principle}{\reset@font\mtcSSfont 148}{subsection.9.4.1}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {9.4.1}Principle}{\reset@font\mtcSSfont 150}{subsection.9.4.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {9.4.2}Force coefficients}{\reset@font\mtcSSfont 148}{subsection.9.4.2}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {9.4.2}Force coefficients}{\reset@font\mtcSSfont 150}{subsection.9.4.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {9.4.3}Power coefficient, and other coefficients}{\reset@font\mtcSSfont 149}{subsection.9.4.3}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {9.4.3}Power coefficient, and other coefficients}{\reset@font\mtcSSfont 151}{subsection.9.4.3}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {9.4.4}The systematic non-dimensionalization of problems}{\reset@font\mtcSSfont 150}{subsection.9.4.4}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {9.4.4}The systematic non-dimensionalization of problems}{\reset@font\mtcSSfont 152}{subsection.9.4.4}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {9.5}Problems}{\reset@font\mtcSfont 151}{section.9.5}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {9.5}Problems}{\reset@font\mtcSfont 153}{section.9.5}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {9.1}Scaling with the Reynolds number}{\reset@font\mtcSSSfont 151}{subsubsection.9.5.0.1}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {9.1}Scaling with the Reynolds number}{\reset@font\mtcSSSfont 153}{subsubsection.9.5.0.1}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {9.2}Fluid mechanics of a giant airliner}{\reset@font\mtcSSSfont 152}{subsubsection.9.5.0.2}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {9.2}Fluid mechanics of a giant airliner}{\reset@font\mtcSSSfont 154}{subsubsection.9.5.0.2}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {9.3}Scale effects on a dragonfly}{\reset@font\mtcSSSfont 153}{subsubsection.9.5.0.3}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {9.3}Scale effects on a dragonfly}{\reset@font\mtcSSSfont 155}{subsubsection.9.5.0.3}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {9.4}Formula One testing}{\reset@font\mtcSSSfont 153}{subsubsection.9.5.0.4}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {9.4}Formula One testing}{\reset@font\mtcSSSfont 155}{subsubsection.9.5.0.4}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {10.1}Motivation}{\reset@font\mtcSfont 157}{section.10.1}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {10.1}Motivation}{\reset@font\mtcSfont 159}{section.10.1}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {10.2}The concept of boundary layer}{\reset@font\mtcSfont 157}{section.10.2}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {10.2}The concept of boundary layer}{\reset@font\mtcSfont 159}{section.10.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {10.2.1}Rationale}{\reset@font\mtcSSfont 157}{subsection.10.2.1}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {10.2.1}Rationale}{\reset@font\mtcSSfont 159}{subsection.10.2.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {10.2.2}Why do we study the boundary layer?}{\reset@font\mtcSSfont 159}{subsection.10.2.2}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {10.2.2}Why do we study the boundary layer?}{\reset@font\mtcSSfont 161}{subsection.10.2.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {10.2.3}Characterization of the boundary layer}{\reset@font\mtcSSfont 159}{subsection.10.2.3}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {10.2.3}Characterization of the boundary layer}{\reset@font\mtcSSfont 161}{subsection.10.2.3}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {10.3}Laminar boundary layers}{\reset@font\mtcSfont 161}{section.10.3}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {10.3}Laminar boundary layers}{\reset@font\mtcSfont 163}{section.10.3}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {10.3.1}Governing equations}{\reset@font\mtcSSfont 161}{subsection.10.3.1}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {10.3.1}Governing equations}{\reset@font\mtcSSfont 163}{subsection.10.3.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {10.3.2}Blasius\IeC {\textquoteright } solution}{\reset@font\mtcSSfont 162}{subsection.10.3.2}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {10.3.2}Blasius\IeC {\textquoteright } solution}{\reset@font\mtcSSfont 164}{subsection.10.3.2}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {10.4}Boundary layer transition}{\reset@font\mtcSfont 163}{section.10.4}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {10.4}Boundary layer transition}{\reset@font\mtcSfont 165}{section.10.4}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {10.5}Turbulent boundary layers}{\reset@font\mtcSfont 164}{section.10.5}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {10.5}Turbulent boundary layers}{\reset@font\mtcSfont 166}{section.10.5}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {10.6}Flow separation}{\reset@font\mtcSfont 165}{section.10.6}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {10.6}Flow separation}{\reset@font\mtcSfont 167}{section.10.6}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {10.7}Problems}{\reset@font\mtcSfont 169}{section.10.7}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {10.7}Problems}{\reset@font\mtcSfont 171}{section.10.7}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {10.1}Water and air flow}{\reset@font\mtcSSSfont 169}{subsubsection.10.7.0.1}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {10.1}Water and air flow}{\reset@font\mtcSSSfont 171}{subsubsection.10.7.0.1}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {10.2}Boundary layer sketches}{\reset@font\mtcSSSfont 170}{subsubsection.10.7.0.2}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {10.2}Boundary layer sketches}{\reset@font\mtcSSSfont 172}{subsubsection.10.7.0.2}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {10.3}Shear force due to boundary layer}{\reset@font\mtcSSSfont 171}{subsubsection.10.7.0.3}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {10.3}Shear force due to boundary layer}{\reset@font\mtcSSSfont 173}{subsubsection.10.7.0.3}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {10.4}Wright Flyer I}{\reset@font\mtcSSSfont 171}{subsubsection.10.7.0.4}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {10.4}Wright Flyer I}{\reset@font\mtcSSSfont 173}{subsubsection.10.7.0.4}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {10.5}Power lost to shear on an airliner fuselage}{\reset@font\mtcSSSfont 172}{subsubsection.10.7.0.5}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {10.5}Power lost to shear on an airliner fuselage}{\reset@font\mtcSSSfont 174}{subsubsection.10.7.0.5}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {10.6}Laminar wing profile}{\reset@font\mtcSSSfont 172}{subsubsection.10.7.0.6}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {10.6}Laminar wing profile}{\reset@font\mtcSSSfont 174}{subsubsection.10.7.0.6}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {10.7}Separation mechanism}{\reset@font\mtcSSSfont 172}{subsubsection.10.7.0.7}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {10.7}Separation mechanism}{\reset@font\mtcSSSfont 174}{subsubsection.10.7.0.7}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {11.1}Motivation}{\reset@font\mtcSfont 177}{section.11.1}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {11.1}Motivation}{\reset@font\mtcSfont 179}{section.11.1}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {11.2}Flow at large scales}{\reset@font\mtcSfont 177}{section.11.2}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {11.2}Flow at large scales}{\reset@font\mtcSfont 179}{section.11.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {11.2.1}Problem statement}{\reset@font\mtcSSfont 177}{subsection.11.2.1}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {11.2.1}Problem statement}{\reset@font\mtcSSfont 179}{subsection.11.2.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {11.2.2}Investigation of inviscid flows}{\reset@font\mtcSSfont 178}{subsection.11.2.2}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {11.2.2}Investigation of inviscid flows}{\reset@font\mtcSSfont 180}{subsection.11.2.2}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {11.3}Plotting velocity with functions}{\reset@font\mtcSfont 179}{section.11.3}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {11.3}Plotting velocity with functions}{\reset@font\mtcSfont 181}{section.11.3}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {11.3.1}Kinematics that fit conservation laws}{\reset@font\mtcSSfont 179}{subsection.11.3.1}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {11.3.1}Kinematics that fit conservation laws}{\reset@font\mtcSSfont 181}{subsection.11.3.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {11.3.2}Strengths and weaknesses of potential flow}{\reset@font\mtcSSfont 180}{subsection.11.3.2}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {11.3.2}Strengths and weaknesses of potential flow}{\reset@font\mtcSSfont 182}{subsection.11.3.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {11.3.3}Superposition: the lifting cylinder}{\reset@font\mtcSSfont 181}{subsection.11.3.3}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {11.3.3}Superposition: the lifting cylinder}{\reset@font\mtcSSfont 183}{subsection.11.3.3}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {11.3.4}Circulating cylinder}{\reset@font\mtcSSfont 183}{subsection.11.3.4}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {11.3.4}Circulating cylinder}{\reset@font\mtcSSfont 185}{subsection.11.3.4}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {11.3.5}Modeling lift with circulation}{\reset@font\mtcSSfont 185}{subsection.11.3.5}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {11.3.5}Modeling lift with circulation}{\reset@font\mtcSSfont 187}{subsection.11.3.5}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {11.4}Flow at very small scales}{\reset@font\mtcSfont 188}{section.11.4}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {11.4}Flow at very small scales}{\reset@font\mtcSfont 190}{section.11.4}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {11.5}Problems}{\reset@font\mtcSfont 191}{section.11.5}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {11.5}Problems}{\reset@font\mtcSfont 193}{section.11.5}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {11.1}Volcanic ash from the Eyjafjallaj\IeC {\"o}kull}{\reset@font\mtcSSSfont 191}{subsubsection.11.5.0.1}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {11.1}Volcanic ash from the Eyjafjallaj\IeC {\"o}kull}{\reset@font\mtcSSSfont 193}{subsubsection.11.5.0.1}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {11.2}Water drop}{\reset@font\mtcSSSfont 191}{subsubsection.11.5.0.2}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {11.2}Water drop}{\reset@font\mtcSSSfont 193}{subsubsection.11.5.0.2}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {11.3}Idealized flow over a hangar roof}{\reset@font\mtcSSSfont 191}{subsubsection.11.5.0.3}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {11.3}Idealized flow over a hangar roof}{\reset@font\mtcSSSfont 193}{subsubsection.11.5.0.3}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {11.4}Cabling of the Wright Flyer}{\reset@font\mtcSSSfont 193}{subsubsection.11.5.0.4}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {11.4}Cabling of the Wright Flyer}{\reset@font\mtcSSSfont 195}{subsubsection.11.5.0.4}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {11.5}Ping pong ball}{\reset@font\mtcSSSfont 193}{subsubsection.11.5.0.5}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {11.5}Ping pong ball}{\reset@font\mtcSSSfont 195}{subsubsection.11.5.0.5}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {11.6}Flow field of a tornado}{\reset@font\mtcSSSfont 196}{subsubsection.11.5.0.6}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {11.6}Flow field of a tornado}{\reset@font\mtcSSSfont 198}{subsubsection.11.5.0.6}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {11.7}Lift on a symmetrical object}{\reset@font\mtcSSSfont 198}{subsubsection.11.5.0.7}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {11.7}Lift on a symmetrical object}{\reset@font\mtcSSSfont 200}{subsubsection.11.5.0.7}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {11.8}Air flow over a wing profile}{\reset@font\mtcSSSfont 198}{subsubsection.11.5.0.8}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {11.8}Air flow over a wing profile}{\reset@font\mtcSSSfont 200}{subsubsection.11.5.0.8}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {A1}Notation}{\reset@font\mtcSfont 202}{section.Alph0.1}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {A1}Notation}{\reset@font\mtcSfont 204}{section.Alph0.1}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {A2}Field operators}{\reset@font\mtcSfont 203}{section.Alph0.2}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {A2}Field operators}{\reset@font\mtcSfont 205}{section.Alph0.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {A2.1}Gradient}{\reset@font\mtcSSfont 203}{subsection.Alph0.2.1}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {A2.1}Gradient}{\reset@font\mtcSSfont 205}{subsection.Alph0.2.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {A2.2}Divergent}{\reset@font\mtcSSfont 203}{subsection.Alph0.2.2}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {A2.2}Divergent}{\reset@font\mtcSSfont 205}{subsection.Alph0.2.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {A2.3}Laplacian}{\reset@font\mtcSSfont 204}{subsection.Alph0.2.3}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {A2.3}Laplacian}{\reset@font\mtcSSfont 206}{subsection.Alph0.2.3}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {A2.4}Curl}{\reset@font\mtcSSfont 204}{subsection.Alph0.2.4}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {A2.4}Curl}{\reset@font\mtcSSfont 206}{subsection.Alph0.2.4}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {A3}Derivations of the Bernoulli equation}{\reset@font\mtcSfont 205}{section.Alph0.3}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {A3}Derivations of the Bernoulli equation}{\reset@font\mtcSfont 207}{section.Alph0.3}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {A3.1}The Bernoulli equation from the energy equation}{\reset@font\mtcSSfont 205}{subsection.Alph0.3.1}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {A3.1}The Bernoulli equation from the energy equation}{\reset@font\mtcSSfont 207}{subsection.Alph0.3.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {A3.2}The Bernoulli equation from the integral momentum equation}{\reset@font\mtcSSfont 205}{subsection.Alph0.3.2}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {A3.2}The Bernoulli equation from the integral momentum equation}{\reset@font\mtcSSfont 207}{subsection.Alph0.3.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {A3.3}The Bernoulli equation from the Navier-Stokes equation}{\reset@font\mtcSSfont 205}{subsection.Alph0.3.3}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {A3.3}The Bernoulli equation from the Navier-Stokes equation}{\reset@font\mtcSSfont 207}{subsection.Alph0.3.3}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {A4}Flow parameters as force ratios}{\reset@font\mtcSfont 208}{section.Alph0.4}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {A4}Flow parameters as force ratios}{\reset@font\mtcSfont 210}{section.Alph0.4}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {A4.1}Acceleration vs. viscous forces: the Reynolds number}{\reset@font\mtcSSfont 208}{subsection.Alph0.4.1}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {A4.1}Acceleration vs. viscous forces: the Reynolds number}{\reset@font\mtcSSfont 210}{subsection.Alph0.4.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {A4.2}Acceleration vs. gravity force: the Froude number}{\reset@font\mtcSSfont 209}{subsection.Alph0.4.2}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {A4.2}Acceleration vs. gravity force: the Froude number}{\reset@font\mtcSSfont 211}{subsection.Alph0.4.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {A4.3}Acceleration vs. elastic forces: the Mach number}{\reset@font\mtcSSfont 209}{subsection.Alph0.4.3}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {A4.3}Acceleration vs. elastic forces: the Mach number}{\reset@font\mtcSSfont 211}{subsection.Alph0.4.3}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {A4.4}Other force ratios}{\reset@font\mtcSSfont 210}{subsection.Alph0.4.4}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {A4.4}Other force ratios}{\reset@font\mtcSSfont 212}{subsection.Alph0.4.4}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {A5}List of references}{\reset@font\mtcSfont 211}{section.Alph0.5}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {A5}List of references}{\reset@font\mtcSfont 213}{section.Alph0.5}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {3.1}Motivation}{\reset@font\mtcSfont 45}{section.3.1}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {3.1}Motivation}{\reset@font\mtcSfont 47}{section.3.1}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {3.2}The Reynolds transport theorem}{\reset@font\mtcSfont 45}{section.3.2}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {3.2}The Reynolds transport theorem}{\reset@font\mtcSfont 47}{section.3.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {3.2.1}Control volume}{\reset@font\mtcSSfont 45}{subsection.3.2.1}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {3.2.1}Control volume}{\reset@font\mtcSSfont 47}{subsection.3.2.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {3.2.2}Rate of change of an additive property}{\reset@font\mtcSSfont 46}{subsection.3.2.2}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {3.2.2}Rate of change of an additive property}{\reset@font\mtcSSfont 48}{subsection.3.2.2}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {3.3}Balance of mass}{\reset@font\mtcSfont 48}{section.3.3}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {3.3}Balance of mass}{\reset@font\mtcSfont 51}{section.3.3}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {3.4}Balance of momentum}{\reset@font\mtcSfont 49}{section.3.4}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {3.4}Balance of momentum}{\reset@font\mtcSfont 52}{section.3.4}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {3.5}Balance of angular momentum}{\reset@font\mtcSfont 51}{section.3.5}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {3.5}Balance of angular momentum}{\reset@font\mtcSfont 54}{section.3.5}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {3.6}Balance of energy}{\reset@font\mtcSfont 52}{section.3.6}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {3.6}Balance of energy}{\reset@font\mtcSfont 55}{section.3.6}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {3.7}Limits of integral analysis}{\reset@font\mtcSfont 52}{section.3.7}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {3.7}Limits of integral analysis}{\reset@font\mtcSfont 55}{section.3.7}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {3.8}Problems}{\reset@font\mtcSfont 55}{section.3.8}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {3.8}Problems}{\reset@font\mtcSfont 57}{section.3.8}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {3.1}Pipe bend}{\reset@font\mtcSSSfont 56}{subsubsection.3.8.0.1}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {3.1}Pipe bend}{\reset@font\mtcSSSfont 58}{subsubsection.3.8.0.1}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {3.2}Exhaust gas deflector}{\reset@font\mtcSSSfont 56}{subsubsection.3.8.0.2}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {3.2}Exhaust gas deflector}{\reset@font\mtcSSSfont 58}{subsubsection.3.8.0.2}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {3.3}Pelton water turbine}{\reset@font\mtcSSSfont 57}{subsubsection.3.8.0.3}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {3.3}Pelton water turbine}{\reset@font\mtcSSSfont 59}{subsubsection.3.8.0.3}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {3.4}Snow plow}{\reset@font\mtcSSSfont 58}{subsubsection.3.8.0.4}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {3.4}Snow plow}{\reset@font\mtcSSSfont 60}{subsubsection.3.8.0.4}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {3.5}Drag on a cylindrical profile}{\reset@font\mtcSSSfont 58}{subsubsection.3.8.0.5}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {3.5}Drag on a cylindrical profile}{\reset@font\mtcSSSfont 60}{subsubsection.3.8.0.5}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {3.6}Drag on a flat plate}{\reset@font\mtcSSSfont 59}{subsubsection.3.8.0.6}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {3.6}Drag on a flat plate}{\reset@font\mtcSSSfont 61}{subsubsection.3.8.0.6}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {3.7}Drag measurements in a wind tunnel}{\reset@font\mtcSSSfont 60}{subsubsection.3.8.0.7}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {3.7}Drag measurements in a wind tunnel}{\reset@font\mtcSSSfont 62}{subsubsection.3.8.0.7}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {3.8}Moment on gas deflector}{\reset@font\mtcSSSfont 61}{subsubsection.3.8.0.8}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {3.8}Moment on gas deflector}{\reset@font\mtcSSSfont 63}{subsubsection.3.8.0.8}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {3.9}Helicopter tail moment}{\reset@font\mtcSSSfont 62}{subsubsection.3.8.0.9}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {3.9}Helicopter tail moment}{\reset@font\mtcSSSfont 64}{subsubsection.3.8.0.9}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {3.10}Pressure losses in a pipe flow}{\reset@font\mtcSSSfont 63}{subsubsection.3.8.0.10}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {3.10}Pressure losses in a pipe flow}{\reset@font\mtcSSSfont 65}{subsubsection.3.8.0.10}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {3.11}Thrust reverser}{\reset@font\mtcSSSfont 63}{subsubsection.3.8.0.11}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {3.11}Thrust reverser}{\reset@font\mtcSSSfont 65}{subsubsection.3.8.0.11}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {4.1}Motivation}{\reset@font\mtcSfont 67}{section.4.1}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {4.1}Motivation}{\reset@font\mtcSfont 69}{section.4.1}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {4.2}Pressure forces on walls}{\reset@font\mtcSfont 67}{section.4.2}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {4.2}Pressure forces on walls}{\reset@font\mtcSfont 69}{section.4.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.2.1}Magnitude of the pressure force}{\reset@font\mtcSSfont 67}{subsection.4.2.1}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.2.1}Magnitude of the pressure force}{\reset@font\mtcSSfont 69}{subsection.4.2.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.2.2}Position of the pressure force}{\reset@font\mtcSSfont 68}{subsection.4.2.2}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.2.2}Position of the pressure force}{\reset@font\mtcSSfont 70}{subsection.4.2.2}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {4.3}Pressure fields in fluids}{\reset@font\mtcSfont 69}{section.4.3}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {4.3}Pressure fields in fluids}{\reset@font\mtcSfont 71}{section.4.3}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.3.1}The direction of pressure}{\reset@font\mtcSSfont 69}{subsection.4.3.1}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.3.1}The direction of pressure}{\reset@font\mtcSSfont 71}{subsection.4.3.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.3.2}Pressure on an infinitesimal volume}{\reset@font\mtcSSfont 70}{subsection.4.3.2}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.3.2}Pressure on an infinitesimal volume}{\reset@font\mtcSSfont 72}{subsection.4.3.2}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {4.4}Special case: pressure in static fluids}{\reset@font\mtcSfont 71}{section.4.4}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {4.4}Special case: pressure in static fluids}{\reset@font\mtcSfont 73}{section.4.4}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.4.1}Forces in static fluids}{\reset@font\mtcSSfont 71}{subsection.4.4.1}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.4.1}Forces in static fluids}{\reset@font\mtcSSfont 73}{subsection.4.4.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.4.2}Pressure and depth}{\reset@font\mtcSSfont 72}{subsection.4.4.2}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.4.2}Pressure and depth}{\reset@font\mtcSSfont 74}{subsection.4.4.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.4.3}Buoyancy}{\reset@font\mtcSSfont 74}{subsection.4.4.3}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.4.3}Buoyancy}{\reset@font\mtcSSfont 76}{subsection.4.4.3}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {4.5}Problems}{\reset@font\mtcSfont 77}{section.4.5}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {4.5}Problems}{\reset@font\mtcSfont 79}{section.4.5}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {4.1}Pressure in a static fluid}{\reset@font\mtcSSSfont 77}{subsubsection.4.5.0.1}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {4.1}Pressure in a static fluid}{\reset@font\mtcSSSfont 79}{subsubsection.4.5.0.1}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {4.2}Pressure measurement}{\reset@font\mtcSSSfont 77}{subsubsection.4.5.0.2}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {4.2}Pressure measurement}{\reset@font\mtcSSSfont 79}{subsubsection.4.5.0.2}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {4.3}Straight water tank door}{\reset@font\mtcSSSfont 78}{subsubsection.4.5.0.3}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {4.3}Straight water tank door}{\reset@font\mtcSSSfont 80}{subsubsection.4.5.0.3}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {4.4}Water canal access door}{\reset@font\mtcSSSfont 78}{subsubsection.4.5.0.4}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {4.4}Water canal access door}{\reset@font\mtcSSSfont 80}{subsubsection.4.5.0.4}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {4.5}Pressure force on a cylinder}{\reset@font\mtcSSSfont 79}{subsubsection.4.5.0.5}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {4.5}Pressure force on a cylinder}{\reset@font\mtcSSSfont 81}{subsubsection.4.5.0.5}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {4.6}Buoyancy of a barge}{\reset@font\mtcSSSfont 79}{subsubsection.4.5.0.6}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {4.6}Buoyancy of a barge}{\reset@font\mtcSSSfont 81}{subsubsection.4.5.0.6}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {4.7}Atmospheric pressure distribution}{\reset@font\mtcSSSfont 80}{subsubsection.4.5.0.7}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {4.7}Atmospheric pressure distribution}{\reset@font\mtcSSSfont 82}{subsubsection.4.5.0.7}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {5.1}Motivation}{\reset@font\mtcSfont 83}{section.5.1}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {5.1}Motivation}{\reset@font\mtcSfont 85}{section.5.1}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {5.2}Shear forces on walls}{\reset@font\mtcSfont 83}{section.5.2}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {5.2}Shear forces on walls}{\reset@font\mtcSfont 85}{section.5.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {5.2.1}Magnitude of the shear force}{\reset@font\mtcSSfont 83}{subsection.5.2.1}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {5.2.1}Magnitude of the shear force}{\reset@font\mtcSSfont 85}{subsection.5.2.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {5.2.2}Direction and position of the shear force}{\reset@font\mtcSSfont 84}{subsection.5.2.2}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {5.2.2}Direction and position of the shear force}{\reset@font\mtcSSfont 86}{subsection.5.2.2}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {5.3}Shear fields in fluids}{\reset@font\mtcSfont 84}{section.5.3}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {5.3}Shear fields in fluids}{\reset@font\mtcSfont 86}{section.5.3}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {5.3.1}The direction of shear}{\reset@font\mtcSSfont 84}{subsection.5.3.1}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {5.3.1}The direction of shear}{\reset@font\mtcSSfont 86}{subsection.5.3.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {5.3.2}Shear on an infinitesimal volume}{\reset@font\mtcSSfont 85}{subsection.5.3.2}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {5.3.2}Shear on an infinitesimal volume}{\reset@font\mtcSSfont 87}{subsection.5.3.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {5.3.3}The no-slip condition}{\reset@font\mtcSSfont 87}{subsection.5.3.3}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {5.3.3}The no-slip condition}{\reset@font\mtcSSfont 89}{subsection.5.3.3}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {5.3.4}Viscosity}{\reset@font\mtcSSfont 88}{subsection.5.3.4}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {5.3.4}Viscosity}{\reset@font\mtcSSfont 90}{subsection.5.3.4}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {5.3.5}Newtonian Fluid}{\reset@font\mtcSSfont 89}{subsection.5.3.5}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {5.3.5}Newtonian Fluid}{\reset@font\mtcSSfont 91}{subsection.5.3.5}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {5.4}Special case: shear in simple laminar flows}{\reset@font\mtcSfont 90}{section.5.4}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {5.4}Special case: shear in simple laminar flows}{\reset@font\mtcSfont 92}{section.5.4}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {5.5}Problems}{\reset@font\mtcSfont 91}{section.5.5}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {5.5}Problems}{\reset@font\mtcSfont 93}{section.5.5}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {5.1}Flow in between two plates}{\reset@font\mtcSSSfont 91}{subsubsection.5.5.0.1}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {5.1}Flow in between two plates}{\reset@font\mtcSSSfont 93}{subsubsection.5.5.0.1}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {5.2}Friction on a plate}{\reset@font\mtcSSSfont 92}{subsubsection.5.5.0.2}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {5.2}Friction on a plate}{\reset@font\mtcSSSfont 94}{subsubsection.5.5.0.2}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {5.3}Viscometer}{\reset@font\mtcSSSfont 92}{subsubsection.5.5.0.3}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {5.3}Viscometer}{\reset@font\mtcSSSfont 94}{subsubsection.5.5.0.3}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {5.4}Boundary layer}{\reset@font\mtcSSSfont 92}{subsubsection.5.5.0.4}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {5.4}Boundary layer}{\reset@font\mtcSSSfont 94}{subsubsection.5.5.0.4}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {5.5}Clutch}{\reset@font\mtcSSSfont 94}{subsubsection.5.5.0.5}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {5.5}Clutch}{\reset@font\mtcSSSfont 96}{subsubsection.5.5.0.5}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {6.1}Motivation}{\reset@font\mtcSfont 97}{section.6.1}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {6.1}Motivation}{\reset@font\mtcSfont 99}{section.6.1}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {6.2}Organizing calculations}{\reset@font\mtcSfont 97}{section.6.2}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {6.2}Organizing calculations}{\reset@font\mtcSfont 99}{section.6.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {6.2.1}Problem description}{\reset@font\mtcSSfont 97}{subsection.6.2.1}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {6.2.1}Problem description}{\reset@font\mtcSSfont 99}{subsection.6.2.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {6.2.2}The total time derivative}{\reset@font\mtcSSfont 98}{subsection.6.2.2}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {6.2.2}The total time derivative}{\reset@font\mtcSSfont 100}{subsection.6.2.2}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {6.3}Equations for all flows}{\reset@font\mtcSfont 101}{section.6.3}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {6.3}Equations for all flows}{\reset@font\mtcSfont 103}{section.6.3}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {6.3.1}Balance of mass}{\reset@font\mtcSSfont 101}{subsection.6.3.1}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {6.3.1}Balance of mass}{\reset@font\mtcSSfont 103}{subsection.6.3.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {6.3.2}Balance of linear momentum}{\reset@font\mtcSSfont 103}{subsection.6.3.2}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {6.3.2}Balance of linear momentum}{\reset@font\mtcSSfont 105}{subsection.6.3.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {6.3.3}Balance of energy}{\reset@font\mtcSSfont 105}{subsection.6.3.3}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {6.3.3}Balance of energy}{\reset@font\mtcSSfont 107}{subsection.6.3.3}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {6.3.4}Other terms and equations}{\reset@font\mtcSSfont 106}{subsection.6.3.4}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {6.3.4}Other terms and equations}{\reset@font\mtcSSfont 108}{subsection.6.3.4}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {6.3.5}Interlude: where does this leave us?}{\reset@font\mtcSSfont 107}{subsection.6.3.5}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {6.3.5}Interlude: where does this leave us?}{\reset@font\mtcSSfont 109}{subsection.6.3.5}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {6.4}Equations for incompressible flow}{\reset@font\mtcSfont 107}{section.6.4}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {6.4}Equations for incompressible flow}{\reset@font\mtcSfont 109}{section.6.4}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {6.4.1}Balance of mass}{\reset@font\mtcSSfont 107}{subsection.6.4.1}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {6.4.1}Balance of mass}{\reset@font\mtcSSfont 109}{subsection.6.4.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {6.4.2}Balance of linear momentum}{\reset@font\mtcSSfont 108}{subsection.6.4.2}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {6.4.2}Balance of linear momentum}{\reset@font\mtcSSfont 110}{subsection.6.4.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {6.4.3}The Bernoulli equation (again)}{\reset@font\mtcSSfont 110}{subsection.6.4.3}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {6.4.3}The Bernoulli equation (again)}{\reset@font\mtcSSfont 112}{subsection.6.4.3}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {6.5}CFD: the Navier-Stokes equations in practice}{\reset@font\mtcSfont 110}{section.6.5}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {6.5}CFD: the Navier-Stokes equations in practice}{\reset@font\mtcSfont 112}{section.6.5}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {6.6}Problems}{\reset@font\mtcSfont 113}{section.6.6}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {6.6}Problems}{\reset@font\mtcSfont 115}{section.6.6}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {6.1}Revision questions}{\reset@font\mtcSSSfont 113}{subsubsection.6.6.0.1}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {6.1}Revision questions}{\reset@font\mtcSSSfont 115}{subsubsection.6.6.0.1}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {6.2}Acceleration field}{\reset@font\mtcSSSfont 113}{subsubsection.6.6.0.2}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {6.2}Acceleration field}{\reset@font\mtcSSSfont 115}{subsubsection.6.6.0.2}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {6.3}Volumetric dilatation rate}{\reset@font\mtcSSSfont 114}{subsubsection.6.6.0.3}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {6.3}Volumetric dilatation rate}{\reset@font\mtcSSSfont 116}{subsubsection.6.6.0.3}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {6.4}Incompressibility}{\reset@font\mtcSSSfont 114}{subsubsection.6.6.0.4}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {6.4}Incompressibility}{\reset@font\mtcSSSfont 116}{subsubsection.6.6.0.4}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {6.5}Missing components}{\reset@font\mtcSSSfont 114}{subsubsection.6.6.0.5}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {6.5}Missing components}{\reset@font\mtcSSSfont 116}{subsubsection.6.6.0.5}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {6.6}Another acceleration field}{\reset@font\mtcSSSfont 114}{subsubsection.6.6.0.6}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {6.6}Another acceleration field}{\reset@font\mtcSSSfont 116}{subsubsection.6.6.0.6}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {6.7}Vortex}{\reset@font\mtcSSSfont 114}{subsubsection.6.6.0.7}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {6.7}Vortex}{\reset@font\mtcSSSfont 116}{subsubsection.6.6.0.7}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {6.8}Pressure fields}{\reset@font\mtcSSSfont 115}{subsubsection.6.6.0.8}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {6.8}Pressure fields}{\reset@font\mtcSSSfont 117}{subsubsection.6.6.0.8}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {7.1}Motivation}{\reset@font\mtcSfont 117}{section.7.1}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {7.1}Motivation}{\reset@font\mtcSfont 119}{section.7.1}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {7.2}Friction-less flow in pipes}{\reset@font\mtcSfont 117}{section.7.2}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {7.2}Friction-less flow in pipes}{\reset@font\mtcSfont 119}{section.7.2}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {7.3}Quantifying losses in pipes}{\reset@font\mtcSfont 118}{section.7.3}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {7.3}Quantifying losses in pipes}{\reset@font\mtcSfont 120}{section.7.3}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {7.4}Laminar flow in pipes}{\reset@font\mtcSfont 119}{section.7.4}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {7.4}Laminar flow in pipes}{\reset@font\mtcSfont 121}{section.7.4}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {7.4.1}Laminar flow between plates}{\reset@font\mtcSSfont 119}{subsection.7.4.1}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {7.4.1}Laminar flow between plates}{\reset@font\mtcSSfont 121}{subsection.7.4.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {7.4.2}Laminar flow in pipes}{\reset@font\mtcSSfont 121}{subsection.7.4.2}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {7.4.2}Laminar flow in pipes}{\reset@font\mtcSSfont 123}{subsection.7.4.2}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {7.5}Turbulent flow in pipes}{\reset@font\mtcSfont 124}{section.7.5}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {7.5}Turbulent flow in pipes}{\reset@font\mtcSfont 126}{section.7.5}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {7.5.1}When is a pipe flow turbulent?}{\reset@font\mtcSSfont 124}{subsection.7.5.1}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {7.5.1}When is a pipe flow turbulent?}{\reset@font\mtcSSfont 126}{subsection.7.5.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {7.5.2}Characteristics of turbulent flow}{\reset@font\mtcSSfont 125}{subsection.7.5.2}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {7.5.2}Characteristics of turbulent flow}{\reset@font\mtcSSfont 127}{subsection.7.5.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {7.5.3}Velocity profile in turbulent pipe flow}{\reset@font\mtcSSfont 126}{subsection.7.5.3}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {7.5.3}Velocity profile in turbulent pipe flow}{\reset@font\mtcSSfont 128}{subsection.7.5.3}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {7.5.4}Pressure losses in turbulent pipe flow}{\reset@font\mtcSSfont 127}{subsection.7.5.4}} {\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {7.5.4}Pressure losses in turbulent pipe flow}{\reset@font\mtcSSfont 129}{subsection.7.5.4}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {7.6}Summary}{\reset@font\mtcSfont 128}{section.7.6}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {7.6}Summary}{\reset@font\mtcSfont 130}{section.7.6}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {7.7}Problems}{\reset@font\mtcSfont 129}{section.7.7}} {\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {7.7}Problems}{\reset@font\mtcSfont 131}{section.7.7}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {7.1}Revision questions}{\reset@font\mtcSSSfont 129}{subsubsection.7.7.0.1}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {7.1}Revision questions}{\reset@font\mtcSSSfont 131}{subsubsection.7.7.0.1}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {7.2}Air flow in a small pipe}{\reset@font\mtcSSSfont 131}{subsubsection.7.7.0.2}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {7.2}Air flow in a small pipe}{\reset@font\mtcSSSfont 133}{subsubsection.7.7.0.2}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {7.3}Water piping}{\reset@font\mtcSSSfont 131}{subsubsection.7.7.0.3}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {7.3}Water piping}{\reset@font\mtcSSSfont 133}{subsubsection.7.7.0.3}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {7.4}Design of a water piping system}{\reset@font\mtcSSSfont 132}{subsubsection.7.7.0.4}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {7.4}Design of a water piping system}{\reset@font\mtcSSSfont 134}{subsubsection.7.7.0.4}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {7.5}Major oil pipeline}{\reset@font\mtcSSSfont 133}{subsubsection.7.7.0.5}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {7.5}Major oil pipeline}{\reset@font\mtcSSSfont 135}{subsubsection.7.7.0.5}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {7.6}Pump with pipe expansion}{\reset@font\mtcSSSfont 134}{subsubsection.7.7.0.6}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {7.6}Pump with pipe expansion}{\reset@font\mtcSSSfont 136}{subsubsection.7.7.0.6}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {7.7}Kugel fountain}{\reset@font\mtcSSSfont 134}{subsubsection.7.7.0.7}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {7.7}Kugel fountain}{\reset@font\mtcSSSfont 136}{subsubsection.7.7.0.7}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {7.8}A more complex ducted flow}{\reset@font\mtcSSSfont 136}{subsubsection.7.7.0.8}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {7.8}A more complex ducted flow}{\reset@font\mtcSSSfont 138}{subsubsection.7.7.0.8}}
{\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {7.9}Politically incorrect fluid mechanics}{\reset@font\mtcSSSfont 136}{subsubsection.7.7.0.9}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {7.9}Politically incorrect fluid mechanics}{\reset@font\mtcSSSfont 138}{subsubsection.7.7.0.9}}
This diff is collapsed.
This diff is collapsed.
This diff is collapsed.
Markdown is supported
0% or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment