...

Commits (3)
 \renewcommand{\lastedityear}{2019} \renewcommand{\lasteditmonth}{03} \renewcommand{\lasteditday}{29} \renewcommand{\lasteditmonth}{04} \renewcommand{\lasteditday}{11} \renewcommand{\numberofthischapter}{2} \renewcommand{\titleofthischapter}{\namechaptertwotitle} \atstartofexercises ... ... @@ -45,7 +45,15 @@ Balance of energy in a considered volume with steady flow: \wherefrom{\cczero \oc} \label{exo_pipe_expansion} Water flows from left to right in a pipe. On the left the diameter is \SI{8}{\centi\metre}, the water comes in with a uniform velocity of \SI{1,5}{\metre\per\second}. The diameter increases gently until it reaches \SI{16}{\centi\metre}; the expansion is smooth, so that losses (specifically, energy losses due to wall friction and flow separation) are negligible. Water flows from left to right in a pipe, as shown in fig.~\ref{fig_simple_pipe_expansion}. On the left the diameter is \SI{8}{\centi\metre}, the water comes in with a uniform velocity of \SI{1,5}{\metre\per\second}. The diameter increases gently until it reaches \SI{16}{\centi\metre}; the expansion is smooth, so that losses (specifically, energy losses due to wall friction and flow separation) are negligible. \begin{figure} \begin{center} \includegraphics[width=7.5cm]{simple_pipe_expansion} \vspace{-0.5cm} \end{center} \supercaption{A simple pipe expansion, with water flowing from left to right.}{\cczero \oc} \label{fig_simple_pipe_expansion} \end{figure} \begin{enumerate} \item What are the mass and volume flows across the pipe? \item What is the average velocity of the water at the right end of the expansion? ... ... @@ -55,13 +63,13 @@ Balance of energy in a considered volume with steady flow: The volume flow of water in the pipe is now doubled. \begin{enumerate} \shift{3} \item What is the new pressure drop? \item What is the new pressure change? \end{enumerate} The water is drained from the pipe, and instead, air with density \SI{1,225}{\kilogram\per\metre\squared} is flowed in the pipe, incoming with a uniform velocity of \SI{1,5}{\metre\per\second}. The water is drained from the pipe, and instead, air with density \SI{1,225}{\kilogram\per\metre\cubed} is flowed in the pipe, incoming with a uniform velocity of \SI{1,5}{\metre\per\second}. \begin{enumerate} \shift{4} \item What is the new pressure drop? \item What is the new pressure change? \end{enumerate} %%%% ... ... @@ -69,7 +77,15 @@ Balance of energy in a considered volume with steady flow: \wherefrom{\cczero \oc} \label{exo_pipe_with_losses} Water flows in a long pipe which has constant diameter; a valve is installed in the middle of the pipe length. Water comes in the pipe with a uniform velocity of \SI{1,5}{\metre\per\second} and the pipe diameter is \SI{250}{\milli\metre}. Water flows in a long pipe which has constant diameter; a valve is installed in the middle of the pipe length (fig.~\ref{fig_simple_straight_pipe_valve}). Water comes in the pipe with a uniform velocity of \SI{1,5}{\metre\per\second} and the pipe diameter is \SI{250}{\milli\metre}. \begin{figure} \begin{center} \includegraphics[width=0.8\textwidth]{simple_straight_pipe_valve} \vspace{-0.5cm} \end{center} \supercaption{A simple, straight pipe, featuring a partially-open valve in the center}{\cczero \oc} \label{fig_simple_straight_pipe_valve} \end{figure} The pipe itself and the valve, together, induce a pressure loss which can be quantified using the dimensionless \vocab{loss coefficient} $K_\text{valve}$ (we later will later encounter it as eq.~\ref{eq_def_loss_coeff} p.\pageref{eq_def_loss_coeff}). With this tool, the pressure loss is related to the average incoming speed $V_\text{incoming}$ as: \begin{IEEEeqnarray}{rCcCl} ... ... @@ -91,7 +107,15 @@ Balance of energy in a considered volume with steady flow: \wherefrom{\cczero \oc} \label{exo_combustor} A jet engine is equipped with several \vocab{combustors} (sometimes also called \vocab{combustion chambers}). We are interested in fluid flow through one such combustor. Air from the compressor enters the combustor, is mixed with fuel, and combustion occurs, which greatly increases the temperature and specific volume of the mix, before it is run through the turbine. A jet engine is equipped with several \vocab{combustors} (sometimes also called \vocab{combustion chambers}). We are interested in fluid flow through one such combustor, shown in fig.~\ref{fig_combustor}. Air from the compressor enters the combustor, is mixed with fuel, and combustion occurs, which greatly increases the temperature and specific volume of the mix, before it is run through the turbine. \begin{figure} \begin{center} \includegraphics[width=0.8\textwidth]{Core_section_of_a_sectioned_Rolls-Royce_Turboméca_Adour_turbofan_cropped.jpg} \vspace{-0.5cm} \end{center} \supercaption{A combustor in a sectioned jet engine (here, a Turboméca Adour). Air enters from the right, out of the compressor (whose blades are painted blue). It leaves the combustor on the left side, into the turbine. In the combustor, high-temperature, steady combustion takes place.}{\wcfile{Core_section_of_a_sectioned_Rolls-Royce_Turboméca_Adour_turbofan.jpg} \ccbysa \oc} \label{fig_combustor} \end{figure} The conditions at inlet are as follows: \begin{itemize} ... ...
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 [1] Config.pm:305> INFO - Logfile is 'fluidmech.blg' [49] biber:313> INFO - === Wed Apr 10, 2019, 22:33:14 [79] Biber.pm:371> INFO - Reading 'fluidmech.bcf' [182] Biber.pm:857> INFO - Found 19 citekeys in bib section 0 [204] Biber.pm:3981> INFO - Processing section 0 [221] Biber.pm:4154> INFO - Looking for bibtex format file '/home/olivier/.fluidmechbib.bib' for section 0 [223] bibtex.pm:1468> INFO - LaTeX decoding ... [284] bibtex.pm:1294> INFO - Found BibTeX data source '/home/olivier/.fluidmechbib.bib' [516] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'normalization = NFD' with 'normalization = prenormalized' [516] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'variable = shifted' with 'variable = non-ignorable' [517] Biber.pm:3809> INFO - Sorting list 'ynt/global//global/global' of type 'entry' with template 'ynt' and locale 'en-US' [517] Biber.pm:3815> INFO - No sort tailoring available for locale 'en-US' [556] bbl.pm:617> INFO - Writing 'fluidmech.bbl' with encoding 'UTF-8' [565] bbl.pm:720> INFO - Output to fluidmech.bbl [0] Config.pm:305> INFO - Logfile is 'fluidmech.blg' [51] biber:313> INFO - === Thu Apr 11, 2019, 22:10:17 [86] Biber.pm:371> INFO - Reading 'fluidmech.bcf' [205] Biber.pm:857> INFO - Found 19 citekeys in bib section 0 [231] Biber.pm:3981> INFO - Processing section 0 [251] Biber.pm:4154> INFO - Looking for bibtex format file '/home/olivier/.fluidmechbib.bib' for section 0 [254] bibtex.pm:1468> INFO - LaTeX decoding ... [316] 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' [548] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'variable = shifted' with 'variable = non-ignorable' [548] 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' [582] bbl.pm:617> INFO - Writing 'fluidmech.bbl' with encoding 'UTF-8' [592] 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) 10 APR 2019 22:35 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 entering extended mode restricted \write18 enabled. file:line:error style messages enabled. ... ... @@ -3616,10 +3616,10 @@ Package logreq Info: Writing requests to 'fluidmech.run.xml'. ) Here is how much of TeX's memory you used: 62588 strings out of 494214 1148099 string characters out of 6166503 1747684 words of memory out of 5000000 64417 multiletter control sequences out of 15000+600000 62594 strings out of 494214 1148262 string characters out of 6166503 1747897 words of memory out of 5000000 64423 multiletter control sequences out of 15000+600000 762686 words of font info for 348 fonts, out of 8000000 for 9000 500 hyphenation exceptions out of 8191 100i,14n,108p,10420b,2113s stack positions out of 5000i,500n,10000p,200000b,80000s ... ... @@ -3632,25 +3632,25 @@ xist, replaced by a fixed one pdfTeX warning (dest): name{equation.6.4.33} has been referenced but does not e xist, replaced by a fixed one pdfTeX warning (dest): name{figure.caption.120} has been referenced but does no pdfTeX warning (dest): name{figure.caption.123} has been referenced but does no t exist, replaced by a fixed one pdfTeX warning (dest): name{figure.caption.119} has been referenced but does no pdfTeX warning (dest): name{figure.caption.122} has been referenced but does no t exist, replaced by a fixed one pdfTeX warning (dest): name{figure.caption.118} has been referenced but does no pdfTeX warning (dest): name{figure.caption.121} has been referenced but does no t exist, replaced by a fixed one pdfTeX warning (dest): name{equation.9.4.15} has been referenced but does not e xist, replaced by a fixed one pdfTeX warning (dest): name{figure.caption.117} has been referenced but does no pdfTeX warning (dest): name{figure.caption.120} has been referenced but does no t exist, replaced by a fixed one pdfTeX warning (dest): name{subsubsection.4.5.0.5} has been referenced but does not exist, replaced by a fixed one pdfTeX warning (dest): name{figure.caption.116} has been referenced but does no pdfTeX warning (dest): name{figure.caption.119} has been referenced but does no t exist, replaced by a fixed one pdfTeX warning (dest): name{equation.11.3.26} has been referenced but does not ... ... @@ -3659,7 +3659,7 @@ exist, replaced by a fixed one pdfTeX warning (dest): name{equation.11.3.25} has been referenced but does not exist, replaced by a fixed one pdfTeX warning (dest): name{figure.caption.115} has been referenced but does no pdfTeX warning (dest): name{figure.caption.118} has been referenced but does no t exist, replaced by a fixed one pdfTeX warning (dest): name{equation.11.4.40} has been referenced but does not ... ... @@ -3688,7 +3688,7 @@ public/libertinust1math/LibertinusT1Math.pfb> Output written on fluidmech.pdf (10 pages, 1689575 bytes). Output written on fluidmech.pdf (10 pages, 1689577 bytes). PDF statistics: 235 PDF objects out of 1000 (max. 8388607) 205 compressed objects within 3 object streams ... ...
 ... ... @@ -11,4 +11,4 @@ {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {2.2}Pipe flow with losses}{\reset@font\mtcSSSfont 40}{subsubsection.2.7.0.2}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {2.3}Combustor from a jet engine}{\reset@font\mtcSSSfont 40}{subsubsection.2.7.0.3}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {2.4}Water jet on a wall}{\reset@font\mtcSSSfont 41}{subsubsection.2.7.0.4}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {2.5}High-speed gas flow}{\reset@font\mtcSSSfont 41}{subsubsection.2.7.0.5}} {\reset@font\mtcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {2.5}High-speed gas flow}{\reset@font\mtcSSSfont 42}{subsubsection.2.7.0.5}}
 ... ... @@ -51,7 +51,7 @@ \contentsline {subsubsection}{\numberline {2.2}Pipe flow with losses}{40}{subsubsection.2.7.0.2} \contentsline {subsubsection}{\numberline {2.3}Combustor from a jet engine}{40}{subsubsection.2.7.0.3} \contentsline {subsubsection}{\numberline {2.4}Water jet on a wall}{41}{subsubsection.2.7.0.4} \contentsline {subsubsection}{\numberline {2.5}High-speed gas flow}{41}{subsubsection.2.7.0.5} \contentsline {subsubsection}{\numberline {2.5}High-speed gas flow}{42}{subsubsection.2.7.0.5} \contentsline {chapter}{\numberline {3}Analysis of existing flows with\nobreakspace {}three\nobreakspace {}dimensions}{45}{chapter.3} \contentsline {section}{\numberline {3.1}Motivation}{45}{section.3.1} \contentsline {section}{\numberline {3.2}The Reynolds transport theorem}{45}{section.3.2} ... ... @@ -221,7 +221,7 @@ \contentsline {subsubsection}{\numberline {11.6}Flow field of a tornado}{196}{subsubsection.11.5.0.6} \contentsline {subsubsection}{\numberline {11.7}Lift on a symmetrical object}{198}{subsubsection.11.5.0.7} \contentsline {subsubsection}{\numberline {11.8}Air flow over a wing profile}{198}{subsubsection.11.5.0.8} \contentsline {chapter}{Appendix}{201}{section*.121} \contentsline {chapter}{Appendix}{201}{section*.124} \contentsline {section}{\numberline {A1}Notation}{202}{section.Alph0.1} \contentsline {section}{\numberline {A2}Field operators}{203}{section.Alph0.2} \contentsline {subsection}{\numberline {A2.1}Gradient}{203}{subsection.Alph0.2.1} ... ...
This diff is collapsed.
This diff is collapsed.