 ...

Commits (3)
 \renewcommand{\lastedityear}{2019} \renewcommand{\lasteditmonth}{04} \renewcommand{\lasteditday}{10} \renewcommand{\lasteditmonth}{05} \renewcommand{\lasteditday}{01} \renewcommand{\numberofthischapter}{2} \renewcommand{\titleofthischapter}{\namechaptertwotitle} ... ... @@ -109,7 +109,7 @@ Looking again at an example case where there were two inlets and two outlets, this equation~\ref{eq_mass_oned} would become: \begin{IEEEeqnarray*}{rCCCCCCCC} 0 & = & \rho_\text{in 1} V_{\perp \text{ in 1}} A_\text{in 1} &+& \rho_\text{in 2} V_{\perp \text{ in 2}} A_\text{in 2} &+& \rho_\text{out 1} V_{\perp \text{ out 1}} A_\text{out 1} &+& \rho_\text{out 1} V_{\perp \text{ out 2}} A_\text{out 1}\nonumber\\ 0 & = & \rho_\text{in 1} V_{\perp \text{ in 1}} A_\text{in 1} &+& \rho_\text{in 2} V_{\perp \text{ in 2}} A_\text{in 2} &+& \rho_\text{out 1} V_{\perp \text{ out 1}} A_\text{out 1} &+& \rho_\text{out 2} V_{\perp \text{ out 2}} A_\text{out 2}\nonumber\\ 0 & = & \left(\rho V_\perp A \right)_\text{in 1} &+& \left(\rho V_\perp A \right)_\text{in 2} &+& \left(\rho V_\perp A \right)_\text{out 1} &+& \left(\rho V_\perp A \right)_\text{out 2}\nonumber\\ 0 & = & -\left(\rho |V_\perp| A \right)_\text{in 1} &-& \left(\rho |V_\perp| A \right)_\text{in 2} &+& \left(\rho |V_\perp| A \right)_\text{out 1} &+& \left(\rho |V_\perp| A \right)_\text{out 2} \end{IEEEeqnarray*} ... ... @@ -184,7 +184,7 @@ In the example case where there is one inlet and one outlet, we would write: \begin{IEEEeqnarray*}{rCCCCCCCC} \vec F_\net & = & \left(\rho V_\perp A \vec V\right)_\inn &+& \left(\rho V_\perp A \vec V \right)_\out\\ \vec F_\net & = & -\left(\rho |V_\perp| A \vec V \right)_\inn &-& \left(\rho |V_\perp| A \vec V \right)_\out \vec F_\net & = & -\left(\rho |V_\perp| A \vec V \right)_\inn &+& \left(\rho |V_\perp| A \vec V \right)_\out \end{IEEEeqnarray*} To make clear a few things, let us focus on the simple case where a considered volume is traversed by a steady flow with mass flow $\dot m$, with one inlet (point~1) and one outlet (point~2). The net force $\vec F_\net$ applying on the fluid is ... ... @@ -335,7 +335,7 @@ With these five restrictions, equation~\ref{eq_sfee} simply becomes: \begin{IEEEeqnarray*}{rCcl} 0 + 0 &=& & \left[\dot m \left(i_\cst + \frac{p}{\rho_\cst} + \frac{1}{2} V^2 + g z \right) \right]_1 \\ && +& \left[\dot m \left(i\cst + \frac{p}{\rho_\cst} + \frac{1}{2} V^2 + g z \right) \right]_2 && +& \left[\dot m \left(i_\cst + \frac{p}{\rho_\cst} + \frac{1}{2} V^2 + g z \right) \right]_2 \end{IEEEeqnarray*} Dividing by $|\dot m|$ and canceling $i_\cst$, as follows, \begin{IEEEeqnarray*}{rCl} ... ...
 \renewcommand{\lastedityear}{2019} \renewcommand{\lasteditmonth}{04} \renewcommand{\lasteditday}{25} \renewcommand{\lasteditmonth}{05} \renewcommand{\lasteditday}{01} \renewcommand{\numberofthischapter}{3} \renewcommand{\titleofthischapter}{\namechapterthreetitle} ... ... @@ -65,25 +65,28 @@ \begin{IEEEeqnarray}{rCl} \timederivative{B_\cv} = \timederivative{} \iiint_\cv \frac{B}{\vol} \diff \vol = \timederivative{} \iiint_\cv \rho b \diff \vol \label{eq_secondbit} \end{IEEEeqnarray} \begin{equationterms} \item where \tab CV \tab is the control volume, \item and \tab $\vol$ \tab\tab\tab is volume (\si{\metre\cubed}). \end{equationterms} The term $\dot B_\net$ can be evaluated by quantifying, for each area element $\diff A$ of the control volume’s surface, the surface flow rate $\rho b V_\perp$ of property $B$ that flows through it, as shown in \cref{fig_cv_da}. The integral over the entire control volume surface CS of this term is: \begin{IEEEeqnarray}{rCl} \dot B_\net = \iint_\cs \rho b V_\perp \diff A = \iint_\cs \rho b \ (\vec V_\rel \cdot \vec n) \diff A \label{eq_thirdbit} \end{IEEEeqnarray} \begin{equationterms} \item where \tab CV \tab\tab is the control volume, \item \tab CS \tab\tab\tab is the the control surface (enclosing the control volume), \item where \tab CS \tab\tab\tab is the control surface (enclosing the control volume CV), \item \tab $\vec n$ \tab\tab\tab\tab is a unit vector on each surface element $\diff A$ pointing outwards, \item \tab $\vec V_\rel$ \tab is the local velocity of fluid relative to the control surface, \item and \tab $V_\perp \equiv \vec V_\rel \cdot \vec n$ is the local cross-surface speed (positive outwards, neg. inwards) \end{equationterms} \begin{figure}[ht] \begin{center} \begin{center}\vspace{-0.25cm}%handmade \includegraphics[width=0.7\textwidth]{concept_vrel_vecn.png} \end{center} \supercaption{Part of the system may be flowing through an arbitrary piece of the control surface with area $\diff A$. The $\vec n$ vector defines the orientation of $\diff A$ surface, and by convention is always pointed outwards.}{\wcfile{System control volume integral analysis.svg}{Figure} \cczero \oc} \label{fig_cv_da} \vspace{-0.8cm}%handmade \vspace{-1cm}%handmade \end{figure} By inserting equations~\ref{eq_secondbit} and~\ref{eq_thirdbit} into equation~\ref{eq_rtt_basic}, we obtain:\dontbreakpage ... ... @@ -182,7 +185,7 @@ To make clear a few things, let us focus on the simple case where a considered volume has only one inlet (point~1) and one outlet (point~2). From equation~\ref{eq_rtt_linearmom}, the net force $\vec F_\net$ applying on the fluid is: \begin{IEEEeqnarray}{rCl} \vec F_\net & = & \timederivative{}\iiint_\cv \rho \vec V \diff \vol + \iint_\out \rho_2 |V_{\perp 2}| \vec V_2 \diff A_2 - \iint_\out \rho_1 |V_{\perp 1}| \vec V_1 \diff A_1 \nonumber\\\label{eq_fnet_twovectors_unsteady} \vec F_\net & = & \timederivative{}\iiint_\cv \rho \vec V \diff \vol + \iint_\out \rho_2 |V_{\perp 2}| \vec V_2 \diff A_2 - \iint_\inn \rho_1 |V_{\perp 1}| \vec V_1 \diff A_1 \nonumber\\\label{eq_fnet_twovectors_unsteady} \end{IEEEeqnarray} In this equation~\ref{eq_fnet_twovectors_unsteady}, what could cause $\vec F_\net$ to be non-zero? ... ...
 \renewcommand{\lastedityear}{2019} \renewcommand{\lasteditmonth}{03} \renewcommand{\lasteditday}{31} \renewcommand{\lasteditmonth}{05} \renewcommand{\lasteditday}{01} \renewcommand{\numberofthischapter}{4} \renewcommand{\titleofthischapter}{\namechapterfour} ... ... @@ -13,7 +13,7 @@ \section{Motivation} \youtubethumb{4MVn1PoxGqY}{pre-lecture briefing for this chapter (back when it had a different chapter number)}{\oc (\ccby)} In fluid mechanics, only three types of forces apply to fluid particles: forces due to gravity, pressure, and shear. This chapter focuses on pressure (we will address shear in \chapterfive), and should allow us to answer two questions: In fluid mechanics, only three types of forces apply to fluid particles: forces due to gravity, pressure, and shear. This chapter focuses on pressure (we will address shear in \chapterfiveshort), and should allow us to answer two questions: \begin{itemize} \item How is the effect of pressure described and quantified? \item What are the pressure forces generated on walls by static fluids? ... ... @@ -151,7 +151,7 @@ \item where $\diff \vol \equiv \diff x \diff y \diff z$ is the volume of the infinitesimal cube. \end{equationterms} Now generalizing eq.\ref{eq_force_pressure_x} for the other two directions, we can write: Now generalizing eq.~\ref{eq_force_pressure_x} for the other two directions, we can write: \begin{IEEEeqnarray*}{rCl} F_{\text{net, pressure}, x} & = & \diff \vol \frac{-\partial p}{\partial x}\\ F_{\text{net, pressure}, y} & = & \diff \vol \frac{-\partial p}{\partial y}\\ ... ... @@ -192,14 +192,14 @@ What are the forces applying on an arbitrary particle in a static fluid? \begin{itemize} \item The force due to pressure is related to the pressure gradient: we just quantified this with eq~\ref{eq_pressure_force_in_fluid}. \item The force due to pressure is related to the pressure gradient: we just quantified this with eq.~\ref{eq_pressure_force_in_fluid}. \item The force due to shear is zero. We will indeed see in \chapterfive that shear efforts can be expressed as a function of viscosity and velocity. All ordinary fluids are unable to exert shear when static. \item The force due to gravity is easy to quantify: it is the mass $m$ of the fluid multiplied by the gravity vector $\vec g$. \end{itemize} In a moving fluid, the sum of these forces would add up to the mass of the particle times its acceleration. But in a static fluid, the velocity is zero and never changes. We can thus write: \begin{IEEEeqnarray}{rCCCCCl} \vec F_\text{net, pressure} &+& \vec F_\text{shear} &=& \vec F_\text{gravity} &=& \vec 0\nonumber\\ \begin{IEEEeqnarray}{cCcCcCc} \vec F_\text{net, pressure} &+& \vec F_\text{shear} &+& \vec F_\text{gravity} &=& \vec 0\nonumber\\ -\diff \vol \ \gradient{p} &+& \vec 0 &+& m \vec g &=& \vec 0\nonumber\\ -\gradient{p} &+& \vec 0 &+& \rho \vec g &=& \vec 0\nonumber \end{IEEEeqnarray} ... ...
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
  Config.pm:302> INFO - This is Biber 2.9  Config.pm:305> INFO - Logfile is 'fluidmech.blg'  biber:313> INFO - === Thu Apr 25, 2019, 18:20:37  Biber.pm:371> INFO - Reading 'fluidmech.bcf'  Biber.pm:857> INFO - Found 19 citekeys in bib section 0  Biber.pm:3981> INFO - Processing section 0  Biber.pm:4154> INFO - Looking for bibtex format file '/home/olivier/.fluidmechbib.bib' for section 0  bibtex.pm:1468> INFO - LaTeX decoding ...  bibtex.pm:1294> INFO - Found BibTeX data source '/home/olivier/.fluidmechbib.bib'  UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'normalization = NFD' with 'normalization = prenormalized'  UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'variable = shifted' with 'variable = non-ignorable'  Biber.pm:3809> INFO - Sorting list 'ynt/global//global/global' of type 'entry' with template 'ynt' and locale 'en-US'  Biber.pm:3815> INFO - No sort tailoring available for locale 'en-US'  bbl.pm:617> INFO - Writing 'fluidmech.bbl' with encoding 'UTF-8'  bbl.pm:720> INFO - Output to fluidmech.bbl  biber:313> INFO - === Wed May 1, 2019, 14:16:29  Biber.pm:371> INFO - Reading 'fluidmech.bcf'  Biber.pm:857> INFO - Found 19 citekeys in bib section 0  Biber.pm:3981> INFO - Processing section 0  Biber.pm:4154> INFO - Looking for bibtex format file '/home/olivier/.fluidmechbib.bib' for section 0  bibtex.pm:1468> INFO - LaTeX decoding ...  bibtex.pm:1294> INFO - Found BibTeX data source '/home/olivier/.fluidmechbib.bib'  UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'variable = shifted' with 'variable = non-ignorable'  UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'normalization = NFD' with 'normalization = prenormalized'  Biber.pm:3809> INFO - Sorting list 'ynt/global//global/global' of type 'entry' with template 'ynt' and locale 'en-US'  Biber.pm:3815> INFO - No sort tailoring available for locale 'en-US'  bbl.pm:617> INFO - Writing 'fluidmech.bbl' with encoding 'UTF-8'  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) 25 APR 2019 18:23 This is pdfTeX, Version 3.14159265-2.6-1.40.18 (TeX Live 2017/Debian) (preloaded format=pdflatex 2018.10.12) 1 MAY 2019 14:19 entering extended mode restricted \write18 enabled. file:line:error style messages enabled. ... ...
This diff is collapsed.
 This is pdfTeX, Version 3.14159265-2.6-1.40.18 (TeX Live 2017/Debian) (preloaded format=pdflatex 2018.10.12) 25 APR 2019 18:19 This is pdfTeX, Version 3.14159265-2.6-1.40.18 (TeX Live 2017/Debian) (preloaded format=pdflatex 2018.10.12) 1 MAY 2019 14:15 entering extended mode restricted \write18 enabled. file:line:error style messages enabled. ... ... @@ -3841,79 +3841,79 @@ g>] File: concept_vrel_vecn.png Graphic file (type png) Package pdftex.def Info: concept_vrel_vecn.png used on input line 82. Package pdftex.def Info: concept_vrel_vecn.png used on input line 85. (pdftex.def) Requested size: 258.91898pt x 165.26117pt. Package mdframed Info: mdframed works in twoside mode on input line 90. Package mdframed Info: mdframed works in twoside mode on input line 93. [49 <./3/images/concept_vrel_vecn.png>] Package mdframed Info: mdframed works in twoside mode on input line 114. Package mdframed Info: mdframed works in twoside mode on input line 117. File: Niccolò Paganini - Caprice No.5 - David Hernando.ogv.jpg Graphic file (t ype jpg) Package pdftex.def Info: Niccolò Paganini - Caprice No.5 - David Hernando.ogv. jpg used on input line 120. jpg used on input line 123. (pdftex.def) Requested size: 103.85237pt x 58.41266pt. File: simple_cv_fnet.png Graphic file (type png) Package pdftex.def Info: simple_cv_fnet.png used on input line 131. Package pdftex.def Info: simple_cv_fnet.png used on input line 134. (pdftex.def) Requested size: 295.9098pt x 202.28143pt. [50 <./3/thumbs/Niccolò Paganini - Caprice No.5 - David Hernando.ogv.jpg>] Package mdframed Info: mdframed works in twoside mode on input line 149. Package mdframed Info: mdframed works in twoside mode on input line 152. File: S6JKwzK37_8.jpg Graphic file (type jpg) Package pdftex.def Info: S6JKwzK37_8.jpg used on input line 169. Package pdftex.def Info: S6JKwzK37_8.jpg used on input line 172. (pdftex.def) Requested size: 103.85237pt x 72.3908pt. Underfull \hbox (badness 2205) in paragraph at lines 169--169 Underfull \hbox (badness 2205) in paragraph at lines 172--172 \T1/fxl/m/n/8 de-flec-tion of the air pass-ing [] Underfull \hbox (badness 1852) in paragraph at lines 169--169 Underfull \hbox (badness 1852) in paragraph at lines 172--172 \T1/fxl/m/n/8 air-plane (a []\T1/fxl/m/sl/8 wal-ka-long glider[]\T1/fxl/m/n/8 ) . [] File: simple_cv_fnet.png Graphic file (type png) Package pdftex.def Info: simple_cv_fnet.png used on input line 177. Package pdftex.def Info: simple_cv_fnet.png used on input line 180. (pdftex.def) Requested size: 295.9098pt x 202.28143pt. [51 <./3/images/simple_cv_fnet.png> <./3/thumbs/S6JKwzK37_8.jpg>] File: nmEe7Dq01AU.jpg Graphic file (type jpg) Package pdftex.def Info: nmEe7Dq01AU.jpg used on input line 206. Package pdftex.def Info: nmEe7Dq01AU.jpg used on input line 209. (pdftex.def) Requested size: 103.85237pt x 58.41266pt.  Package mdframed Info: mdframed works in twoside mode on input line 212. Package mdframed Info: mdframed works in twoside mode on input line 215. <4cvGGxTsQx0.jpg, id=990, 642.4pt x 361.35pt> File: 4cvGGxTsQx0.jpg Graphic file (type jpg) Package pdftex.def Info: 4cvGGxTsQx0.jpg used on input line 222. Package pdftex.def Info: 4cvGGxTsQx0.jpg used on input line 225. (pdftex.def) Requested size: 103.85237pt x 58.41266pt. Underfull \hbox (badness 3471) in paragraph at lines 222--222 Underfull \hbox (badness 3471) in paragraph at lines 225--225 []\T1/fxl/m/n/8 Video: rocket land-ing gone [] Underfull \hbox (badness 3386) in paragraph at lines 222--222 Underfull \hbox (badness 3386) in paragraph at lines 225--225 \T1/fxl/m/n/8 mo-ment ex-erted by the top [] File: simple_cv_mnet.png Graphic file (type png) Package pdftex.def Info: simple_cv_mnet.png used on input line 230. Package pdftex.def Info: simple_cv_mnet.png used on input line 233. (pdftex.def) Requested size: 221.93376pt x 154.61145pt. [53 <./3/thumbs/nmEe7Dq01AU.jpg> <./3/thumbs/4cvGGxTsQx0.jpg> <./3/images/simpl e_cv_mnet.png>] Package mdframed Info: mdframed works in twoside mode on input line 246. Package mdframed Info: mdframed works in twoside mode on input line 249.   [56 ]) ... ... @@ -5729,7 +5729,7 @@ legacy/fxlr.pfb> Output written on fluidmech.pdf (214 pages, 14925449 bytes). Output written on fluidmech.pdf (214 pages, 14925399 bytes). PDF statistics: 4235 PDF objects out of 4296 (max. 8388607) 3710 compressed objects within 38 object streams ... ...