Commit e347785b authored by Olivier's avatar Olivier

Chapter 4: updated video slides

parent cefadcf3
\documentclass[17pt]{beamer}
\usepackage{fluidmechslides} % from https://framagit.org/olivier/sensible-styles
% Syntax for single-image slides:
% (the first argument (number) being the maximum fraction of the
% slide width that the image is allowed to have.)
% \figureframe{1}{filename}{Title}{Attribution}
% Do I want the print version? (no \pause, larger preamble)
\printversion
\begin{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{}
Pressure as force perpendicular to a flat plate:
\begin{IEEEeqnarray*}{rCl}
p &\equiv& \frac{F_\perp}{A} \label{eq_first_def_pressure_two}
\end{IEEEeqnarray*}\pause
We need to go beyond this!
\end{frame}
%%%%%%
\begin{frame}{Weird thing \#1}\pause
\begin{center}
In fluid mechanics,
\emph{there is no flat plate}
\end{center}
\end{frame}
\begin{frame}{}
Let us shrink the plate down:
\begin{IEEEeqnarray*}{rCl}
p &\equiv& \lim_{A \to 0} \frac{F_\perp}{A} \label{eq_def_pressure}
\end{IEEEeqnarray*}
\end{frame}
\begin{frame}{Weird thing \#2}\pause
\begin{center}
Pressure on the infinitesimal flat plate\pause
is the same regardless of orientation
\end{center}
\end{frame}
\begin{frame}{Weird thing \#2}
\begin{center}
\emph{Pressure has no direction}
$\to$ there is only one (scalar) value\\
at any point
\end{center}
\end{frame}
\begin{frame}{Key concept}
in a fluid,
\textbf{there is only “one” pressure at a given point}.\pause
Pressure can vary in space and time: $p_{(x, y, z, t)}$\\\pause
but it does not have a direction ($p_x = p_y = p_z$): it is a \vocab{scalar property field}.
\end{frame}
\end{document}
\documentclass[17pt]{beamer}
\usepackage{fluidmechslides} % from https://framagit.org/olivier/sensible-styles
% Syntax for single-image slides:
% (the first argument (number) being the maximum fraction of the
% slide width that the image is allowed to have.)
% \figureframe{1}{filename}{Title}{Attribution}
% Do I want the print version? (no \pause, larger preamble)
\printversion
\begin{document}
\begin{frame}{}
Pressure has no direction,\\\pause
but it may not be the same everywhere…\pause
If you had a field of pressure values,\\\pause
how would you compute the\\
“direction in which pressure is pushing”?
\end{frame}
\begin{frame}{}
Put an infinitesimal cube inside the pressure field:\pause
\includegraphics[width=8cm]{particle_pressure_cube}\pause
Six different pressure values!
\end{frame}
\begin{frame}{}
Six different pressure values:\pause
\hspace{-0.05\textwidth}\includegraphics[width=1.05\textwidth]{particle_pressure_faces}\pause
Three pairs of pressure values
\end{frame}
\begin{frame}{Three key information}
\includegraphics[width=1\textwidth]{particle_pressure_faces}\pause
The \emph{difference} in $x$\\
The \emph{difference} in $y$\\
The \emph{difference} in $z$\\
\end{frame}
\begin{frame}{Key concept}
\begin{centering}
in a fluid,\\
the pressure is a (1D) scalar field; \pause
the \emph{effect} of pressure\\ on a submerged volume\\ is a (3D) \textbf{vector field}.
\end{centering}
\end{frame}
\begin{frame}{The force due to pressure}
\includegraphics[width=1\textwidth]{particle_pressure_faces}
The \emph{difference} in $z$:\pause
\begin{IEEEeqnarray*}{rCl}
F_{\text{net, pressure}, z} &=& \diff y \diff x \left[ p_{3} - p_{6}\right]\\
\end{IEEEeqnarray*}
\end{frame}
\begin{frame}{The force due to pressure}
\includegraphics[width=1\textwidth]{particle_pressure_faces}
The \emph{difference} in $z$:
\begin{IEEEeqnarray*}{rCl}
F_{\text{net, pressure}, z} &=& \diff y \diff x \left[-\partialderivative{p}{z} \diff z\right] \nonumber\\\pause
&=& \diff \vol \frac{-\partial p}{\partial z}\label{eq_force_pressure_x}
\end{IEEEeqnarray*}
\end{frame}
\begin{frame}{The force due to pressure}
\includegraphics[width=1\textwidth]{particle_pressure_faces}
\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}\\
F_{\text{net, pressure}, z} & = & \diff \vol \frac{-\partial p}{\partial z}
\end{IEEEeqnarray*}
\end{frame}
\begin{frame}{The force due to pressure}
\begin{small}
\begin{IEEEeqnarray*}{rCcCcCcCc}
\vec F_{\text{net, pressure}} &=& \vec F_{\text{net, pressure}, x} &+& \vec F_{\text{net, pressure}, y} &+& \vec F_{\text{net, pressure}, z}\\\pause
&=& \diff \vol \frac{-\partial p}{\partial x} \ \vec i &+& \diff \vol \frac{-\partial p}{\partial y} \ \vec j &+& \diff \vol \frac{-\partial p}{\partial z} \ \vec k\pause
\end{IEEEeqnarray*}
\end{small}
\begin{IEEEeqnarray*}{rCl}
\vec F_{\text{net, pressure}} &=& -\diff \vol \left(\partialderivative{p}{x} \ \vec i + \partialderivative{p}{y} \ \vec j + \partialderivative{p}{z} \ \vec k \right)
\end{IEEEeqnarray*}\pause
\textit{there has to be a better way of writing this!}
\end{frame}
\begin{frame}{Cool new tool}
The \vocab{gradient} operator\pause
\begin{equation*}
\gradient{} \equiv \vec i \ \partialderivative{}{x} + \vec j \ \partialderivative{}{y} + \vec k \ \partialderivative{}{z}
\end{equation*}\pause
“in which direction (and by how much) is the scalar getting larger”\pause
\end{frame}
\begin{frame}{The force due to pressure}
\begin{IEEEeqnarray*}{rCl}
\vec F_{\text{net, pressure}} &=& -\diff \vol \left(\partialderivative{p}{x} \ \vec i + \partialderivative{p}{y} \ \vec j + \partialderivative{p}{z} \ \vec k \right)\nonumber\\\pause
&=& - \diff \vol \ \gradient{p}
\end{IEEEeqnarray*}\pause
\textit{cool huh?}
\end{frame}
\begin{frame}{The force due to pressure}
\begin{mdframed}
\begin{IEEEeqnarray*}{rCl}
\frac{1}{\diff \vol} \vec F_\text{net, pressure} & = & -\gradient{p}\label{eq_pressure_force_in_fluid}
\end{IEEEeqnarray*}
\end{mdframed}
“the pressure force per unit volume is minus the pressure gradient”.
\end{frame}
\end{document}
\documentclass[17pt]{beamer}
\usepackage{fluidmechslides} % from https://framagit.org/olivier/sensible-styles
% Syntax for single-image slides:
% (the first argument (number) being the maximum fraction of the
% slide width that the image is allowed to have.)
% \figureframe{1}{filename}{Title}{Attribution}
% Do I want the print version? (no \pause, larger preamble)
\printversion
\begin{document}
\sectionwithsubtitle{Buoyancy}{will it float?}
\pictureframe{1}{Webysther_20140125062438_-_Balao_boituva}{What is so special about hot air?}{\wcfile{Webysther_20140125062438_-_Bal\%C3\%A3o_boituva.jpg}{Photo} \ccbysa by \wcun{Webysther}{Webysther Nunes}}
\begin{frame}
\begin{centering}
What is so special about buoyancy?\pause
\emph{nothing.}
\end{centering}
\end{frame}
\begin{frame}
Stand in a static fluid, and you are subject to pressure forces:\pause
This net force is called \vocab{buoyancy}.\pause
\small may or may not compensate weight!
\end{frame}
\begin{frame}
Buoyancy is just a big word
for “force due to pressure in the static fluid”
\end{frame}
\figureframe{1}{buoyancy1}{}{Figure \cczero \oc}
\figureframe{1}{buoyancy2}{}{Figure \cczero \oc}
\figureframe{1}{buoyancy3}{}{Figure \cczero \oc}
\figureframe{1}{buoyancy4}{}{Figure \cczero \oc}
\begin{frame}
\begin{centering}
\includegraphics[width=0.8\textwidth]{buoyancy_diagram}
Buoyancy is just a big word
for “force due to pressure in the static fluid”
\end{centering}
\end{frame}
\figureframe{1}{buoyancy5}{}{Figure \cczero \oc}
\figureframe{1}{buoyancy6}{}{Figure \cczero \oc}
\figureframe{1}{buoyancy7}{}{Figure \cczero \oc}
\begin{frame}
\begin{centering}
\includegraphics[width=0.8\textwidth]{buoyancy_diagram}
Buoyancy is just a big word
for “force due to pressure in the static fluid”
\end{centering}
\end{frame}
\begin{comment}
\oldpictureframe{}{Bell_jar_apparatus_during_low-pressure_test}{1}{\wcfile{Bell_jar_apparatus_during_low-pressure_test.jpg}{Photo} \pd NASA}
\figureframe{1}{buoyancy_force_demo_1.png}{}{\wcfile{Atmospheric buoyancy demonstration experiment 2.svg}{Figure} \cczero \oc}
\figureframe{1}{buoyancy_force_demo_2.png}{}{\wcfile{Atmospheric buoyancy demonstration experiment 2.svg}{Figure} \cczero \oc}
\figureframe{1}{buoyancy_force_demo_3.png}{}{\wcfile{Atmospheric buoyancy demonstration experiment 2.svg}{Figure} \cczero \oc}
\end{comment}
\pictureframe{1}{283894837_a21d301850_o}{Is buoyancy like weightlessness?}{\flickrfile{johnjoh/283894837/}{Photo} \ccbysa by \flickruser{johnjoh}}
\pictureframe{1}{STS007-14-629}{Is buoyancy like weightlessness?}{\wcfile{STS007-14-629.jpg}{Photo} credit NASA (\pd)}
\end{document}
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