Commit f9d25d06 authored by Olivier's avatar Olivier

Chapter 4: fix typo in lead-up to eq. 4/15

(plus a couple of other small typos)
parent 0816fdac
\renewcommand{\lastedityear}{2019}
\renewcommand{\lasteditmonth}{03}
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\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}
......
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