 ### 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} \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} ... ...
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