...
 
Commits (4)
This diff is collapsed.
\renewcommand{\lastedityear}{2018}
\renewcommand{\lasteditmonth}{06}
\renewcommand{\lasteditday}{18}
\renewcommand{\lastedityear}{2019}
\renewcommand{\lasteditmonth}{04}
\renewcommand{\lasteditday}{12}
\atstartofexercises
\fluidmechexercisestitle
......@@ -9,8 +9,8 @@
\mecafluexboxen
\begin{boiboite}
In boundary layer flow, we accept that transition occurs at $\rex \gtrsim \num{5e5}$.
\begin{boiboiboite}
In boundary layer flow, we assume that transition occurs at $\rex \gtrsim \num{5e5}$.
The wall shear coefficient $c_f$, a function of distance $x$,\\
is defined based on the free-stream flow velocity~$U$:
......@@ -22,7 +22,7 @@ Exact solutions to the laminar boundary layer along a smooth surface yield:
\begin{align}
\frac{\delta}{x} &= \frac{\num{4,91}}{\sqrt{\rex}}
&\frac{\delta^*}{x} &= \frac{\num{1,72}}{\sqrt{\rex}} \tag{\ref{eq_deltastar_lam}}\\
\frac{\theta}{x} &= \frac{\num{0,664}}{\sqrt{\rex}}
\frac{\delta^{**}}{x} &= \frac{\num{0,664}}{\sqrt{\rex}}
&c_{f_{(x)}} &= \frac{\num{0,664}}{\sqrt{\rex}} \tag{\ref{eq_cf_lam}}
\end{align}
......@@ -30,11 +30,11 @@ Solutions to the turbulent boundary layer along a smooth surface yield the follo
\begin{align}
\frac{\delta}{x} &\approx \frac{\num{0,16}}{\rex^{\frac{1}{7}}}
&\frac{\delta^*}{x} &\approx \frac{\num{0,02}}{\rex^{\frac{1}{7}}} \tag{\ref{eq_deltastar_turb}}\\
\frac{\theta}{x} &\approx \frac{\num{0,016}}{\rex^{\frac{1}{7}}}
\frac{\delta^{**}}{x} &\approx \frac{\num{0,016}}{\rex^{\frac{1}{7}}}
&c_{f_{(x)}} &\approx \frac{\num{0,027}}{\rex^{\frac{1}{7}}} \tag{\ref{eq_cf_turb}}
\end{align}
\Cref{fig_viscosities_various_fluids_three} quantifies the viscosity of various fluids as a function of temperature.
\end{boiboite}
\end{boiboiboite}
\begin{figure}
\begin{center}
......
\renewcommand{\lastedityear}{2018}
\renewcommand{\lasteditmonth}{06}
\renewcommand{\lasteditday}{18}
\renewcommand{\lastedityear}{201}
\renewcommand{\lasteditmonth}{04}
\renewcommand{\lasteditday}{02}
\renewcommand{\numberofthischapter}{11}
\renewcommand{\titleofthischapter}{\namechaptereleven}
......@@ -8,22 +8,20 @@
\label{chap_eleven}
\mecafluboxen
\mecafluboxtmp
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Motivation}
\youtubethumb{qEE-tyXgWLI}{pre-lecture briefing for this chapter}{\oc (\ccby)}
\youtubethumb{qEE-tyXgWLI}{pre-lecture briefing for this chapter (back when it had a different chapter number)}{\oc (\ccby)}
This exploratory chapter is not a critical component of fluid dynamics; instead, it is meant as a brief overview of two extreme cases: flows for which viscous effects are negligible, and flows for which they are dominant.
This exploration should allow us to answer two questions:
\begin{itemize}
\item How can we model large-scale flows analytically?
\item How can we model small-scale flows analytically?
\item How can we model large-scale flows?
\item How can we model small-scale flows?
\end{itemize}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Flow at large scales}
......
This diff is collapsed.