 ...

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.

337 KB

83.7 KB