root/trunk/matml/transport/problems/bllamturb/bllamturb-solution.tex

\documentclass{article}
\usepackage{fullpage}
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\begin{document}
\begin{enumerate}
\item Laminar and turbulent boundary layers

  \begin{enumerate}
  \item Your velocity boundary layer sketch should have looked something like:
    \begin{center}
      \PSbox{boundlamturb.ps}{420pt}{128pt}
    \end{center}
    
  \item For laminar flow, $\delta_u\propto x^{0.5}$; for turbulent flow,
    $\delta_u\propto x^{0.8}$.  The turbulent boundary layer grows faster
    because the turbulent eddies mix momentum much more effectively than
    viscosity ``diffuses'' it.

  \item If the flow can be made laminar at a given Reynolds number, the drag
    force will be lower than for turbulent flow.  This is evident from the $f$
    vs. Reynolds number curve for flow past a flat plate.

    Note that some people were confused by the decreasing nature of the $f$
    vs. Re curve.  Although $f$ is decreasing with $Re$, drag force is
    proportional to $fK=f\cdot\frac{1}{2}\rho U^2$, so for a given fluid and
    plate, drag force will increase with Reynolds number.
  \end{enumerate}
\end{enumerate}
\end{document}