@@ -138,6 +138,7 @@ Solutions to the turbulent boundary layer along a smooth surface yield the follo

\end{enumerate}

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\subsubsection{Separation according to Pohlhausen}

\wherefrom{non-examinable, based on Richecœur 2012~\cite{richecoeur2012}}

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@@ -148,7 +149,7 @@ Solutions to the turbulent boundary layer along a smooth surface yield the follo

According to the Pohlhausen model (eq.~\ref{eq_modele_Pohlhausen} p.\pageref{eq_modele_Pohlhausen}), at which distance downstream will separation occur? Is the boundary layer still laminar then?

How could one generate such a deceleration in practice?

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\subsubsection{Laminar wing profile}

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@@ -199,7 +200,7 @@ Solutions to the turbulent boundary layer along a smooth surface yield the follo

Identify these two equations, list the conditions in which they apply, and explain shortly (e.g. in 30 words or less) why a boundary layer cannot separate when a favorable pressure gradient is applied along the~wall.

\begin{comment}

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\subsubsection{Thwaites’ separation model}

\wherefrom{non-examinable, from White \smallcite{white2008} E7.5}

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@@ -220,6 +221,7 @@ Solutions to the turbulent boundary layer along a smooth surface yield the follo

and then went on to show that for the model above, separation ($c_f =0$) occurs when $\lambda_\theta=\num{-0,09}$.

A classical model for flow deceleration is the Howarth longitudinal velocity profile $U_{(x)}= U_0\left(1-\frac{x}{L}\right)$, in which $L$ is a reference length of choice. In this velocity distribution with linear deceleration, what is the distance at which the Thwaites model predicts the boundary layer separation?

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\subsubsection*{Answers}

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@@ -244,7 +246,7 @@ Solutions to the turbulent boundary layer along a smooth surface yield the follo

\item [\ref{exo_bl_friction_fuselage}]%

\tab 1) $x_\text{transition}=\SI{7,47}{\centi\metre}$ (the laminar part is negligible). With the equations developed in exercise 7.3, we get $F =\SI{24,979}{\kilo\newton}$ and $\dot W =\SI{6,09}{\mega\watt}$. Quite a jump from the Wright Flyer I!

\tab\tab 2) When the longitudinal pressure gradient is zero, the boundary layer cannot separate. Thus separation from the fuselage skin can only happen if the fuselage is flown at an angle relative to the flight direction (e.g. during a low-speed maneuver).

\item [\ref{exo_bl_separation_model}]%

\tab Once the puzzle pieces are put together, this is an algebra exercise: $\left(\frac{x}{L}\right)_\text{separation}=\num{0,1231}$. Bryan beats Ernst!

% \item [\ref{exo_bl_separation_model}]%

% \tab Once the puzzle pieces are put together, this is an algebra exercise: $\left(\frac{x}{L}\right)_\text{separation} = \num{0,1231}$. Bryan beats Ernst!