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{\bf EML 4711/5710 \hfill Gas Dynamics \hfill 12/9/02}\\
{\it Closed notes \hfill Van Dommelen \hfill 5:30-7:30 pm}
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(1) The book, a calculator, and MathCad with Charney's formulae
may be used.
(2) Show all reasoning and intermediate results leading to your
answer, or credit will be lost.
(3) Where tables are used, list table and column number.
(4) Unless otherwise noted, the gas is air, $R$ = 287 m$^2$/sec$^2$
K = 1716 ft$^2$/sec$^2$ R.
(5) You must use only the unit system (SI or British) used in the
question to answer them. 1 BTU = 778 ft lbf,
1 slug = 32.2 lbm.
(6) Standard sea level conditions are $p$ = 101,325 Pa =
2116 lbf/ft$^2$, $T$ = 288 K = 518.4 R.

\begin{enumerate}

\item

Design the windtunnel sketched below to operate at a Mach number
2.9 in the measurement section, which should have a 1 ft$^2$ cross
section.
The stagnation temperature completely upstream is 300 K at all times.
The exit area should also be 1 ft$^2$; it is at atmospheric
pressure. Ignore the effects of any oblique shocks.  Find:
\begin{enumerate}
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\item Static air temperature in the measurement section.
\item Upstream throat area.
\item Optimum diffuser throat area.
\item Minimum upstream stagnation pressure required to start the tunnel.
\item Upstream stagnation pressure at which the tunnel unstarts.
\item Diffuser efficiency at the unstarting pressure.
\end{enumerate}

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<A HREF="figures/1.gif">Solution.</A>
<A HREF="figures/1.out">Gaseqs log.</A>
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\item

The shock tube with the $x,t$-diagram below has an initial air temperature
of 300 K, and the initial pressure is 4 atm to the left of the
membrane and 1 atm to the right of it.  Neatly and accurately draw
both $u$ and $a$ versus $x$ for the time corresponding to the grey
line A-F in the $x,t$-diagram.  Identify all the $u$ and $a$ values
occurring in the two graphs.  Also find $u$ and $a$ behind the
reflected shock and behind the reflected expansion wave.

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<A HREF="figures/2.gif">Solution.</A>
<A HREF="figures/2.out">Gaseqs log.</A>
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\end{enumerate}

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