Find the reservoir pressure for a nozzle of a supersonic wind tunnel.

Find the reservoir pressure for a nozzle of a supersonic wind tunnel which has an exit-to-throat area ratio of \(4.441\). The test section pressure measured by a pitot tube is \(1.5\, atm\).

Asked on 26th March 2021 in Design.
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    A supersonic wind tunnel produces supersonic speeds in the test section. It consists of a nozzle, test section and a diffuser. Nozzle is convergent-divergent in design. It supplies a uniform supersonic flow into the test section which is a constant area duct. Diffuser which is also convergent-divergent slows the supersonic flow to subsonic.

    A high-pressure reservoir is placed at the inlet of the nozzle to run the wind tunnel. A vacuum storage tank at the exit of the diffuser or a combination of both the high-pressure reservoir and a vacuum storage tank can also be used to run the supersonic wind tunnel.

    From isentropic flow properties, for \(\frac{A_{e}}{A^{*}}=4.441\), \(M_{e}=3.05\)

    From normal shock properties, for \(M_{e}=3.05\), \(\frac{p_{02}}{p_{01}}=0.3145\)

    Therefore,
    \[p_{01}=\left ( \frac{p_{01}}{p_{02}} \right )
    p_{02}=\left ( \frac{1}{0.3145} \right )\left ( 1.5 \right )=4.7695\,atm\]

    Answered on 9th April 2021.
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