Find the coefficient of pressure at a point on the wing.

Find the coefficient of pressure at a point on the wing where the velocity is \(58\,m/s\). The airplane is flying at a low speed of \(50\,m/s\).

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    Since, the airfoil is flying at a low speed, incompressible flow can be considered. We can apply the Bernoulli’s equation with density as constant. From Bernoulli’s equation

    \[\begin{gathered}
    p + \frac{1}{2}\rho {V^2} = {p_\infty } + \frac{1}{2}\rho V_\infty ^2 \hfill \\
    \Rightarrow p – {p_\infty } = \frac{1}{2}\rho \left( {V_\infty ^2 – {V^2}} \right) \hfill \\
    \end{gathered} \]

    \[{C_p} = \frac{{p – {p_\infty }}}{{{q_\infty }}} = \frac{{\frac{1}{2}\rho \left( {V_\infty ^2 – {V^2}} \right)}}{{\frac{1}{2}\rho V_\infty ^2}} = \frac{{V_\infty ^2 – {V^2}}}{{V_\infty ^2}} = 1 – \left( {\frac{V}{{V_\infty }}} \right)^2\]

    Therefore, coefficient of pressure,

    \[{C_p} = 1 – {\left( {\frac{V}{{{V_\infty }}}} \right)^2} = 1 – {\left( {\frac{{58}}{{50}}} \right)^2} = – 0.3456\]

    Answered on 14th January 2021.
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