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