# An airplane is flying at an velocity of \(100\,m/s\). Find the pressure coefficient at a point on the surface of the wing where the flow velocity is \(140\,m/s\).

An airplane is flying at an velocity of \(100\,m/s\). Find the pressure coefficient at a point on the surface of the wing where the flow velocity is \(140\,m/s\).

Pressure coefficient is given as \[C_{p}=\frac{p_{1} – p_{\infty }}{q_{\infty }}\]This is used for incompressible to compressible flow. However, for incompressible flow, this expression can be used in terms of velocity alone, on applying the Bernoulli’s equation. On using Bernoulli’s equation for two points in a flow, \[p_{1}+\frac{1}{2}\rho V_{1}^{2} = p_{\infty } + \frac{1}{2}\rho v_{\infty }^{2}\]\[p_{1}-p_{\infty} = \frac{1}{2} \rho \left ( V_{\infty}^{2}-V_{1}^{2} \right )\]Considering \(p_{1}\) as the pressure at a point on the wing of the aircraft, and \(p_{\infty}\) as freestream pressure, coefficient of pressure is,\[C_{p} = \frac{p_{1} – p_{\infty }}{q_{\infty}}=\frac{\frac{1}{2}\rho \left ( V_{\infty}^{2}-V_{1}^{2} \right )}{\frac{1}{2}\rho V_{\infty}^{2}}=1-\left ( \frac{V_{1}}{V_{\infty}} \right )^{2}\]\[\Rightarrow C_{p} = 1 – \left ( \frac{140}{100} \right )^{2}=-0.96\]