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.

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    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

    techAir Answered on 6th July 2021.
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