Consider an airfoil in a flow at standard sea level conditions with a free stream velocity of 70 m/s.

Consider an airfoil in a flow at standard sea level conditions with a freestream velocity of {\rm{70m/s}}. At a given point on the airfoil, the pressure is {\rm{0}}{\rm{.4 \times 1}}{{\rm{0}}^{\rm{5}}}{\rm{N/}}{{\rm{m}}^{\rm{2}}}. Calculate the velocity at this point.

Worldtech Asked on 28th December 2018 in Aerodynamics.
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    The free stream velocity of the flow is 70\,m/s .  Bernaulli’s equation relates pressure and velocity of a fluid motion along a streamline.p + \frac{1}{2}\rho {v^2} = \mathrm{Constant}Therefore,{p_\infty } + \frac{1}{2}\rho v_\infty ^2 = p + \frac{1}{2}\rho {v^2}At sea level conditions, freestream pressure and density are {{\rm{\rho }}_\infty }{\rm{ = 1}}{\rm{.23kg/}}{{\rm{m}}^{\rm{3}}} and  {p_\infty }{\rm{ = 1}}{\rm{.01}} \times {\rm{1}}{{\rm{0}}^5}{\rm{N/}}{{\rm{m}}^{\rm{2}}}. Velocity at the given point will bev = \sqrt {\frac{{2\left( {{p_\infty } – p} \right)}}{\rho } + v_\infty ^2} Substituting the valuesv = \sqrt {\frac{{2\left( {1.01 – 0.4} \right) \times {{10}^5}}}{{1.23}} + {{\left( {70} \right)}^2}} \Rightarrow v = 322.63\,{\rm{m/s}}{\rm{.}}

    techAir Answered on 28th December 2018.
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