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.
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 be\[v = \sqrt {\frac{{2\left( {{p_\infty } – p} \right)}}{\rho } + v_\infty ^2} \]Substituting the values\[v = \sqrt {\frac{{2\left( {1.01 – 0.4} \right) \times {{10}^5}}}{{1.23}} + {{\left( {70} \right)}^2}} \]\[ \Rightarrow v = 322.63\,{\rm{m/s}}{\rm{.}}\]
