# Pressure coefficient on fluid mechanics

I have to solve numerically a fluid mechanics problem. I have an airfoil with a flap deployed downwards, under the airfoil I have set a mesh with some nodes. I have already computed stream function values ( $\psi$) on every node, and velocity values ( $V$ ) on every node.

But, there is another thing I must compute the pressure coefficient. I know that the equation is:

$$CP = 1 - \left( \dfrac{V(i,j)} {V_\infty} \right) ^2$$

Where $V(i,j)$ is the velocity at every node of the mesh, and $V_\infty$ is the velocity far away from the airfoil.

My trouble is that I don't know how to determine the value of $V_{\infty}$. They state on the problem that velocity at the entrance of the of the mesh (left-hand side) is 30 m/s. And the flow is 2-D, steady, inviscid and incompressible.

• The mesh should go up to the non-perturbed region, thus $V_{\infty}=30 m/s$ – Wolphram jonny Dec 20 '14 at 14:32

The "far away" phrase indicates that the airfoil does not disturb the velocity flow. In the image below (source), you can see how the airfoil affects the flow near the airfoil itself. But "far" above and below the airfoil, the flow isn't affected. This is your $v_\infty$ and, as WolphramJonny points out in the comments, this is equal to your $v_{in}=30$ m/s.