How to find the velocity of air flow around the aerofoil?

[TimeRip496]

Homework Statement

How to find the velocity of the air flow around the aerofoil?

Homework Equations

U - freesteam velocity
β - angle of wing camber

The Attempt at a Solution

To find the velocity of the air flow at each section of the aerofoil, am I right to say that the horizontal velocity of the air flow is constant throughout the chord while the vertical component of the velocity varies along the chord depending on the angle of chord w.r.t. horizontal?

So velocity at first plane is U/cosβ? Subsequently, the velocity at the 2nd and 3rd plane will be U and U/cosδ respectively?

If that is the case, will shifting the air upwards, not push the wing down? Or am I right to say that as the airflow around the wings, there is no net upward motion of air, thus it does not push the wing downwards?

 

[rcgldr]

I'm not sure what aerodynamic model you are using. In order for the air to remain attached (to the boundary layer) around the curved upper surface, there will be a pressure gradient where pressure decreases perpendicular to the relative flow, with the lowest pressure just outside the boundary layer. The air will also accelerate in the direction of relative flow towards the low pressure areas that coexist with the curvature of the flow. Again assuming the flow remains reasonably attached, then the air flowing past the trailing edge will have a downwards component coexistent with lift.

I don't know how you are supposed to calculate lift, but it's complicated, and calculating drag is even more complicated.