Mass flow and airfoils

Question

My understanding of airfoils is that the fluid flowing over the top of an airfoil moves faster than the fluid on the bottom, causing a net pressure that lifts the aircraft, where the air pressure on either side is described with Bernoulli's equation. I've also heard explanations that use the law of the conservation of momentum, where the airfoil, overall, sends air downward with enough momentum to lift the aircraft. Both models are valid.

However, I am interested in the mass flow over the top and bottom of the airfoil. Is there any predictable way to describe this parameter? Or does it depend entirely on the shape of the airfoil. Volumetric flow would also be fine.

Intuitively, I'm guessing that there is more volumetric flow over the top side since the velocity of the fluid is higher, but I'm not sure, because maybe the thickness of the fluid layer is less.

Answer 1

Consider a subsonic, symmetrical airfoil at zero angle of attack. Mass flows above and below are equal. Now give it a positive incidence so that it produces net lift.

According to the circulation theory of lift, there must now be a net circulation component of flow; backwards over the top, down behind (downwash), forwards underneath and up in front of the leading edge.

This circulation is accompanied by (even comprises) equivalent variations in mass flow, so your intuition is correct - the mass flow over the top comprises both that due to steady motion plus that due to circulation, while the mass flow below comprises that due to steady motion less that due to circulation.