To understand the implication of the asymmetry of the pressure field in terms of the forces acting on the cylinder, the last animation shows the elementary forces as vectors on the cylinder surface.
Each elementary force is given by
where p is pressure, is the normal unit vector directed away from the surface and ds is the surface arc.
The resulting force (the vectorial sum of all the elementary forces on the body) is clearly zero when circulation is zero (D'Alambert paradox).
As circulation increases the component of the resulting force in the direction of the uniform flow is still zero (no drag), whereas a component in the direction perpendicular to the uniform flow (lift) appears that increases as circulation is enhanced.
The modulus of the lift can be evaluated analytically (Kutta-Joukowski theorem) and is