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FORCES ACTING ON THE CYLINDER

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