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Circulation
Insight
into the production of lift is provided by the flow around a cylinder.
The diagram shows (a) the streamlines of an inviscid flow. In (b) a circulatory
flow is obtained with a viscous fluid by rotating the cylinder in the
direction shown by the arrow. Combining this with the inviscid flow gives streamlines
for the 'real' flow situation (c) for a rotating object moving through
the fluid.
The symmetry of the streamlines shown in (a) implies
that there is no imbalance in the pressure forces acting on the body due to
the inviscid flow so that the body experiences neither lift nor drag. The circulation
(vortex) shown in (b) requires a viscous coupling between the
rotating body and the fluid. Adding these two flows produces the flow shown
in (c). The two stagnation points have moved from the symmetry axis towards
the bottom of the body and the flow velocity over the top is now larger than
the flow velocity over the underside. This change in flow modifies the pressure
distribution, the top pressure being reduced as the flow velocity increases
as the streamtubes contract and the bottom pressure increased as the stream
tubes diverge. The cylinder now experiences upward lift . This effect is
exploited by pitchers and golfers who attempt to change the path taken by a
ball by inducing spin.
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