D O C . 4 6 6 T H E F L E T T N E R S H I P 4 6 7
The following remarkable law is valid for all fluid (liquid and gaseous) motions
in which the influence of friction is negligible. Given various velocities of a fluid
at different places along a (steady) current, lower pressure exists at places of greater
velocity and vice versa. This is easily grasped from the elementary law of motion.
If, for instance, there is a fluid motion swelling from left to right—a velocity di-
rected toward the right—then the individual fluid particle must experience an ac-
celeration along its way from left to right.
In order for this acceleration to occur, a force toward the right must act on the
particle. This requires that the pressure exerted on the left boundary be greater than
that exerted on its right boundary. It therefore follows that the fluid’s leftward pres-
sure is greater than rightward if, conversely, the velocity on the right is greater than
on the left.
This law of the (inverse) dependence of the pressure on velocity evidently per-
mits one to assess the pressure forces generated by the motion of a liquid (or gas)
when one only knows the velocity distribution in the liquid. Next, I would like to
show by a generally known, simple example, namely, the perfume spray, how this
law should be applied.
Air is forced at great velocity through opening A out of a some-
what broadened tube by means of a compressible rubber ball. It
then flows further in a stream steadily expanding on every side,
whereby the flow velocity gradually diminishes to zero. Accord-
ing to our law, it is clear that, due to the high velocity, the pres-
sure is lower at A than at a greater distance from the opening; at
A there is an underpressure compared to the ¢free² air at rest far-
ther away. If an open-ended tube R is positioned with its upper
end in the zone of high velocity, and its lower end in a container filled with liquid,
then the underpressure at A sucks liquid upward out of the container, which, after
exiting at A, is dispersed by the stream of air and carried along as small droplets.
Following this preparation, let us look at the fluid motion around a Flettner cyl-
inder. Z is this cylinder seen from above. Let it initially not rotate.