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National Advisory Committee for Aeronautics, Technical Notes - Notes on Aerodynamic Forces - I - Rectilinear Motion

The study of the motion of perfect fluids is of paramount
importance for the understanding of the chief phenomena occurring
in the air surrounding aircraft, and for the numerical determina-
tion of their effects. In connection with the computation of the
air forces of airship hulls I recently employed successfully some
simple methods for the investigation of the flow of a perfect
fluid, new for the greatest part and at least never mentioned in
connection with aerodynamical problems. These methods appeal par—
ticularly to the engineer who is untrained in the performing of.
laborious mathematical developments and computations, as they do
away with these and allow one to obtain many interesting results
by the mere application of some general and well-known principles
of mechanics.

In this note I apply these methods on problems of rectilin—
ear motions. The fluid is always supposed to be perfect and the
flow irrotational.

It is often mentioned that the forces between a fluid and a
rigid body moving rectilinearly in it are the same whether the '
fluid flows around the resting body, or the body moves in the
fluid otherwise at rest. This holds true whether the rectilinear
motion is steady or accelerated. In conseguence of this, the ki-
netic energy contained in the resting fluid added to the kinetic
energy of the fluid flowing around the body gives the kinetic en-
ergy of the entire fluid moving with constant velocity. The rest~
ing body decreases the velocity of the fluid in front of it and
behind it, thus diminishing the kinetic energy of the fluid by a
certain amount and this negative energy is edual and opposite to
the kinetic energy contained in the gtherwise resting fluid sur—
rounding the moving body. The energy of the moving fluid is fur—
ther decreased for another reason: The fluid contained in the space
occupied by the body is removed and hence the kinetic energy of
this fluid moving with the velocity of motion is therefore missing-
This energy however is contained in the system if the body has the
same density as the fluid and if not only the kinetic energy of the
fluid alone but also the complete kinetic energy of the system is
considered. The kinetic energy of the fluid alone may be called
additional kinetic energy.