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National Advisory Committee for Aeronautics, Technical Notes - New Data on the Laws of Fluid Resistance

While very noteworthy results have been ob pained, especially
in recent years, with the aid of the theory of the frictionless‘
fluid, this is the case in a much smaller degree for the results
of the th neory based on a f uid with *.nternal friction or viscos—
ity. The fluids with which he actually have to do always possess
some viscosity, which is the very reason for the resistance en—
countered by a body moving in a fluid. When this resistance or
drag has been reduced to a minimum by streamlining the body, the
effect of the viscosity becomes so small that the actual flow very'
nearly agrees with that calculated on the basis of the theory of
the frictionless or non~viecous fluid.** This is not the case:
however, with shapes which cause a great resists nce, since the vie--
cosity of the fluid here plays a decisive role. Thus far all at—
tempts at the quantitative determination of the drag, on the basisq
of the theory of viscous fluids, with the exception of a few spec—l
ial cases, have met with but slight success. For this reason,
whenever a more accurate knowledge of the drag is desirable, it
must be determined by experiment. In this article a few experi—
mental results will be given on the drag of a cylinder exposed
to a stream of air at right angles to its axis. It will be shown
that the drag depends on the absolute dimensions of the body and
the velocity and viscosity of the fluid in a much more complex
manner than has heretofore been supposed.

It is customary to represent the drag D encountered by a
body in moving through a_fluid of the density p, by the formula
in which V denotes the velocity with which the body moves
through the fluid and 8 generally represents the projected area
of the body on a plane perpendicular to the direction of motion.
Instead of this area, we may take any other characteristic area
of the body; for example, in the case of aerofoiis, the greatest
projected area. The dimensionless coefficient 0 is termed the
coefficient of drag. For a long time the opinion held, mainly on
the strength of Newton’s conception of the‘resistance of the air,
that for a given fluid this coefficient of drag is independent

of the velocity and of the absolute size of the body and may ac—
cordingly be regarded as a constant whose value depends only on
the geometrical shape of the body. It was thought possible, from
the knowledge of the drag coefficient (obtained for a single ve-
looity of a given body by means of the above drag formula), to
determine the drag for any other size of the body and for any
other velocity, geometrical similarity of shape being assumed.