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National Advisory Committee for Aeronautics, Technical Notes - Friction Coefficients in the Inlet Length of Smooth Round Tubes

An experimental study was made of friction coefficients near the inlet
of smooth, round tubes with bellmouth entrances; The range of Reynolds
number (based on tube diameter) was from 39,000 to 590,000; these values
corresponded to turbulent flew in the region of a fully developed velocity
profile. The tube size ranged from 3/8 inch to 1l- inches. Four different
combinations of approach section and bellmouth entry were used. Tests
were made both with water and with air at low Mach numbers.

The results are reported in terms of the apparent friction coefficient,
which is directly a measure of the pressure drop and which includes the
effects of both friction and of changes in momentum flux associated with
changes in velocity profile.

Near the inlet the tests indicated a zone in which the developing
boundary layer is laminar, followed by a zone in which the boundary layer
is turbulent. Transition from a laminar to turbulent boundary layer was
found to occur gt a Reynolds number (based on distance from the tube inlet)
of about 5 X 10 , which compares well. with the corresponding value for
a flat plate.

In the inlet region the friction coefficient was found to vary widely
from the Karmén-Nikuradse coefficient for fully developed turbulent flow
and was. sometimes greater and sometimes less than the Karmén-Nikuradse
value, depending on the value of the Reynolds number. About 50 tube
diameters were required for the local friction coefficient to come within
5 percent of the Karman—Nikuradse value and about 80 diameters for the
integrated friction coefficient to come within 5 percent of the mah-
Nikuradse value.

The effects ‘of inducing turbulence artificalJy by wire screens and
by an obstruction on the tube wall were studied.

In the laminar inlet zone the results were found to be in accord
with the theory of Langhaar.

Values of the friction coefficient measured at large distances from
the tube inlet were found to be systematicaljy about 1 3 percent higher
than the values given by the Karman-Nikuradse formula .

An approximate method. for predicting the discharge coefficient of
rounded-entrance flow nozzles, based. on the reported results, is presented
and is shown to compare well with published data on flow nozzles.