Laws of Flow in Rough Pipes Page: 2 of 63
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NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
TECHNICAL MEMORANDUM 1292
LAWS OF FLOW IN ROUGH PIPES
By J. Nikuradse
INTRODUCTION
Numerous recent investigations (references 1, 2, 3, 4., and 5)
have greatly increased our knowledge of turbulent flow in smooth tubes,
channels, and along plates so that there are now available satisfactory
data on velocity distribution, on the laws controlling resistance, on
impact, and on mixing length. The data cover the turbulent behavior of
these flow problems. The logical development would now indicate a
study of the laws governing turbulent flow of fluids in rough tubes,
channels, and along rough plane surfaces. A study of these problems,
because of their frequent occurrence in practice, is more important
than the study of flow along smooth surfaces and is also of great
interest as an extension of our physical knowledge of turbulent flow.
Turbulent flow of water in rough tubes has been studied during the
last century by many investigators of whom the most outstanding will be
briefly mentioned here. H. Darcy (reference 6) made comprehensive and
very careful tests on 21 pipes of cast iron, lead, wrought iron,
asphalt-covered cast iron, and glass. With the exception of the glass
all pipes were 100 meters long and 1.2 to 50 centimeters in diameter.
He noted that the discharge was dependent upon the type of surface as
well as upon the diameter of the pipe and the slope. If his results
are expressed in the present notation and the resistance factor X is
considered dependent upon the Reynolds number Re, then it is found that
k
according to his measurements X, for a given relative roughness -,
varies only slightly with the Reynolds number (k is the average depth
d
of roughness and r is the radius of the pipe; Reynolds number Re =
in which U is the average velocity, d is the pipe diameter, and v
is the kinematic viscosity). The friction factor decreases with an
increasing Reynolds number and the rate of decrease becomes slower for
greater relative roughness. For certain roughnesses his data indicate
that the friction factor K is independent of the Reynolds number.
*"Stromungsgesetze in rauhen Rohren." VDI-Forschungsheft 361.
Beilage zu "Forschung auf dem Gebiete des Ingenieurwesens" Ausgabe B
Band 4, July/August 1933.
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Nikuradse, J. Laws of Flow in Rough Pipes, report, November 1950; (https://digital.library.unt.edu/ark:/67531/metadc63009/m1/2/: accessed April 18, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.