Geodesic
Hydrodynamic initial section in the flow of very viscous Newtonian fluid in a circular tube
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2012), pp. 98-102

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The general problem of identification of an initial section of a round pipe on the assumption of laminar flow of high-viscosity liquid and within the limits of representation about creeping flow is reduced to two-dimensional Poisson equation in the cylindrical coordinates which solution is obtained by a classical method of applying finite integral Hankel transform. The relation between differential pressure and fluid velocity is established which is correlated with already known results. From the condition of 1$\%$ deviation of the axial velocity in the center of the pipe from the fully developed flow the length of a hydrodynamic section is defined. The coefficient of the length of a hydrodynamic section which has been found in the given research, practically coincides with experimentally-theoretical results which are obtained by Schiller, Ekkert and Mak-Kompas.
Keywords: newtonian fluid, hydrodynamic initial section, Navier–Stokes equations. 
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     author = {A. V. Ryazhskikh},
     title = {Hydrodynamic initial section in the flow of very viscous {Newtonian} fluid in a circular tube},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {98--102},
     publisher = {mathdoc},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2012_3_a9/}
}
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A. V. Ryazhskikh. Hydrodynamic initial section in the flow of very viscous Newtonian fluid in a circular tube. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2012), pp. 98-102. http://geodesic.mathdoc.fr/item/VSPUI_2012_3_a9/