Hydrodynamic initial section in the flow of very viscous Newtonian fluid in a circular tube

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.