回転二重管の入口流れ

概要

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In this paper the inlet length and the head given at the entrance of rotating annular pipes in which the fluid flows, are investigated. The moment of momentum of the fluid passes in a unit time through a section at a distance x from the entrance of pipes, is as follows : M=2πp∫^<r_2>_<r_1>v_zv_θr_2dr, where v_z : axial velocity of fluid (const.), v_θ : tangential velocity (function of r), r_1 : inner radius, r_2 : outer radius. The increment of M for a distance dx (dM/dx) dx must be equal to the sum of moment of frictional force for the same distance onthe both surfaces of pipes, so dM/dx=2π (r_2^2r_θ-r_1^2r_<θ1>), where r_θ1 : frictional stress on the inner surface, r_θ2 : frictional stress on the outer surface. Consequently the inlet length is given by [numerical formula]. The head given at the entrance is led in the same manner as follows : [numerical formula], where ω : angular velocity of one side pipe. As the results of calculations it is shown that the inlet length is proportional to 3/4 ths power of angular velocity ω and grows shorter against the ratio r_1/r_2 and that the head increases in proportion to a square of angular velocity ω and to the ratio r_1/r_2.