Research on Wave Phenomena in Hydraulic Lines : (8th Report, Theoretical Investigation on End Correction Problem - Part 2, Estimation of Viscous Resistance

Abstract

Theoretical estimation of viscous loss in the 'end correction' problem remains unsolved. Stewart or Sivian has applied to this purpose Rayleigh's imaginary correction tube originally proposed to explain fluid inertia effects. However such a hypothesis is expedient and groundless. This paper intends to theoretically analyze an oscillatory viscous flow around a circular aperture in a plane wall. By assuming concentrically hemispherical equipressure surfaces around an aperture, the flow is mathematically solved. The resulting flow model reasonably simulates the unsteady boundary layer on a wall, and gives a resistive end correction one-fourth as small as the resistance of an imaginary tube. It is pointed out that a large value of the non-dimensional frequency α√(ω/ν) deteriorates the accuracy of resistance measurement. The former experiments lack in this necessary precaution. Presumably that is why the experimental results by Sivian or others seem to support the questionable hypothesis.