Electrokinetic-potential fluctuations produced by pipe-flow turbulence

Abstract

The distribution across a pipe of turbulent intensities, shearing stress, and energy spectra are inferred from measured electrokinetic-potential fluctuations in a fully developed flow of distilled water in a 2.54 cm diameter glass pipe. These quantities are shown to be in good agreement with those obtained by Laufer and Sandborn with hot-wire anemometers for air flows at the same mean Reynolds number. A tentative analytical model of the phenomena is constructed and analyzed by Maxwell's electrodynamic field equations for a nonmagnetized medium moving with a velocity which is much smaller than the velocity of light. A set of equations governing the interrelation between the electrokinetic- potential fluctuations and the turbulent velocity-fluctuation components of the flow field in fully developed pipe flow is deduced. The equations are simplified and assumed to have the form: σ▽ѱ = ρu. Fourier transforms are then introduced and simple relations between the electrokinetic-potential fluctuations and velocity fluctuations are obtained.