The dispersion of matter in turbulent flow through a pipe

The dispersion of soluble matter introduced into a slow stream of solvent in a capillary tube can be described by means of a virtual coefficient of diffusion (Taylor 1953a) which represents the combined action of variation of velocity over the cross-section of the tube and molecluar diffusion in a radial direction. The analogous problem of dispersion in turbulent flow can be solved in the same way. In that case the virtual coefficient of diffusionKis found to be 10∙1av_*orK= 7∙14aU√γ. Hereais the radius of the pipe,Uis the mean flow velocity,γis the resistance coefficient andv_*‘friction velocity’. Experiments are described in which brine was injected into a straight 3/8 in. pipe and the conductivity recorded at a point downstream. The theoretical prediction was verified with both smooth and very rough pipes. A small amount of curvature was found to increase the dispersion greatly. When a fluid is forced into a pipe already full of another fluid with which it can mix, the interface spreads through a lengthSas it passes down the pipe. When the interface has moved through a distanceX, theory leads to the formulaS²= 437aX(v_*/U). Good agreement is found when this prediction is compared with experiments made in long pipe lines in America.