# The Dispersion of Matter in Turbulent Flow through a Pipe

Geoffrey Taylor

## Abstract

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 diffusion K is found to be 10$\cdot$1av$_{\ast}$ or K = 7$\cdot$14aU $\surd \gamma$. Here a is the radius of the pipe, U is the mean flow velocity, $\gamma$ is the resistance coefficient and v$_{\ast}$ 'friction velocity'. Experiments are described in which brine was injected into a straight $\frac{3}{8}$ 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 length S as it passes down the pipe. When the interface has moved through a distance X, theory leads to the formula S$^{2}$ = 437aX(v$_{\ast}$/U). Good agreement is found when this prediction is compared with experiments made in long pipe lines in America.