Axial dispersion in turbulent flow. Taylor showed that the following expression is suitable for the calculation of the axial dispersion coefficient for turbulent flow in a pipe:

\[D_{\mathrm{E}}=10 R V_{\mathrm{f}}\]

Here \(R\) is the pipe radius and \(V_{\mathrm{f}}\) is the friction velocity. Show the basis for this equation, and write a review of the many correlations proposed for this and the improvements suggested for the original Taylor model.