## Pipe

*diameter d*is the only relevant length scale in the homogeneous region.## ,

*g*and*d*decide the flow dynamics; and are not important. Dimensional arguments give the mixing length scales.## Flux

## A fluid particle (a coherent region of fluid) scales like

*d*.## `Free fallâ€™ velocity of a fluid particle heavier by through a distance

*d*; the flow becomes decorrelated over distances d