ESTIMATING THE MEAN SPEED OF LAMINAR OVERLAND FLOW USING DYE INJECTION-UNCERTAINTY ON ROUGH SURFACES

Abstract

A common method for estimating mean flow speeds in studies of surface runoff is to time the travel of a dye cloud across a measured flow path. Motion of the dye front reflects the surface flow speed, and a correction must be employed to derive a value for the profile mean speed, which is always lower. Whilst laminar flow conditions are widespread in the interrill zone, few data are available with which to establish the relationship linking surface and profile mean speeds, and there are virtually none for the flow range 100<Re<500 (Re=Reynolds number) which is studied here. In laboratory experiments on a glued sand board, mean flow speeds were estimated from both dye speeds and the volumetric flow relation v=Q/wd with d measured using a computer-controlled needle gauge at 64 points. In order to simulate conditions applicable to many dryland soils, the board was also roughened with plant litter and with ceramic tiles (to simulate surface stone cover). Results demonstrate that in the range 100<Re<500, there is no consistent relation between surface flow speeds and the profile mean. The mean relationship is v=0·56 vsurf, which departs significantly from the theoretical smooth-surface relation v=0·67 vsurf, and exhibits a considerable scatter of values that show a dependence on flow depth. Given the inapplicability of any fixed conversion factor, and the dependence on flow depth, it is suggested that the use of dye timing as a method for estimating v be abandoned in favour of precision depth measurement and the use of the relation v=Q/wd, at least within the laminar flow range tested.