The use of the salt-velocity method for the precise measurement of resistance to flow in rough-boundary open channels

Abstract

Present methods of measuring the hydraulic radius and mean velocity in very rough channels are shown to be arbitrary and inconsistent. Rough bed streams are conceptually divided into a flow zone, in terms of whose properties a rational friction factor is defined and calculated, and dead zones (or stationary eddies), which do not contribute to the discharge and whose role as energy dissipators is reflected in the value of the friction factor.

A mean velocity for a non-prismatic flow zone is defined, and a tracer technique for measuring it is presented, in which tracer is detected using electrodes which extend to the full depth of the flow and are wide in the direction of flow. It is shown by a combination of a mathematical model and measurements of electric potential gradient that their behaviour closely approximates that of an ideal hypothetical detection apparatus which responds equally to tracer at any point on the detection cross-section, and not at all to tracer on any other cross-section.

It is shown that the true mean velocity of tracer particles is not given by the traditional ratio of distance divided by the time value at the centroid of the conductivity time curve, but rather by distance multiplied by the position on the inverse time axis of the centroid of a conductivity curve transformed by plotting inverse time as abscissa. At the instant of plane injection in the flow zone the mean tracer velocity is equal to the flow zone mean velocity, and thereafter decreases continuously for some considerable distance downstream owing to the trapping and slow release of tracer by dead zones. Tracer is detected at four distances downstream from injection, and the trend in mean tracer velocity is extrapolated to zero distance from injection to give a flow zone mean velocity. Because the mean tracer velocity is measured over lengths of channel greater than one roughness pattern wavelength, this method can be used for non-prismatic flow zones. The validity of this procedure for flow over strip roughness was checked by flow visualisation experiments, which gave an independent measure of flow zone mean velocity. Application of this technique to gravel and boulder beds, in conjunction with a measurement of the variation of porosity with elevation which quantifies the relationship of flow cross-sectional area to depth of flow in such beds, allows realistic flow datum levels to be determined.

Finally, by measuring the surface area per unit volume of the stones in the rough bed, rational hydraulic radii are calculated. Friction factors calculated from these hydraulic radii and the tracer-measured flow zone mean velocities are presented and compared with those found in other research. Results for the two rough beds tested indicate that the new friction factor is less sensitive to the relative depth than are friction factors found in other research on flow at small relative depths.