Flow resistance in steep streams: An experimental study

Abstract

Frequently, an assessment of the mean water velocity in a stream is necessary to estimate the discharge associated with a particular flow depth or, conversely, the mean depth associated with a particular discharge. In the absence of a direct measurement of flow velocity, a flow resistance approach, which establishes the relation between depth and velocity, can be applied. Two approaches have been used in the past: traditional approaches based on the use of a resistance coefficient (e.g., Darcy‐Weisbach) or dimensionless hydraulic geometry approaches. To examine if one approach is more appropriate for steep streams, data from 31 flume experiments conducted to examine flow resistance in self‐formed cascade channels were analyzed. A dimensionless hydraulic geometry approach developed using at‐a‐station data to characterize the q* exponent and between‐site data to characterize the exponent on the channel slope term was more accurate than more traditional approaches. The developed relation was similar to the established rational relation (v α g0.2q0.6s−0.4S0.2), suggesting that the rational relation has merit. The approach does not utilize a flow partitioning approach since, in steep streams with small relative depths, the grains themselves generate form and spill resistance. The observation that a single dimensionless hydraulic geometry flow resistance relation can describe measurements across a range of grain sizes and bed slopes (3–21%) suggests that steep streams may follow a single scaling relation similar to the regime equations associated with lowland rivers.