17 December 2021 | By: Anshul Yadav

Predicting flow velocity in gravel-bed rivers

The estimates of cross-sectional averaged flow velocity are essential in flood risk assessment for high flows, aquatic habitat protection in case of low flows, and a wide variety of scientific purposes in river research applications. However, direct measurements are difficult in high-gradient rivers, and a flow resistance equation is usually preferred for the velocity estimates. The flow resistance equations provide reliable estimates in low gradient rivers. But in the case of high-gradient rivers, some additional losses occur in case of low relative depth (y/D84), other than the form drag and friction drag. In this work, we hypothesized that the poorly sorted sediments would increase the flow resistance as the protrusions from the bed will increase, leading to distortions of free water surface, increase in spill losses, and turbulent wakes behind the large protruding elements. We tested our hypothesis using the eight well-known flow resistance equations, i.e., Strickler (1923), Keulegan (1938), Hey (1979), Smart and Jaggi (1983), Bathurst (1985), Ferguson (2007), Recking et al. (2008), Rickenmann and Recking (2011). The velocity predictions for the dataset characterized by σg > 7.5 were affected significantly for all the considered equations. Therefore we proposed an empirical approach to assess the additional losses occurring in the case of poorly sorted sediments as:


The coefficients a1, a2, and a3 were obtained by minimizing the difference between the actual observed values and values calculated using the conventional equations for the calibration dataset.

For example, the modified Ferguson (2007) equation would be expressed as:


The modified equations were found to be considerably better than their performances in the conventional form, both in terms of statistical indices and velocity predictions.

For more information, please have a look at our paper.

Yadav, A., Sen, S., Mao, L., & Schwanghart, W. (2022). Evaluation of flow resistance equations for high gradient rivers using geometric standard deviation of bed material.
Journal of Hydrology, 605, 127292.