Using dimensional and theoretical analysis together with available experimental data, it has been shown how flow conditions and stream bed slope affect the beginning of sediment transport. The dimensional analysis shows that, in general, the Shields parameter is a function of the stream slope and the Reynolds number. The traditional Shields diagram is a special case of this relationship for a zero of near zero slope. The theoretical treatment is an adaptation of work from earlier authors, which is used in conjunction with dimensional analysis to show the interdependence of flow conditions and forces contributing to the critical point of particle motion. Additional experiments are recommended.
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Lau et al. (1999) studied this question.
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