The drag coefficient and settling velocity of natural sediment particles

Abstract

This article reports a study in which drag coefficient is defined more comprehensively. The coefficient is defined as a function of particle nominal diameter, gravitational acceleration, the ambient fluid kinematic viscosity, and the particle shape. This new definition is different from the conventional definitions proposed in the literature based on direct equations as a function of particle Reynolds number. The conventional definitions appear to be a simplification of drag coefficient and thus decreasing the accuracy of the estimations. Instead, the proposed equation in this article indicates that on average the drag coefficient estimation can be improved at least 3.77% compared to the proposed drag coefficient widely used in the literature. The improved drag coefficient was used to derive a more accurate settling velocity equation in which the effect of particle shape is directly incorporated in the settling velocity equation. Both equations were validated using well known datasets and accurate experiments from the literature as well as new experiments conducted for this purpose in the current research. The experiments cover a wide range of particle shape and a variety of specific gravity. The outcomes of the current study contribute to the use of settling velocity in river hydraulic applications proposing a simpler but more accurate procedure.

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Abbreviations

A, B, m :

Variables

A p :

Particle projected area

a, b, c :

Particles long, intermediate, and short orthogonal dimensions, respectively

a 1 , a 2 , a 3 , a 4 , a 5 :

Shape factor related variables

S :

Specific gravity of the sediment particle

g :

Gravitational acceleration (m2/s)

d :

Sediment particle diameter (m)

d n :

Sediment particle nominal diameter (m)

F d :

Drag force (N)

C D :

Drag coefficient

n :

Number of experiments

ω :

Settling velocity (m/s)

ν :

Fluid kinematic viscosity (m2/s)

ρ :

Density of the fluid (kg/m3)

Sf :

Corey shape factor

D * :

Dimensionless particle diameter

V :

Particle volume

Re p :

Particle Reynolds number

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Acknowledgements

Authors would like to thank Professor Weiming Wu for sharing his valuable dataset and his comments on an earlier draft of this article, and to Professor Mehdi Riazi for his careful reading and editing and his suggestions for the improvement of the text structure. Authors would like to also thank the anonymous reviewers for their helpful and constructive comments that greatly contributed to improving the final version of the article.

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Correspondence to Amin Riazi.

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Riazi, A., Türker, U. The drag coefficient and settling velocity of natural sediment particles. Comp. Part. Mech. 6, 427–437 (2019). https://doi.org/10.1007/s40571-019-00223-6

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Keywords

  • Drag coefficient
  • Sediment
  • Settling velocity
  • Particle shape
  • Particle size