# Influence of shape on the fall velocity of sedimentary particles

1953-05

## Authors

Schulz, Edmund F., author
Wilde, Robert Harris, author
Albertson, Maurice L., author
Colorado Agricultural and Mechanical College, Department of Civil Engineering, publisher

## Abstract

Techniques used in modern sediment engineering require knowledge of the fall velocity of sediment particles in water. Under certain conditions the fall velocity of a sphere can be computed using Stokes Law. Stokes Law, however, considers only the viscous forces on the particle. The resistance of particles falling in water is attributed to (1) viscous deformation of the fluid, and (2) inertial losses in the fluid caused by acceleration (both tangential and normal acceleration) of the fluid around the particle. The Reynolds number (a ratio of the inertial forces to the viscous forces) is a dimensionless parameter which expresses the relative importance of the inertial forces to the viscous forces in the motion of the fluid around the particle. Stokes Law is valid when the viscous forces are the predominate cause of the resistance of the particle. As Reynolds numbers become greater than 1.0 the inertial forces assume greater importance and any equation which considers only the viscous forces (such as Stokes Law) becomes less and less valid. A quartz sphere approximately 0.1 mm diameter falling in water at 20°C (67°F) would have a Reynolds number of 1.0. To study the fall velocity of natural particles, dimensionless parameters were employed to give general solutions to the equations involved. The principal parameters employed were the Reynolds number (ratio of inertial forces to viscous forces), the drag coefficient (intensity of drag force) and the shape factor. Particles were selected at random from a number of samples of sediment having different geographical and geologic origins. The shape factor of these particles was measured. The particles were then dropped in water and the fall velocity measured. By measuring the weight, the volume, the fall velocity and the shape of the particle, the dimensionless parameters previously listed could be computed and a graph of drag coefficient versus Reynolds number with the shape factor as a third variable could be prepared. The particles studied in this manner ranged in size from 0.25 mm to 25 mm. To verify the results from the tests on the small particles, the gravel-sized particles were also dropped in oil. Because of the viscosity difference between the water and the oil, the larger gravel-sized particles had Reynolds numbers between 1.0 and 500 when dropped in oil. It was found that the affects of surface roughness could not be ignored; therefore, data obtained from the extremely rough particles were separated from the more rounded material by plotting on separate graphs. The data obtained by Krumbein and Malaika in tests on artificial particles were also plotted on these two graphs. Other information regarding the extent of variation of the shape factor, relation of average shape factor to sieve size, relation of sieve size to nominal diameter and intermediate axes, relation of sieve diameter to sedimentation diameter and shape factor have also been investigated. All the available data have been assembled in the Appendix.

## Description

Prepared for District Engineer, Omaha District, Corps of Engineers, Department of the Army under contract no. DA-15-075-eng 2266 through the Colorado A & M Research Foundation.
Includes bibliographical references (pages 86-89).
May 1953.

## Subject

Hydrodynamics
Sedimentation and deposition