TECHNICAL PAPERS
May 1, 1985

Near‐Bed Velocity Distribution

Publication: Journal of Hydraulic Engineering
Volume 111, Issue 5

Abstract

A continuous velocity distribution is derived for the laminar, transition, and logarithmic regions of the near‐bed portions of boundary layers for smooth and rough surfaces and drag‐reducing fluids. The solution is based on the equations of motion for uniform flow and a parabolic distribution of eddy viscosity over the turbulent portion of the boundary layer. Effects of increased roughness are accounted for by a shift of the distribution of eddy viscosity toward the flow boundary. The resulting velocity distribution agrees with published data and has an advantage over the classical logarithmic distribution for flow over rough surfaces in that the lower velocity limit is zero at the assigned origin for distance measurements near the boundary. The distribution function approaches the logarithmic expression in the outer regions of the boundary layer and has an advantage that the predicted slope of the velocity distribution is zero at the top of the boundary layer. Although the parabolic distribution of eddy diffusivity does not account for velocity distributions with wake components, other distributions of eddy diffusivity to account for these effects are suggested.

Get full access to this article

View all available purchase options and get full access to this article.

References

1.
Cebeci, T., and Bradshaw, P., Momentum Transfer in Boundary Layers, McGraw‐Hill Book Company, New York, N.Y., 1977, 391 pp.
2.
Coleman, N. L., “Velocity Profiles with Suspended Sediment,” Journal of Hydraulic Research, Vol. 19, No. 3, 1981, pp. 211–229.
3.
Coles, D., “The Law of the Wake in the Turbulent Boundary Layer,” Journal of Fluid Mechanics, No. 1, 1956, pp. 191–226.
4.
Dou Guoren, “Turbulent Flow of Polymer Solution and Its Friction Reduction Law,” Scientia Sinica, Vol. XXV, No. 7, 1982, pp. 759–770.
5.
Nikuradse, J., Laws of Turbulent Flow in Rough Pipes, Translation by National Advisory Committee for Aeronautics (NACA), TM 1292, (Originally published in German in 1933).
6.
Prandtl, L., Recent Results of Turbulence Research, Translations by NACA, TM 720 (Originally published in German in 1933).
7.
Schlichting, Hermann, Boundary Layer Theory, 6th Ed., McGraw Hill Book Company, New York, N.Y., 1968, pp. 565–574.
8.
Schubauer, G. B., and Tchen, C. M., Turbulent Flow, Princeton University Press, Princeton, N.J., 1961, 123 pp.
9.
Streeter, V. L., “Steady Flow in Pipes and Conduits,” Engineering Hydraulics, Chapter VI, Rouse, ed., John Wiley & Sons, Inc., New York, N.Y., 1950, pp. 387–401.
10.
Von Karman, T., Mechanical Similitude and Turbulence, Translation by NACA, TM 611 (Originally published in German in 1930).
11.
Willis, J. C., “A New Mathematical Model for the Velocity Distribution in Turbulent Shear Flow,” Journal of Hydraulic Research, Vol. 10, No. 2, 1972, pp. 205–225.
12.
Willis, J. C., “Analytical Velocity Distribution,” Journal of the Hydraulics Division, ASCE, Vol. 104, No. HY11, 1978, pp. 1541–1549.
13.
Zagustin, A., and Zagustin, K., “Analytical Solutions for Turbulent Flow in Pipes,” La Houille Blanche, No. 2, 1969, pp. 113–118.

Information & Authors

Information

Published In

Go to Journal of Hydraulic Engineering
Journal of Hydraulic Engineering
Volume 111Issue 5May 1985
Pages: 741 - 753

History

Published online: May 1, 1985
Published in print: May 1985

Permissions

Request permissions for this article.

Authors

Affiliations

Joe C. Willis
Research Hydr. Engr., USDA Sedimentation Lab., Southern Region, ARS, Oxford, Miss.

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share