TECHNICAL NOTES
Nov 15, 2004

Efficient Algorithm for Computing Einstein Integrals

This article has a reply.
VIEW THE REPLY
This article has a reply.
VIEW THE REPLY
This article has a reply.
VIEW THE REPLY
This article has a reply.
VIEW THE REPLY
Publication: Journal of Hydraulic Engineering
Volume 130, Issue 12

Abstract

Analytical approximations to Einstein integrals are proposed. The approximations represented by two fast-converging series are valid for all values of their arguments. Accordingly, the algorithm can be easily incorporated into professional software like HEC-RAS or HEC-6 with minimum computational effort.

Get full access to this article

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

References

1.
Andrews, L.C. ( 1985). Special functions of mathematics for engineers, McGraw–Hill, New York.
2.
Einstein, H.A. ( 1950). “The bed load function for sediment transportation in open channel flows.” U.S. Department of Agriculture, Soil Conservation Service, Washington, D.C.
3.
Guo, J. ( 2002). “Approximations of gamma function and psi function and their applications in sediment transport.” Advances in hydraulics and water engineering, Proc. 13th IAHR-APD Congress, World Scientific, Singapore, 1, 219–223.
4.
Guo, J., and Hui, Y. J. (1991). “A further study on Einstein’s sediment transport theory.” Adv. Water Sci., 2(2), 81–91 (in Chinese).
5.
Guo, J., and Wood, W. L. (1995). “Fine suspended sediment transport rates.” J. Hydraul. Eng., 121(12), 919–922.
6.
Julien, P.Y. ( 1995). Erosion and sedimentation, Cambridge University Press, Cambridge, U.K.
7.
Nakato, T. (1984). “Numerical integration of Einstein’s integrals, I1 and I2.” J. Hydraul. Eng., 110(12), 1863–1868.
8.
U.S. Army Corps of Engineers. ( 1993). HEC-6 user’s manual, version 4.1, Hydrologic Engineering Center, Davis, Calif.
9.
U.S. Army Corps of Engineers. ( 2003). HEC-RAS user’s manual, Version 3.1.1, Hydrologic Engineering Center, Davis, Calif.

Information & Authors

Information

Published In

Go to Journal of Hydraulic Engineering
Journal of Hydraulic Engineering
Volume 130Issue 12December 2004
Pages: 1198 - 1201

History

Published online: Nov 15, 2004
Published in print: Dec 2004

Permissions

Request permissions for this article.

Authors

Affiliations

Junke Guo
Dept. of Civil Eng., Univ. of Nebraska-Lincoln, 205C PKI, 1110 S. 67th St., Omaha, NE 68182; and, Affiliate Faculty, State Key Lab of Water Resources and Hydropower Eng. Sci., Wuhan Univ., Hubei 430072, PRC.
Pierre Y. Julien
Professor, Engineering Research Center, Dept. of Civil Engineering, Colorado State Univ., Fort Collins, CO 80523. E-mail: [email protected]

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