Next Article in Journal
Dimensionless Analysis for Designing Domestic Rainwater Harvesting Systems at the Regional Level in Northern Taiwan
Previous Article in Journal
Rehabilitation Priority Determination of Water Pipes Based on Hydraulic Importance
Article Menu

Export Article

Open AccessArticle
Water 2014, 6(12), 3888-3912; doi:10.3390/w6123888

Application of Displacement Height and Surface Roughness Length to Determination Boundary Layer Development Length over Stepped Spillway

1,†,* , 2,†
and
1,†
1
School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510640, China
2
St. Anthony Falls Laboratory, Department of Civil Engineering, University of Minnesota, Minneapolis, MN 55112, USA
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Received: 27 August 2014 / Revised: 12 November 2014 / Accepted: 24 November 2014 / Published: 12 December 2014
View Full-Text   |   Download PDF [1082 KB, uploaded 9 June 2015]   |  

Abstract

One of the most uncertain parameters in stepped spillway design is the length (from the crest) of boundary layer development. The normal velocity profiles responding to the steps as bed roughness are investigated in the developing non-aerated flow region. A detailed analysis of the logarithmic vertical velocity profiles on stepped spillways is conducted through experimental data to verify the computational code and numerical experiments to expand the data available. To determine development length, the hydraulic roughness and displacement thickness, along with the shear velocity, are needed. This includes determining displacement height d and surface roughness length z0 and the relationship of d and z0 to the step geometry. The results show that the hydraulic roughness height ks is the primary factor on which d and z0 depend. In different step height, step width, discharge and intake Froude number, the relations d/ks = 0.22–0.27, z0/ks = 0.06–0.1 and d/z0 = 2.2–4 result in a good estimate. Using the computational code and numerical experiments, air inception will occur over stepped spillway flow as long as the Bauer-defined boundary layer thickness is between 0.72 and 0.79. View Full-Text
Keywords: displacement height; surface roughness length; stepped spillway; boundary layer development; numerical simulations; logarithmic law; inception of air entrainment displacement height; surface roughness length; stepped spillway; boundary layer development; numerical simulations; logarithmic law; inception of air entrainment
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Cheng, X.; Gulliver, J.S.; Zhu, D. Application of Displacement Height and Surface Roughness Length to Determination Boundary Layer Development Length over Stepped Spillway. Water 2014, 6, 3888-3912.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Water EISSN 2073-4441 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top