Explicit Solution for the Specific Flow Depths in Partially Filled Pipes
This article has a reply.
VIEW THE REPLYThis article has a reply.
VIEW THE REPLYPublication: Journal of Pipeline Systems Engineering and Practice
Volume 8, Issue 4
Abstract
This paper presents an explicit solution for the specific flow depths in partially filled pipes of circular cross-sectional area. Four depths encounter in most classical free-surface flow problems, namely the normal depth, the critical depth, the sequent depths from the specific momentum equation, and the alternate depths from the specific energy equation. This paper proposes new equations derived from dimensional analysis and gene expression programming to estimate directly those flow depths. The equations are examined over a wide range of flow and geometric conditions, providing satisfactory predictions when compared with the exact solution obtained from the governing hydraulic equations. Maximum error encountered in the critical and normal flow depths predictions is less than 1.25%, and maximum error encountered in the alternate and sequent flow depths predictions is less than 3.85%, which are acceptable in most hydraulic engineering practice. The equations are simple and would be useful in hydraulic engineering practice when quick and accurate estimates are needed of those depths, and can also be used to find the initial values for the flow depth in various theoretical and numerical schemes.
Get full access to this article
View all available purchase options and get full access to this article.
References
Akgiray, O. (2005). “Explicit solutions of the Manning equation for partially filled circular pipes.” Can. J. Civil Eng., 32(3), 490–499.
Barr, D. H., and Das, M. M. (1986). “Direct solutions for normal depth using the Manning equation.” Proc. Inst. Civ. Eng., 81(3), 315–333.
Bashiri-Atrabi, B. H., Hosoda, T., and Shirai, H. (2016a). Development of an undular bore in a circular pipe: Experimental and numerical assessment, Taylor & Francis Group, Boca Raton, FL, 167–171.
Bashiri-Atrabi, B. H., Hosoda, T., and Shirai, H. (2016b). “Propagation of an air-water interface from pressurized to free-surface flow in a circular pipe.” J. Hydraul. Eng., 04016055.
Chaudhry, M. H. (2008). Open channel flow, Springer, New York.
Chow, V. T. (1959). Open channel hydraulics, McGraw-Hill, New York.
Draper, N., and Smith, H. (1998). Applied regression analysis, 3rd Ed., John Wiley & Sons, Inc., Hoboken, NJ.
Elhakeem, M., and Sattar, A. M. (2015). “An entrainment model for nonuniform sediment.” Earth Surf. Processes Landforms, 40(9), 1216–1226.
Ettema, W., Papanicolaou, T., Wilson, C., and Abban, B. (2014). “Alternative tile intake design for tile drainage: A case study.” World Environmental and Water Resources Congress, ASCE, Portland, OR, 1272–1281.
Ferreira, C. (2001). “Gene expression programming: A new adaptive algorithm for solving problems.” Complex Syst., 13(2), 87–129.
Finney, R. L., Weir, M. D., and Giordano, F. R. (2001). Thomas’ calculus, 10th Ed., Addison Wesley Longman, New York.
French, R. H. (1985). Open channel hydraulics, McGraw-Hill, New York.
Ghani, A., and Azamathulla, H. (2011). “Gene-expression programming for sediment transport in sewer pipe systems.” J. Pipeline Syst. Eng. Practice, 102–106.
Guo, J., and Meroney, R. N. (2013). “Theoretical solution for laminar flow in partially-filled pipes.” J. Hydraul. Res., 51(4), 408–416.
Henderson, F. M. (1966). Open channel flow, Prentice-Hall, New York.
Jeppson, R. W. (1965). “Graphical solutions to frequently encountered fluid flow problems.”, Utah State Univ., Logan, UT.
Lotfi, Z., Lakhdar, D., Larbi, H., and Nouredin, R. (2014). “New equation for the computation of flow velocity in partially filled pipes arranged in parallel.” Water Sci. Technol., 70(1), 160–166.
Mays, L. (2010). Water resources engineering, 2nd Ed., John Wiley & Sons, Inc., Somerset, NJ.
Najafzadeh, M., and Lim, S. Y. (2015). “Application of improved neuro-fuzzy GMDH to predict scour depth at sluice gates.” Earth Sci. Inf., 8(1), 187–196.
Politano, M., Odgaard, A. J., and Klecan, W. (2007). “Case study: Numerical evaluation of hydraulic transients in a combined sewer overflow tunnel system.” J. Hydraul. Eng., 1103–1110.
Sattar, A. M. (2014). “Gene expression models for the prediction of longitudinal dispersion coefficients in transitional and turbulent pipe flow.” J. Pipeline Syst. Eng. Practice, 04013011.
Sattar, A. M., Radecki-Pawlik, A., and Ślizowski, R. (2013). “Using genetic programming to predict scour downstream rapid hydraulic structures from experimental results.” Int. Workshop on Hydraulic Design of Low-Head Structures 2013, S. Pagliara and D. Bung, eds., FH Aachen Univ. of Applied Sciences, Aachen, Germany.
Silvester, R. (1964). “Hydraulic jump in all shapes of horizontal channels.” J. Hydraul. Div., 90(1), 23–55.
Stahl, H., and Hager, W. H. (1999). “Hydraulic jump in circular pipes.” Can. J. Civil Eng., 26(3), 368–373.
Straub, W. O. (1978). “A quick and easy way to calculate critical and conjugate depths in circular open channels.” Civil Eng., 48(12), 70–71.
Swamee, P. K. (1993). “Critical depth equations for irrigation channels.” J. Irrig. Drain. Eng., 400–409.
Vatankhah, A. R., and Easa, S. M. (2011). “Explicit solutions for critical and normal depths in channels with different shapes.” Flow Meas. Instrum., 22(1), 43–49.
Information & Authors
Information
Published In
Journal of Pipeline Systems Engineering and Practice
Volume 8 • Issue 4 • November 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Jan 6, 2017
Accepted: Apr 4, 2017
Published online: Jun 23, 2017
Published in print: Nov 1, 2017
Discussion open until: Nov 23, 2017
Authors
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.