Empirical Modeling of Flow Characteristics in Suddenly Expanding Channels

Document Type : Regular Article


Department of Civil Engineering, Jaypee University of Engineering & Technology, Guna (MP), India



Different flow characteristics namely sequent depth ratio, relative height of jump, relative energy loss, efficiency, relative length of jump and relative length of roller in suddenly expanding channel against inflow Froude number varying between 2 to 9 at different expansion ratios B1/B2 (0.4, 0.5, 0.6 and 0.8) as third variable are experimentally studied. Physical explanations of the variation of these characteristics with Froude number are discussed based on the results from experiments. Empirical models are proposed for all the six characteristics for rectangular and suddenly expanding channels using Buckingham π-method which gives quite satisfactory results when compared with other researchers result. Effectiveness of baffle blocks and sills (with different configurations) were also discussed in dissipating maximum energy. Due weightage has been given to Froude and Reynold’s number in present study as reported literature as well. As a result, baffle block and sills caused a significant improvement in sequent depth ratio by an amount of 30%, reduction in relative length of jump ratio and relative length of the roller by an amount of 38% and 37% respectively. Hence, energy dissipation increases due to appurtenances.


Main Subjects

Achor, B. (2000). Hydraulic Jump in a Suddenly Widened Circular Channel. Journal of Hydraulic Research, 38 (4), 307 – 311. https://doi.org/10.1080/00221680009498330
Afzal. N., & Bushra. A. (2002). Structure of Turbulent Hydraulic Jump in a Trapezoidal Channel. Journal of  Hydraulic Research, 40 (2), 205 – 214. https://doi.org/10.1080/00221680209499863
Agarwal, V. C. (2001, March). Graphical solution to the problem of sequent depth and energy loss in spatial hydraulic jump. Proceedings of the Institution of Civil Engineers-Water and Maritime Engineering. Thomas Telford Ltd. https://doi.org/10.1680/wame.2001.148.1.1

Alhamid, A. A. (2004). S-jump characteristics on sloping basins. Journal of Hydraulic Research, 42(6), 657-662. https://doi.org/10.1080/00221686.2004.9628319

Bai, R. (2023). Prototype air-water flow measurements in D-type hydraulic jumps. Journal of Hydraulic Research, 61(1), 145-161. https://doi.org/10.1080/00221686.2022.2132310
Bai, R., Ning, R., Wang, H., & Liu, S. (2022). Hydraulic jump on a partially vegetated bed. Water Resources Research, 58, e2022WR032013. https://doi.org/10.1029/2022WR032013
Bai, R., Wang, H., Tang, R., Liu, S., and Xu, W. (2021), Roller characteristics of pre-aerated high-Froude-number hydraulic jumps. Journal of Hydraulic Engineering, 147(4), 04021008. https://doi.org/10.1061/(ASCE)HY.1943-7900.00018
Bakhmeteff, B. A., & Matzke, A. E. (1936). The hydraulic jump in terms of dynamics similarity. Transaction of ASCE, 100, 630 - 680.
Belanger, J. B. (1849). Notes sur le Cours d’Hydraulique (Lectures Notes on Hydraulic Engineering). Me´m. Ecole Nat. Ponts et Chausse´es, Paris, France, session 1849–1850.
Bidone, G. (1819). Observation on height of hydraulic jump: A report presented in December 12. Meeting of the Royal Academy of Science, Turin.
Bremen, R. (1990). Expanding stilling basin. Communication (Laboratoire de constructions hydrauliques, Ecole polytechnique fédérale de Lausanne), 3. Lausanne, EPFL-LCH, ISSN: 1661-1179.
Bremen, R., & Hager, W. H. (1993). T - jump in abruptly expanding channel. Journal of Hydraulic Research, 31(1), 61-73. https://doi.org/10.1080/00221689309498860.
Bretz, N.V. (1987). Ressaut Hydraulique Force par Seuil. Thesis No. 699, presented to the Swiss Federal Insitute of Technology, Lausanne (EPFL). Appeared also as Communication No. 2, laboratorie de Construction Hydrauliques, EPFL, ed. R. Sinniger, Lausanne, Switzerland.
Chow, V. T. (1959). Open Channel Hydraulic. McGraw-Hill Book Company, Inc., New York.
Daneshfaraz, R., Aminvash, E., Di Francesco, S., Najibi, A., &Abraham, J. (2021a). Three-dimensional study of the effect of block roughness geometry on inclined drop. Journal of  Numerical  Methods in Civil Engineering 6, 1–9. https://doi.org/10.52547/NMCE.6.1.1
Daneshfaraz, R., Aminvash, E., Ghaderi, A., Kuriqi, A., & Abraham, J. (2021b). Three-dimensional investigation of hydraulic properties of vertical drop in the presence of step and grid dissipators. Symmetry, 13, 895. https://doi.org/10.3390/sym13050895
Daneshfaraz, R., Hasannia, V., Norouzi, R., Sihag, P., Sadeghfam, S., & Abraham, J. (2021c). Investigating the effect of horizontal screen on hydraulic parameters of vertical drop. Overview. The Iranian Journal of Science and Technology, 45, 1909–1917. https://doi.org/10.1007/s40996-020-00572-w
Daneshfaraz, R., Majedi Asl, M., & Mirzaee, R. (2019a). Experimental study of expanding effect and sand roughened bed on hydraulic jump characteristics. Iranian Journal of Soil and Water Research, 50(4), 885-896. (In Persian). https://doi.org/10.22059/IJSWR.2018.261923.667968
Daneshfaraz, R., Mirzaee, R., Ghaderi, A., & MajediAsl, M. (2019b). The S-jump’s characteristics in the rough sudden expanding stilling basin. AUT Journal of Civil Engineering, 4(3), 349-354. (In Persian). https://doi.org/10.22060/AJCE.2019.16427.5586.
Esmaeeli, V. M. (2005). Modeling Hydraulic Jumps with Artificial Neural Networks. Journal of Water Management, 158 (WM2), 65 – 70. https://doi.org/10.1680/wama.2005.158.2.65
Ghaderi, A., & Abbasi, S. (2019). CFD simulation of local scouring around airfoil-shaped bridge piers with and without collar. Sadhana, 44(10), 216. https://doi.org/10.1007/s12046-019-1196-8
Ghaderi, A., Abbasi, S., Abraham, J., et al. (2020). Efficiency of trapezoidal labyrinth shaped stepped spillways. Flow Measurement and Instrumentation. https://doi.org/j.flowmeasinst. 2020.101711
Graber, S. D., Ohtsu, I., Yasuda, Y., & Ishikawa, M. (2001). Submerged hydraulic jumps below abrupt expansions–discussions. Journal of Hydraulic Engineering, 127(1), 84-85. https://doi.org/10.1061/(ASCE)0733-9429(2001)127:1(84)
Hager, W. H. (1989). Hydraulic Jump in U -Shaped Channel. Journal of Hydraulic Engineering, 115(5), 667–675. https://doi.org/10.1061/(ASCE)0733-9429(1989)115:5(667)
Hager, W. H. (1985). Hydraulic jump in non-prismatic rectangular channels. Journal of Hydraulic Research, 23, 21–35. https://doi.org/10.1080/00221688509499374
Herbrand, K. (1973). The spatial hydraulic jump. Journal of Hydraulic Research, 11(3), 205-217. https://doi.org/10.1080/00221687309499774
Jamil, M., & Khan S. A. (2008). Theoretical Study of Hydraulic Jump in Trapezoidal Channel Section. Journal of Institution of Engineer (India), 89, 28–32.
Jan, C., & Chang, C. (2009). Hydraulic jumps in an inclined rectangular chute contraction. Journal of Hydraulic Engineering, 135(11), 949-958. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000100
Jesudhas, V., Balachandar, R., & Bolisetti, T. (2019). Numerical study of a symmetric submerged spatial hydraulic jump. Journal of Hydraulic Research, 58(2), 335-349. https://doi.org/10.1080/00221686.2019.1581668
Khosravinia, P., Sanikhani, H., & Abdi, C. (2018). Application of soft computing techniques to Predict of hydraulic jump length on rough beds. Journal of Rehabilitation in Civil Engineering, 6(2), 147-162. https://doi.org/10.22075/JRCE.2017.11047.1180
Kumar, M., & Lodhi, A. (2016). Hydraulic jump over sloping rough floors, ISH Journal of Hydraulic Engineering, 22(2), 127-134. https://doi.org/10.1080/09715010.2015.1088409
Negm, A. M. (2000). Empirical prediction of properties of R-jump and submerged S-jump in abruptly expanding stilling basins. Egyptian Journal for Engineering Sciences and Technology, (EJEST), Zagazig University, Zagazig, Egypt.
Negm, A. M., Ibrahim, A. A., & Salem, M. N. (2000). Modeling of depth ratio of hydraulic jumps in abruptly enlarged stilling basins. Civil Engineering Research Magzine (CERM), Faculty of Engineering, Ain Shams University, Cairo, Egypt.
Noor, A, & A. Bushra (2002). Structure of the turbulent hydraulic jump in a trapezoidal channel. Journal of Hydraulic Research, 40(2), 205-214, https://doi.org/10.1080/00221680209499863.
Ohtsu, I., Y. Yasuda, & H. Gotoh (2003). Flow Conditions of Undular Hydraulic Jumps in Horizontal Rectangular Channels.  Journal of Hydraulic Engineering, 2003. 129(12), 948–955. https://doi.org/10.1061/(ASCE)0733-9429(2003)129:12(948)
Ohtsu, I., Yasuda Y., & Gotoh H. (1997). Discussion of characteristics of undular hydraulic jumps: experimental apparatus and flow patterns, Journal of Hydraulic Engineering ASCE, 123(2), 161-162. https://doi.org/10.1061/(ASCE)0733-9429(1997)123:2(161
Ohtsu, I., Yasuda Y., & Gotoh H. (1996). Discussion of non breaking undular hydraulic jumps, Journal of Hydraulic Research IAHR, 34(2), 567–572. https://doi.org/10.1080/00221689609498479
Ohtsu, I., Yasuda Y., & Gotoh H. (1995). Characteristics of undular hydraulic jumps in rectangular channels, Proceeding of 26th IAHR Congress, 1C14, London, UK.
Omid, M. H. Esmaeeli M., and Narayanan R. (2008). Gradually Expanding Hydraulic Jump in a Trapezoidal Channel. Journal of Hydraulic Research, 45 (4), 512 – 518. https://doi.org/10.1080/00221686.2007.9521786
Pagliara, S., & Chiavaccini, P. (2006). Energy dissipation on block ramps. J. Hydraulic Engineering, 132(1), 41-48. https://doi.org/10.1061/(ASCE)0733-9429(2006)132:1(41)
Peterka, A. J. (1958). Hydraulic Design of Stilling Basins and Energy Dissipaters. US Department Interior, Bureau of Reclamation, Engineering Monograph 25, Denver, Colorado.
Rajaratnam, N. (1964). Discussion to silvester. Journal of Hydraulic Division, 90(HY4), 341-350.
Ranga Raju, K. G. (1993). Flow Through Open Channels. McGraw Hill, New Delhi, 1993, 2nd Edn. ISBN: 007096565X, 9780070965652
Ranga Raju, K. G., Mittal, M. K., Verma, M. S., & Ganeshan, V. R. (1980). Analysis of flow over baffle blocks and end sills. Journal of Hydraulics Research, 18(3), 227-241. https://doi.org/10.1080/00221688009499549.
Reinauer, R., and Hager, W. H. (1995). Non-Breaking Undular Hydraulic Jump- Discussion. Journal of Hydraulic Research, 34 (4), 567 – 573. https://doi.org/10.1080/00221689609498479
Sadeghfam, S., Khatibi, R., Hassanzadeh, Y., Daneshfaraz, R., & Ghorbani, M. A. (2017). Forced hydraulic jumps described by classic hydraulic equations reproducing cusp catastrophe features. Arabian Journal for Science and Engineering, 42, 4169–4179. https://doi.org/10.1007/s13369-017-2616-x
Tyagi, D. M., Pande, P. K. and Mittal, M. K. (1978). Drag on baffle walls in Hydraulic jump. Journal of the hydraulic Division, Proceeding of ASCE, 104 (4), 515 – 525. https://doi.org/10.1061/JYCEAJ.0004976
Torkamanzad, N., Hosseinzadeh Dalir, A., Salmasi, F., & Abbaspour, A. (2019). Hydraulic jump below abrupt asymmetric expanding stilling basin on rough bed. Water, 11(9), 1756. https://doi.org/10.3390/w11091756
Unny, T. E. (1961). The spatial hydraulic jump. Proc. 9th Convention International Association for Hydraulic Research, IAHR, Belgrad.
Zare, H. K., & Doering, J. C. (2011). Forced hydraulic jumps below abrupt expansions. Journal of Hydraulic Engineering, 137, 825–835. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000369
Zhou, Y., Wu, J., & Ma, F., et al. (2020). Uniform flow and energy dissipation of hydraulic jump stepped spillways. Water Supply. https://doi.org/10.2166/ws.2020.056