Abstract
A common and practical type of hydraulic jump at sloping bed (e.g., concrete, gabion or rock cover bed chutes) is B-jump which its toe located on the sloping bed and ended at the downstream horizontal channel. Determination of hydraulic jump characteristics such as the sequent depth ratio can help to design a safe and economic stilling basin. Many studies have been carried out for B-jump on smooth sloping bed; however on the effect of roughness on jump characteristics no relation is available. In this paper first a general non-dimensional relation was developed using Buckingham theorem. Then by applying the incomplete self similarity theory and using a new dimensionless parameter, N, a new non dimensional relation was developed. The significant of such relation is that it is independent of bed slope. To verified such relation two series of tests were conducted at the hydraulic lab using three different slope angles, five different roughness heights and five different flow conditions both on smooth and roughened bed. The collected data were analyzed by SPSS15.0 software and the required coefficients were obtained. The proposed expression was tested using wide range of data and the average absolute error was found to be 6.4%.
Similar content being viewed by others
References
Adam, A. M. (1986). Boundary shear stress and pressure fluctuations on sloping surfaces, PhD Thesis, Colorado State University, Fort Colinns, Colo, USA.
Adam, A. M., Ruff, J. F., AlQaser, G., and Abt, S. R. (1993). “Characteristics of B-jump with different toe locations.” J. Hydraul. Eng., Vol. 119, No. 8, pp. 938–948, DOI: 10.1061/(ASCE)0733-9429(1993)119:8(938).
Beirami, M. and Chamani, M. (2006). “Hydraulic jumps in sloping channels: Sequent depth ratio.” J. Hydraul. Eng., Vol. 132, No. 10, pp. 1061–1068, DOI: 10.1061/(ASCE)0733-9429(2006)132:10(1061).
Bradley, J. N. and Peterka, A. J. (1957). “Hydraulic design of stilling basins: Stilling basin with sloping apron (Basin V).” J. Hydraul. Div., Vol. 83, No. 5, pp. 1–32.
Bureau of Reclamation (1987). Design of small dams, United State Department of the Interior, Bureau of Reclamation, Water Resource technical Publication, 880p.
Carollo, F., Ferro, V., and Pampalone, V. (2007). “Hydraulic jumps on rough beds.” J. Hydraul. Eng., Vol. 133, No. 9, pp. 989–999, DOI: 10.1061/(ASCE)0733-9429(2007)133:9(989).
Carollo, F., Ferro, V., and Pampalone, V. (2009). “New solution of classical hydraulic jump.” J. Hydraul. Eng., Vol. 135, No. 6, pp. 527–531, DOI: 10.1061/(ASCE)HY.1943-7900.0000036.
Carollo, F., Ferro, V. and Pampalone, V. (2011). “Sequent depth ratio of a B-jump.” J. of Hydraul. Eng., Vol. 137, No. 6, pp. 651–658, DOI: 10.1061/(ASCE)HY.1943-7900.0000042.
Hager, W. H. (1988). “B-jump in sloping channel.” J. Hydraul. Res., Vol. 26, No. 5, pp. 539–558, DOI: 10.1080/00221689009499150.
Hager, W. H. (1992). Energy dissipators and hydraulic jump, Kluwer Academic, Dordrecht, Netherlands.
Hager, W. H. and Bremen, R. (1989). “Classical hydraulic jump: Sequent depths.” J. Hydraul. Res., Vol. 27, No. 5, pp. 565–585, DOI: 10.1080/00221688909499111.
Hughes, W. C. and Flucks, J. E. (1984). “Hydraulic jump properties over a rough bed.” J. Hydraul. Eng., Vol. 110, No. 12, pp. 1755–1771, DOI: 10.1061/(ASCE)0733-9429(1984)110:12(1755).
Kawagoshi, N. and Hager, W. H. (1990). “B-jump in sloping channel, II.” J. Hydraul. Res., Vol. 28, No. 4, pp. 461–480, DOI: 10.1080/00221689009499060.
Kindsvater, C. E. (1944). “The hydraulic jump in sloping channels.” Trans., ASCE, Vol. 109, pp. 1107–1120.
Ohtsu, I. and Yasuda, Y. (1991). “Hydraulic jump in sloping channels.” J. Hydraul. Eng., Vol. 117, No. 7, pp. 905–921, DOI: 10.1061/(ASCE)0733-9429(1991)117:7(905).
Rajaratnam, N. (1965). “The hydraulic jump as a wall jet.” J. Hydraul. Div., Vol. 91, No. 5, pp. 1–5.
Rajaratnam, N. and Murahari, V. (1974). “Flow characteristics of sloping channel jumps.” J. Hydr. Div., Vol. 100, No. 6, pp. 731–740.
Shokrian, M. and Shafai Bejestan, M. (2013). “Accuracy of available empirical relationships useful for estimating the sequent depth ratio of a B-jump by using of experimental data.” 9th Int. River Eng. Conference, 22–24 Jan, Shahid Chamran University, Ahwaz, Iran, pp. 1–8.
SPSS (2006). SPSS 15 Command Syntax Reference, SPSS Inc., Chicago, IL.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bejestan, M.S., Shokrian, M. Mathematical expression for the B-Jump sequent depth ratio on sloping bed. KSCE J Civ Eng 19, 790–795 (2015). https://doi.org/10.1007/s12205-013-0434-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-013-0434-6