B-f jump characteristics in smooth sloping beds

Document Type : Research Paper

Abstract

Beacause of the hydraulic jump unstable behavior in adverse-slope stilling basins downstream of sloping beds, the jump toe is transmitted on sloping bed. Therefore, formation of the B-F jump is common in practice. In this research, using dimensional analysis and Incomplete Self-Similarity (ISS) theorem, a general equation was derived to computation of the sequent depth ratio of a B-F jump on smooth sloping bed. The experiments were conducted in a physical model for three different slopes of upstream channel (13.5, 21.5 and 29.5 degree) and downstream stilling basin (-0.05, -0.1 and -0.15 %). The results showed that the sequent depth ratio decreases as the slope of stilling basin increases so that for the stilling basin with the slope of 0.15 % and for the constant position of the jump (E0=0.5), the sequent depth ratio decreases about 60% compared with the slope of 0.05% . Then, the roller length was investigated and based on relative energy loss in the jump a general equation was derived to calculate the roller length of a B-F jump. The results showed that the equation of roller length is independent of upstream channel and stilling basin slopes. Finally, using all of the experimental data the required coefficients were calculated and the mean percentage errors were obtained 8.71 and 13.31 % for the sequent depth and roller lenghth equations respectively

Keywords

• Hydraulic jump
• energy dissipation
• sloping bed
• B-F jump
• Stiling basin

20.1001.1.20086377.1398.12.41.6.4

---

References

1)       Barenblatt, G.M.1979. Self-similarity and intermediate asymptotics. Consultants Bureau, New York.

2)       Bradley, J., and Peterka, A.1957. Hydraulic design of stilling basins Stilling basin with sloping apron (Basin V).  Journal of Hydraul Div 83(5):1–32.

3)       Beirami, K., and Chamani, R. 2006. Hydraulic jump in sloping channel: Sequent depth.Journal of Hydraulic Engineering. 132, No. 1, 1061–1068.

4)       Bateni, S. M., and Yazdandoost, F. 2009. Hydraulics of B-F and F jumps in adverse-slope stilling basins. Institution of Civil Engineers,162(5): 321-327.

5)       Carollo,  F., Ferro, V., and Pampalone, V. 2009. New solution of classical hydraulic jump. Journal of  Hydraulic  Engineering135(6): 527–531.

6)       Carollo, F., Ferro, V., and Pampalone, V. 2011. Sequent depth ratio of a B- jump. Journal of Hydraul Engineering 137(6): 651–658.

7)       Ferro, V. 2006. The arrangement of the river basins. 2nd Ed,McGraw-Hill Milano, Italy (in Italian).

8)       Hager, W. 1988. B-jump in sloping channel. Journal of Hydraulic Research  26(5): 539–558.

9)       Kindsvater, C.1944. The hydraulic jump in sloping channels. Trans ASCE 10(9): 1107–1120.

10)   Kawagoshi, N., and Hager, W.1990. B-jump in sloping channel  II. Journal of Hydraulic Research 28(4): 461–480.

11)   Khadara, M. H., and Rajagopals.1972. Hydraulic jump inadverse channel slopes.India Irrigation and Power Journal 29(1): 77–81.

12)   Mccorquodale, J. A., and Mohamed, S. 1994. Hydraulic jumpson adverse slope. IAHR Journal of Hydraulic Research 32(1): 119–130.

13)   Ohtsu, I., and Yasuda,Y.1991. Hydraulic jump in sloping channels. Journal of Hydraulic Engineering 117(7): 905–921.

14)   Ohashi, K., Skabe, I., and Akis. 1973. Design of combinedhydraulic jump and ski-jump energy dissipaters of floodspillway.Proceedings of 13th ICOLD Congress, Madrid. Q41(R.19), 311–333.

15)   Shokrian, M., and Shafai bejestan, M. 2014. Mathematical expression for the B-jump sequent depth ratio on sloping bed. KSCE Journal of Civil Enginnering 19(3): 790–795.

16)   Stevense, J. 1944. Discussion on the hydraulic jump in slopingchannels by C. E. Kindsvater.Transactions of the AmericanSociety of Civil Engineers. paper no. 2228, 1125–1135.