New Expression for The Length of Free, Submerged, and B- Jumps

A hydraulic jump is used for energy dissipators below hydraulic structures, such as spillways and outlet conduits. When the downstream depth is greater than the subcritical depth sequent to a supercritical depth immediately downstream of an outlet, a submerged jump is formed. If a high speed discharge flowing down a steep spillway connected to a horizontal channel, a hydraulic jump is formed partly in the sloping portion and partly in the horizontal channel portion. This jump is referred to as B-jump. The hydraulic condition for the formation of B-jump has been determined by Ohtsu and Yasuda (1991). The submerged jump and the B-jump for θ > 19°~23° given by Ohtsu and Yasuda (1991) (θ = angle of sloping bed to horizontal) may be in the same category for hydraulic design of stilling basins (Rajaratnam, 1967).

For the length of the submerged jump, Rao and Rajaratnam (1963) proposed an empirical equation. Also, Rajaratnam (1965) recommended Stepanov’s empirical equation for the roller length. However, further study is required for the expression of the jump length and roller length (Ramaprasad and Ramamoorthy, 1966).

For B-jumps, the length of the roller was studied by Hager (1988) for θ = 45° and by Kawagoshi and Hager (1990) for θ = 30°. However, a general expression has not been derived because each study has been performed on the single channel slope θ.

In this study, the length of the free, submerged, and B-jumps for θ ≥ 22° can be represented by a unified empirical equation that demonstrates excellent correlation and considers the physical meaning of the jump length. The result may be useful in the hydraulic design of energy dissipators.

References

Hager (1988), J. Hydr. Res., 26(5), 539-558.

Kawagoshi and Hager (1990), J. Hydr. Res., 28(4), 461-480.

Ohtsu and Yasuda (1991), J. Hydr. Engrg., 117(7), 905-921.

Rajaratnam (1965), Proc. ASCE, 91(HY4), 71-96.

Rajaratnam (1967), Advances in Hydroscience, ed. Chow, Academic Press, 232-233.

Ramaprasad and Ramamoorthy (1966), Proc. ASCE, 92(HY1), 146-155.

Rao and Rajaratnam (1963), Proc. ASCE, 89(HY1), 139-162.