LAUSR

The paper deals with hydraulic jump characteristics in a stilling basin (called basin hereafter) provided with an adverse slope and a positive step at the end of the basin. Different characteristics of hydraulic jump, studied both analytically and experimentally, include (i) conjugate depth relation (D2/D1) (ii) lengths of roller (Lr) (iii) jump length (Lj) and (iv) relative loss of energy (∆E/E1) in the jump within the basin. Studies were made for four different slopes (0; 0.01; 0.03 and 0.05) combined with three positive steps of heights (0; 3 cm and 5 cm.). In total, 144 experiments were performed with inflow Froude’s no. (F1) varying from 4 to 10. It is concluded that the sequent depth ratio, jump length and roller length reduce with increase in slope and height of positive step by 20%, 39.3% and 32.6%, respectively, as compared to those in a classical jump on level floor. Relative energy loss increased with rise in slope and step height by 13% more than that in a classical jump. Fig. 7(a) and 7(b) illustrate the variation of the above jump characteristics with slope and step height, compared to ones in classical jump. Fig. 8(a) and 8(b) indicate the variation of relative energy loss (∆E/E1) and jump efficiency (ɳ) respectively with pre-jump Froude’s number (F1) for different slopes and step heights. Values of ∆E/E1 and ɳ are compared with those in a classical jump on level floor. Authors are, however, silent about how to decide the slope and step height combined together for best performance of stilling basin operated under different F1 -values corresponding to different flows. Too high step may cause flow choking and jump submergence and too low step may result in repelled jump. In case tail water depth is less than sequent depth, Ranga Raju (1993) plotted relation between F1 and D2/D1 for different values of positive step height such that the hydraulic jump ends at the step in a stilling basin of length 5(D2+∆Z) where ∆Z is the height of positive step. Earlier a similar paper on ‘Characteristics of hydraulic jump on rough bed with adverse slope’ (Parsamehr et al. 2017) was published in ISH J. of Hyd. Engg. and discussed by Mazumder (2017). Discusser (Mazumder and Naresh 1988) performed a series of experiments to find hydraulic jump characteristics with both horizontal floor, as well as floor with adverse slope. Variation of conjugate depth, length of jump, roller length and relative energy loss were plotted against pre-jump Froude’s no. of flow (F1) for different slopes. Results obtained were almost similar to the ones found by the authors of the paper. Use of chute blocks, baffle blocks and end sill has been prescribed by Bradley and Peterka (1957) for reducing length and conjugate depth and for improving the efficiency of USBR type stilling basins (1968). SAF basin was developed in St. Anthony Falls Hydraulics Laboratory in USA. Depending upon the prejump Froude’s number of flow (F1), several types of stilling basins were developed by USBR (1968). Stilling basin – an integral part of dams and barrages and other hydraulic structures – is provided to dissipate the differential energy (ΔE), i.e. the difference of energy levels between the entry of a basin and tail channel downstream of the basin as shown in Figure 1. It is presumed that the differential energy (ΔE) is completely dissipated within the basin due to hydraulic jump formation within the basin. Basin length usually varies from 4 to 6 times the conjugate depth (D2) depending upon inflow pre-jump Froude’s number (F1). It is well established that the jump is steady and perfect only when F1 is greater than 4.5 as in high dams. In many of the low height hydraulic structures, e.g. barrages, canal drops, regulators, etc., F1 is found to be less than 4.5. Since authors have studied jump characteristics and energy loss for 4 < F1 < 10, the results may not be applicable in such situations. For example, inflow F1 – values at design flood discharge in Farakka and Kosi barrages in India are F1 = 2.8 and F1 = 3.4, respectively. In these low height dams/barrages, drops, regulators, etc., the jump is not perfect as the basin efficiency is poor and hence considerable amount of residual kinetic energy leaves the basin as shown in Figure 1. From Figs.7 and 8 in the paper, it is observed that both ∆E/E1 and η-values decrease with reduction in F1-values. Efficiency of a stilling basin (as energy dissipater) is different from hydraulic jump efficiency. Referring to Figure 1, if the actual energy dissipated within the basin is ΔEand the differential energy required to be dissipated is (ΔE), the residual kinetic energy of flow leaving the basin is (ΔEΔE). As the tail water depth D2 after the basin remains the same, the only way the residual energy can be contained by the flow with same depth (D2) and same mean velocity of flow (V2) is through non-uniformity of velocity distribution as indicated in Figure 2(a) and 2(b). Coriolis’ coefficient (α) is an index by which nonuniformity of velocity can be expressed as