Formerly Addl. Director
Central water and Power research Station, Pune, India
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All other factors remaining the same, coefficient of discharge of a spillway decreases as the height of the crest relative to the head on the crest (P/Hd) decreases. The crest shape, though, has an influence to some extent as seen from figure 1. The elliptical shape retains some superiority over other shapes. However, trying to estimate the reduction in the coefficient Cd corresponding to the zero approach depth, viz. P=0, from figure 1 would not yield any result. The flow conditions substantially change as the approach depth diminishes to zero. No specific reference is available in the literature. Theoretically, a level broad crested weir should have a value of Cd =1.706 or C=0.577 in the equation Cd=2/3 (2g)0.5 C.
Figure 1: Effect of approach depth on coefficient of discharge
This issue was particularly addressed by B.D.Suryavanshi, then Director, Irrigation Research, MP, India, in 1972. He conducted studies on a 1:24 scale model of a 7m high ungated weir which was getting silted up. In his experiments, in addition to the original bed, he also simulated a hypothetical condition whereby the weir was silted up fully up to the crest level. It was found that the coefficient of discharge in the equation q=Cd H3/2, of 2.143 corresponding to the original bed condition (P/Hd =1.33) decreased to a value of 1.96 for the bed silted up to the crest (P/Hd =0), a reduction of about 9.5%. Both the above values were worked out considering the head due to the velocity of approach. The corresponding C values were 0.725 and 0.663 respectively, considerably higher than theoretical. The head over the crest, however, reduced from 5.27 m for the original bed condition to 4.52 m corresponding to the silted bed condition, for the design discharge of 28 cumec. It is surmised that the free over fall just downstream of the level crest may be the reason for increase in C beyond the theoretical vale of 0.577.
A noticeable finding from the above studies was that the afflux upstream of the reach increased in comparison to that caused by the original bed condition. Also, the maximum additional afflux was caused at a section up to which silting was extended. Therefore, if a reservoir behind a low dam or barrage is likely to be silted up in future, the additional afflux should be considered and provided for in the design itself. The results are shown in figure 2.
Figure 2: Effect of siltation upstream on flow profiles
In the above case, although the reservoir was silted up to the spillway crest, a free over fall in the downstream contributed to a better value of C. However, in the case of low height barrages, silted up to the crest level, such a free over fall would not be available as the downstream portion would not be too deep. In such a case, C value of 0.577 would be applicable, provided the downstream water level is not more than about 80 percent of the upstream level. For higher submergence, weir formula can not be applied and discharge should be calculated assuming fully developed open channel flow and corresponding velocity profile.
A particular case of interest would be a low height barrage with crest piers and bridge. When silted up to the crest level, it would virtually be the case of a bridge with the intervening spans filled with level bed of concrete. This case offers calculations involving bridge pier losses. All the possible combinations of upstream and downstream water levels, shown in figure 3, are amenable to calculations by application of US Army Corps of Engineers Hydraulic Design Criteria charts 010-6 to 010-6/5.
Figure 3: Various combinations of upstream and downstream water levels