| dc.description.abstract | This thesis presents an extensive and systematic study of the free and submerged flow characteristics of rectangular and trapezoidal finite crest width weirs and triangular profile weirs. Aspects studied include the variations of free flow coefficient of discharge, submergence limit, reduction of discharge under submerged flow, and flow characteristics such as free surface and pressure profiles and the geometry of the separation zone. In all, studies are made on 75 test weirs, with 13 trapezoidal profile weir shapes and 9 triangular profile weirs with upstream slope varying from 0 to 3 and downstream slope Z? varying from 1 to 5 (Z? or Z? horizontal:vertical). For rectangular and trapezoidal finite crest width weirs, l/P ratio is varied from 0.2 to 2.0 which gives a range of h/L up to 3.0 and h/P up to 1.5 (L is the crest length, P is the height of the weir and h is the head over the weir). A total of 5800 runs is made for free and submerged flow observations. For the rectangular finite crest width weirs, observations are made for both ventilated and unventilated free flow, as in several field situations ventilation may be inadequate or absent.
Experiments are conducted in a rectangular horizontal flume 17 m long, 1.2 m deep and 0.6 m wide with full-width two-dimensional weirs. Studies on scale effects indicate that the height of the weir should not be less than 15 cm and in view of this, a minimum height of 20 cm is adopted. Based on expected uncertainties in the measurements, an uncertainty estimate is obtained for the free flow coefficient of discharge. The accuracy of the experimental observations is verified by conducting repeatability tests on two weirs in a completely different experimental setup.
Rectangular and trapezoidal finite crest width weirs are characterized by a free surface which is parallel to the crest at least over a short length for 0.08 ? h/L ? 0.33. In the range 0.33 < h/L < 0.65, the free surface is curvilinear with a point of inflexion on the crest while for h/L > 0.65, it is fully curvilinear. For the rectangular weirs, the lower nappe leaves the crest for h/L > 1.5–1.7 if adequate ventilation is provided. This tendency is also shown by trapezoidal profile weirs with Z? = 1 and Z? = 1.
The roller or separation zone at the crest entry is found to be significant for rectangular profile weirs, particularly in the parallel flow range. The height of the roller reduces with flattening of the upstream slope and becomes negligible for Z? ? 3. Correlations are obtained for the height and the length of the roller for rectangular and trapezoidal profile weirs. The variation of pressure within the roller has also been studied and it is found that the pressure is constant up to the peak of the roller and increases thereafter.
Correlations are also provided for free surface parameters such as the parallel flow depth (0.08 ? h/L ? 0.33), depth at the crest entry and crest end for rectangular and trapezoidal profile weirs and the depth at the crest for triangular profile weirs. The dependence of these parameters on h/L, h/P, Z? and Z? are studied in detail.
Observations show that the ventilated and unventilated flow over rectangular finite crest width weirs differ significantly only for h/L ? 1.5. It is found that a unique correlation can be obtained for the coefficient of discharge as a function of h/L and h/P for unventilated flow also, provided the nappe is not of a clinging type. The variation of the total head coefficient of discharge (C) for the ventilated and unventilated flows is within 2% for h/L up to 1.5. For h/L ? 1.5, the ventilated flow C is much lower than the unventilated flow value as the nappe springs clear off the crest. Correlations for C are obtained for both ventilated and unventilated conditions of flow for h/L up to 3.0 and h/P up to 1.5. These new results extend the existing range available in literature. While C increases with h/P at all h/L values for ventilated flow, for the unventilated flow the effect of h/P on C is of a dual nature, with C decreasing with increasing h/P for h/L > 1.5.
The effect of h/P on C for trapezoidal and triangular profile weirs is less than that for the rectangular finite crest width weirs. It is relatively more significant at lower h/L values for trapezoidal profile weirs. As h/L increases, the h/P effect decreases for trapezoidal profile weirs (except for weirs with a vertical upstream face) and C tends to reach a constant value corresponding to the value of the triangular profile weirs with the same upstream and downstream slopes. As the upstream slope is made flatter, C increases for a trapezoidal profile weir for all h/L values for Z? ? 2. However, as Z? is increased to 3, the coefficient of discharge increases slightly only in the parallel flow range, thus indicating that further flattening of the upstream slope is not effective in increasing C. For a given upstream slope, if the downstream slope is made flatter, C decreases beyond the parallel flow range. It is independent of the downstream slope in the parallel flow range.
Correlations are provided for C for thirteen trapezoidal profile weir shapes and nine triangular profile weirs. The effects of Z?, Z?, h/P and h/L are discussed in detail.
The nature of the free surface under conditions of incipient submergence is different in the parallel flow and the curvilinear flow ranges for finite crest width weirs, and the submergence limit varies with h/L quite significantly.
For rectangular and all the trapezoidal profile weirs, the submergence limit is maximum in the parallel flow range and decreases with increasing h/L. For rectangular and trapezoidal weirs with Z? = 0 and Z? = 5, the submergence limit depends on h/L and h/P. For all the trapezoidal weir shapes with Z? ? 1 and Z? = 1, the submergence limit is practically independent of h/P and attains a constant value for h/L ? 1.5.
It is observed that the submergence limit increases significantly with the flattening of the downstream slope, while it is found to increase slightly with flattening of the upstream slope. This trend is observed for triangular profile weirs also. The submergence limit in the constancy range is as high as 0.80 for trapezoidal weirs and triangular profile weirs with Z? = 1 and Z? = 5. The submergence limit is practically constant for triangular profile weirs with Z? = 1 and Z? = 5. Correlations for submergence limit are provided for the rectangular and thirteen shapes of trapezoidal finite crest width weirs and nine shapes of triangular profile weirs.
For all the rectangular and trapezoidal finite crest width weirs and triangular profile weirs, correlations are obtained for the discharge reduction factor, Q/Q? (where Q is the actual discharge corresponding to head h and Q? is the corresponding modular discharge) with submergence ratio. The dependence of submerged flow characteristics on h/L and h/P is discussed in detail. It is found that unique correlations independent of h/P can be provided for triangular profile weirs with Z? ? 1, Z? = 5 and Z? = Z? = 3.
These weirs as well as trapezoidal profile weirs with Z? = 1 and Z? = 5 are well suited for submerged flow conditions. The present studies on the submerged flow characteristics of the rectangular and trapezoidal finite crest width weirs and triangular profile weirs form one of the most exhaustive experimental investigations in the weir literature for submerged flow.
The momentum principle is applied to a limited extent to study the variation of the coefficient of discharge and the submergence limit. | |
