Jannati, Mohammad H.


Vertical Drop With a Contraction Transition and Subcritical Flow Upstream


Student Name

Mohammad H. Jannati



Mohammad Reza Chamani
(Assoc. Prof._Civil Engineering Department_Isfahan University of Technology)

Mohammad Karim Beirami
(Assoc. Prof. _Civil Engineering Department_Isfahan University of Technology)









A vertical drop structure or free over fall is a common feature in both natural and artificial channels. Natural drops are formed by river’s bed erosion while artificial drops are built in irrigation system to reduce the channel slope to designed slope. Due to more energy dissipation, drops are also applied in stepped spillways. More energy dissipation is obtained through mixing of the falling jet in the pool downstream of the drop. Vertical drop structures and stepped spillways usually have the same upstream and downstream widths. This condition leads to the formation of negative pressure under the nape of falling jet and to the cavitation of the brink depth of drop. In this work, contraction transitions are used at drops to eliminate the negative pressure and to increase the energy loss.

Based on some previous investigators’ assumptions and some new assumptions, five analytical models are presented to predict end-depth ratio, relative energy loss, relative rolling depth and relative drop length. Experiments on physical models of six different contracting transitions and two drops of different heights are conducted in the Hydraulics Lab. The ratio of the critical depth to the drop height was in the range of 0.07 to 0.41. Time-averaged point velocities at upstream and downstream sections (three transverse sections) were measured with a prandtl tube.

For the proposed model of the end-depth ratio, the continuity equation, based on the Ferro‘s work (1999) was used. The model of the end-depth ratio (Model I) is based on simulation of the flow over a sharp-crested weir and predicts the flow discharge and Froude number over a free over fall. To evaluate the energy loss, White’s, Gill’s and free jet models have been modified. The modified models of White, Gill and free jet model were called Models II, III and IV, respectively. In Model V, the relative drop length was investigated using the relationship of Models II to IV.

Model II predicts the energy loss and the relative pool depth relatively well. The experimental values of energy losses are mostly higher than the predicted ones. A good agreement was observed between the theoretical and the experimental results for the relative pool depth. Model III didn’t estimate the energy losses well. The experimental values of energy losses are considerably higher than the Model III’s predicted values. The experimental results of the relative pool depth were very close to the results of the Model II. Comparing with experimental results, Model IV was more accurate in predicting the flow characteristics as compared with the other models. As the ratio of the width of the brink drop to the width of channel increases, the accuracy of the model predictions also increases. The results of Model V were in good agreement with the experimental results.