Experimental study of the effect of sidewall slope over the triangular PK weir

Document Type : Research Article


1 Tarbiat Modares Uni,Tehran, Iran

2 Tarbiat Modarres



One of the critical consequences of climate change is prolonged droughts with floods. In these conditions, maintaining the maximum possible water level without wasting it and high discharge capacity in critical situations is essential to preserving the reservoir's health. The most suitable solution for sending excess water can be considered as creating a proper spillway. According to ICOLD, one-third of dam failures are due to weir disproportion. Unfortunately, due to the designers' lack of experience in using the nonlinear spillway, irreparable accidents sometimes happen. Therefore, choosing the proper spillway with the appropriate discharge have undeniable importance. This paper focuses on a new solution to improve the piano key weir capacity. By correcting the sidewalls of weirs, three goals were pursued simultaneously. In the first step, better performance than conventional PK weirs on the occasion of a flood. The second goal is to store the maximum water level upstream in non-critical situations and use only part of the weir.
The ultimate goal is to make this method economical. This research is a continuation of previous research on PK weirs. Figure 4 shows the rotating flume environment, which experiments were performed in that laboratory at the Tarbiat Modares University of Tehran (Dimensions: 10 meters long, 2 meters wide, and 0.9 meters high)( Figure 4). Experiments have been performed on a triangular weir with a zero slope (i.e., Tri-Base model) (Fig. 1 and 2) and 10 degrees in the flow direction (Fig. 1 and 3). In this article, Pk weir with horizontal and sloped crest is called Tri-Base and Tri-B1 models. The weir characters used in the laboratory are provided in Table1. Eq (4) and (5).
The dimensional analysis of the (Tri-B1) model, and the (Tri-Base) model, respectively. In the analysis of laboratory data, an effective length (wet length of walls) was defined for the weir. Then for this geometry, Eq. (6) and (7) were provided to calculate the discharge coefficient, which in addition to the new weir, is used in typical weir (i.e., The Tri-Base model) can also be used with great precision. Fig.10 shows the comparison of measured and calculated values of triangular pk weir.
For the Head-Discharge curves, firstly, the discharge-head curves for triangle Pk weir with horizontal crest (Fig. 7) have been plotted and compared with the present study and other researchers' results. The differences between results are because of the differences in geometric characteristics shown in Table 2. Because the head and weir height changes for every discharge, Fig. 6 and have been plotted curves of (Q-P+Ht). Based on these figures, water height in triangle PK weir with a sloped crest (i.e., The Tri-B1 model) is higher than triangle pk weir with a horizontal crest (i.e., The Tri-Base model), but head height over the (Tri-B1) model is less than the (Tri_Base) model. On the other hand, for the (The Tri-Base) model, discharge coefficients have been plotted in Figure 8.This figure also compared the results of other researchers the results with this study. Fig. 9 also shows the discharge coefficient for the (Tri-B1) model. The discharge coefficient in the (Tri-B1) model has increased by an average of 3.8% than the (Tri-Base) model, with the maximum and average discharge coefficients shown in Table 3.
Also, about the flowing blade, in the weir of a triangular Piano key weir with a horizontal crest, at 8 Cm 〖>H〗_t > 4 Cm, air penetrates under the blades of the flow, and the flow is vented. At higher values (12 Cm 〖>H〗_t > 8 Cm), the flow under the blade is connected to the open-air with increasing water head. In this case, have been seen fluctuations in the current blade. At higher values ( H_t>12 Cm), the flow completely covers the weir (immersion) and passes over the weir. In these conditions, the fluctuations of the flowing blade can be observed. According to Fig. 5 in Q=40lit/sec have seen an Air cavity on the weir body. Also, in analyze were seen, the weir of a piano key weir with a sloping crest (i.e., The Tri-B1 model) increased. But with the sinking whole of the weir, the discharge coefficient rate decreases. Also, in connection with the weir blade of the Pk weir with a sloped crest (The Tri-B1 model) in some discharges, all three types of flow blades can be seen on the sidewalls of the weir (i.e., sticky, compressed, and free baled.
In conclusion, in Pk weir with slope crest, have been seen the level of water behind the weir increases while the head of water on the weir decrease. So this means that in drought seasons and when the level of water decreases in the reservoir, this spillway can increase the water level. Use this weir's high capacity in the critical season (especially during flood time). On the other hand, this spillway has a high capacity in all situation and increase the discharge coefficient.


  • Receive Date: 23 January 2022
  • Revise Date: 21 May 2022
  • Accept Date: 04 June 2022
  • First Publish Date: 04 June 2022