Energy Dissipation of Triangular Piano Key Weir

Introduction
Piano key weirs (PKW) is the newest type of long crest weirs, which achieve more crest length in the same width as congress weirs, and therefore, the capacity of the void is higher than that of the mounted piano key weirs, with the aim of increasing the amount of energy dissipation in them. It was noticed that the piano key weir oscilloscopes are used in the crest of reservoir dams and in irrigation and drainage networks. This has been implemented due to the importance of the issue of energy dissipation in these types of instruments. So far, many studies have been done on the discharge coefficient of the piano key weir, but no research has been done on the relative energy dissipation of the triangular Piano key weir.

Methodology
This research is a continuation of previous research on PK weirs. Figure 1 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). Experiments have been performed on a triangular weir with a zero slope (i.e., Tri-Base model) (Fig. 2 and 3) and 10 degrees in the flow direction (Fig. 2 and 4). 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 (3).
The upstream depth (ho = P+h) and downstream (h1) was measured with an accuracy of ± 0.1 mm at a distance of 4P for the upstream depth (Crookston, 2010) and 10P for the downstream of the overflow (Eslinger & Crookston, 2020).

Results and Discussion
For the ∆E/E0
curves, firstly, the relative energy dissipation curves for triangle PK weir with horizontal crest have been plotted (Fig 5) and compared with the present study and other researchers' results. The differences between results are because of the differences in geometric characteristics. Because the head and weir height changes for every discharge, Fig 6 has been plotted curves of (q - E1/E0).
The trend of the relative energy dissipation curve of nonlinear weir may be according to a logarithmic curve (Lopes et al., 2011). Figure 5 shows the changes in energy consumption for the Tri-Base and Tri-B1 models and their comparison with the results of other researchers. According to Figure 5, the highest relative consumption of energy is for the Tri-Base model. In other words, at the same flow rate, the highest relative amount of energy dissipation is related to the weir model with a horizontal crest. It is also clear that the highest relative energy loss in all samples occurred at the lowest flow rates.
As the flow rate increases, the relative dissipation of energy decreases in both models. The reason for this is that with the increase in flow rate and flow speed, the amount of flow friction is reduced, and as a result, the dissipation of the flow is reduced.
With the increase of Froude Number, the acceleration increases, and the flow travels a longer path towards the separation, which causes the separation area to decrease and the Drag force to decrease. Because of the slope of the weir walls, the flow speed in the Tri-B1 model is higher than the Tri-Base model (the flow moves like a slide from the spillway to the downstream side), so the separation area in the Tri-B1 model is reduced, and the Drag force and consequently the relative depreciation The energy in the Tri-B1 model (about 24%) is lower than the Tri-Base model.
Figure 6 shows the residual energy curve of the piano key weir in relation to the flow rate per unit of the overflow width. According to Figure 6, the E1/E2 ratio increases with the increase of flow per unit width. In other words, the relative residual energy in both models occurs at high flow rates. Also, in both models, at low flow rates, the increase in E1/E2 ratio is higher than at high flow rates. The reason for this is the local sinking upstream of the weir in high discharges; so that in high heads, the aeration on the weir is reduced.
Finally, Fig 7 shows the comparison of measured and calculated values of triangular PK weir.

Conclusion
In the triangular piano key weir, by increasing the slope of the side walls (θ) from zero to 10 degrees in the flow direction, the relative dissipation of energy has decreased by 24%. Also, the highest dissipation of energy in the weir with a horizontal crest occurred in the lower heads, and this value decreases with the increase of the head.
The highest amount of energy dissipation for Tri-Base and Tri-B1 models is 0.74 and 0.85, respectively, in this case. Finally, relationships (9) and (10) are proposed to calculate the relative energy consumption of the overflow of the piano key with horizontal and sloping crest, respectively.