Laboratory investigation of the discharge coefficient of the rectangular piano key weir with a discontinuous sloping crest

Introduction :

Spillways are simple and widely used hydraulic structures in water transfer and irrigation, and drainage systems. They are used in dams to pass excess water caused by floods and control the reservoir water level, as well as in irrigation and drainage canals to regulate the water level and measure the flow rate. Piano key weirs are the newest type of nonlinear weirs are piano key weir (PK weir), which this type of weir can increase the capacity of discharge coefficient 3-4 times to a linear spillway. However, the discharge coefficient of PK weirs decreases with increasing the head over the weir.

This study aims to check the discontinuous wall over the crest of the piano key weir to improve the discharge coefficient of the piano key weir in the high heads. To achieve this goal, Two weirs with a ratio of W/B = 2/3 have been used (Figures 1 to 3). The desired weirs were installed and carried out in a rotating flume in the Tarbiat Modares University of Tehran (Figure 4). The range of testing was from Q = 55 lit/sec to Q = 180 lit/sec ; and with steps of 5 lit/sec. To conduct the tests, first, the tests were performed on the Rec-Base model, and then the tests were performed on the Rec-B1 model. The geometric features of these two models are presented in Table 1.In order to extend the results of the prototype to the real sample, the dimensional analysis of the weir has been done. For this purpose, the effective parameters are shown in Eq. 2, and then, after performing the dimensional analysis techniques, it can be seen in the form of Eq. 3. By removing the constant values, the discharge coefficient will depend on the parameters of Eq. 4.

Figure 5 shows the Q-Ht curve of two Rec-Base and Rec-B1 models. According to this figure, the upstream head of the weir of the Rec-B1 model has increased by an average of 8.35% compared to the Rec-Base model. Also, regarding the behavior of the flowing blade, in the model (Re-Base) in the range of Ht<8 cm, air penetrates under the flow blades, and the flow becomes aerated. In the interval (Ht < 12 Cm < 8 Cm), with the increase of water head, the flow under the blade goes to the free air, and the blade takes an oscillating state. At higher values (Ht < 12 cm), The flow passes over the weir crest in the form of a thick blade. In this condition, fluctuations are observed on the flowing blade. Equation 5 has been used to calculate the discharge coefficient of the Rec-Base model. This issue is while Eq.12 has been used to calculate the water discharge coefficient of the Rec-B1 model. In this regard, QT is obtained from Eq. 10, and QE is the laboratory discharge. Figure 8 shows the discharge coefficient of the two models. According to this figure and the numbers in Table 2, the discharge coefficient has increased by 6.7% in the Rec-B1 model compared to the Rec-Base model. Figure 11 also shows a 7.22% increase in efficiency of the Rec-B1 model compared to the Rec-Base model. Also, coefficient C was calculated using equation 13 and its curve was drawn in figure 9. Figure 10 is also calculated according to Figure 14. Finally, Eq. 16 to estimate the water discharge coefficient has been presented. Also, the coefficients of this equation are presented in Table 3. Figure 12 shows the comparison between the estimated water discharge coefficient of equation 10 with the actual value of the discharge coefficient, which indicates the high accuracy of the presented equations. Table 4 indicates the equation proposed by other researchers to calculate the discharge coefficient of the PKW as well.

In conclusion, it can be mentioned that although the slope over part of the weir crest increases the upstream head of the piano key weir, however the efficiency of the weir increase by 7.33%. Also, the discharge coefficient in the Rec-B1 model increases by 6.7% compared to the Rec-Base model. Considering that in the Rec-Base model, with the increase of the head, interference of the flow increase, it is possible to reduce the decreasing rate of efficiency in higher discharge by modifying the weir crest.