Flow Measurement in Trapezoidal Canals Using Prismatic Piers

Flumes are one of the simple tools for measuring flow rate in canals that the flow rate can be calculate only by measuring the flow depth at specific points of control section of them. Blanger (1849) and Bazin (1896) were the first to conduct experimental and theoretical studying on flumes. Since then, many research was done about hydraulic characteristics of different flumes by researchers such as Parshl (1900), Robinson (1968), Samani and Magalanez (1992, 1993), Proginelly and Bonacci (1997), Prabhat (1998), Samani and Magalanez (2000), Bdar and Gare (2014), Davis and Samani (2016) and Mohammadi and Vatankhah (2020). Many of mentioned researchers have done their research on rectangular channels. In this research, possibility of the creating control section by installing a prismatic pier on the central axis of floor in trapezoidal canal and flow measurement in free and submerged flow condition was investigated.

To achieve discharge equations, many experiments were performed in free and submerged flow condition in a trapezoidal laboratory canal with length of 6 m, width of 46 cm, height of 70 cm and with adjustable side slope. Four prismatic piers with head angle of 90◦, width of 42, 40, 38 and 36 cm were tested. The height of each pier was considered equal to its width. The experiments were performed on 4 side slopes.Based on dimensional analysis, the following dimensionless equation was considered as basis of experiments for both free and submerged flow condition.(1)where Q is discharge, g is gravity acceleration, y1 is flow depth upstream of prismatic pier and Bc is calculated from the following equation.(2)where z is side slope of canal, B is width of canal and b is width of prismatic pier.On the base of 96 experiment in free flow condition (in a certain side slope, 6 experiment for a pier) and 288 experiment in submerged flow condition (in a certain side slope, 18 experiment for a pier with different submergence ratios) discharge equations for both free and submergence flow condition were obtained separately.

On the base of performed experiments , variation of dimensionless parameters Q/(gBc5)0.5 versus y1/Bc corresponding to all 4 side slopes is presented in figure 1 and equations 3 and 4 in free and submerged flow condition respectively.(a) (b)Fig. 6- Variation of y1/Bc vs. Q/(gBc5)0.5 for different side slopes, a; free flow b; submerged flow(3 (4) According to equation 3 and 4, exponent of y1 in both equation 3 and 4 is larger than circular, trapezoidal and S-M flumes which are presented by Samani and Magallanes (1992, 1993 and 2000). This makes this flume ideal for water level variations than circular, trapezoidal and S-M flumes. To determine accuracy of the obtained relationships and graphs, statistical parameters, ME, RMSE and MARE, were used. Based on the relationship for all side slopes (equation 3 and 4) MARE is 8.3 and 10.2% for free and submerged flow conditions respectively. The results showed that, using of the flow measurement method in trapezoidal canals is Suitable for free flow conditions and can be used by accepting 12% error for submerged conditions.

The results showed that, using of the flow measurement method in trapezoidal canals is ideal for free flow conditions (equation 3). The flow measurement method in trapezoidal canals can be used by accepting 12% error for submerged flow conditions (equation 4). Compared to circular, trapezoidal and S-M flumes, this flow measurement method has large sensitivity to variation of upstream water level It is suggested that, the results of this research be used within the range of studied parameters.