Analytical model for variations of water depth in downstream channel of four-branch junction with subcritical flow

Study of water depth variations in downstream of channel junctions, in order to get suitable situations in intakes, is necessary. In this research, analytical model for investigation of different hydraulic and geometrical factors on water depth variations at downstream of the four-branch junction with subcritical flow were presented and results were compared with experimental data. The results showed that as inlet discharge ratio, ratio of height of weir at the end of lateral channel to the height of weir at end of main channel , bed level of lateral channels and the height of outlet weirs increased, water depth in main outlet channel increased too. Increase of Froude number in the main inlet channel caused decrease of the water depth in the main outlet channel. As change of junction angle, quantity of the discharge turned into the main outlet channel changed which affected the water depth so that maximum water depth occurred for angle of 90 degrees and decreased as junction angle decreased. Comparison of the results for analytical and experimental models about flow depth in downstream channel showed a good agreement so that maximum error was less than 10%.
Due to the importance of this phenomenon, researchers around the world have focused and lots of experimental and analytical studies have been carried out in this case. Researches were mostly about three-branch junctions and there was less study about four-branch junctions. Teylor (1994) was the first person studied open channel flow by analytical model and simulated water depth into lateral channel. Rivie’re et al. (2011) studied flow in four-branch channel experimentally and extended one-dimensional model for flow distribution and compared experimental results with analytical. In this research, analytical model for investigation of different hydraulic and geometrical factors on water depth variations at downstream of the four-branch junction with subcritical flow were presented and results were compared with experimental data. The suggested analytical model was one-dimensional and base on mass, energy and momentum conservation laws with some hypothesis such as: Inlet and outlet flows were considered as uniform; Flow was vertically uniform; Pressure was hydrostatic in channels; Energy and momentum coefficients were considered 1; Head losses due to friction of wall and bed, also, due to turbulence and shear stress were ignored. Considering variables, in order to solve problem, 6 equations were needed: two energy equations, two momentum and two stage-discharge equations. For solving equation systems (6 equations and 6 unknown variables) MATLAB 2011 was used. Experimental study was carried out in hydraulic lab of Tabriz University, Iran. Length of the main channel was 8.4 m and the lateral channel was 2.4 m. Width and height of the both channels was 0.4m and 0.5m, respectively. The slope of the channels was zero. In order to measure of discharge weirs used, which were installed at first and end of the channel. In the experiments, height of weirs considered 15, 17.5, 20, 22.5, 25 cm and the discharge ratio was 0.2, 0.4, 0.6, 0.8 and 1.
Results showed that as increasing of discharge ratio, water depth in outlet main channel increased. When inlet discharge ratio increased, the flow that deviated into the outlet main channel increased that leads to increase of water depth. Amount of the error in prediction of the water depth by analytical models was less than 10%. Increase of the height of the weirs at the end of the outlet channels caused increase of water depth. The error of the predicted water depth also was less than 10%. As increasing , deviated flow into the outlet lateral channel decreased while the deviated flow into the outlet main channel increased and therefore the water depth increased. The amount of the error for prediction of water depth by analytical was about 5%. Expanding the bed channel of the outlet lateral caused decrease of deviated flow into the outlet lateral channel that leads to increase of the deviated flow into outlet main channel and increase of water depth. Also, increasing the Froude number of the outlet main channel, flow velocity increased and water depth decreased. Maximum water depth in outlet main channel observed for the angle of 90 degrees and minimum water depth happened when the angle of the channel junctions was 60 degrees.