Explicit calculation equations for conjugate depths of channels in parabolicshaped crosssection
LENG Chang-Jian, WANG Yi, WANG Zheng-Zhong
(1.College of Water Resources and Architecture Engineering, Northwest A＆F University, Yangling, Shaanxi 712100, China; 2.Institute of Water Resources and Hydropower Engineering, Northwest A＆F University, Yangling, Shaanxi 712100, China)
Abstract：To develop an explicit function for the conjugate depths of hydraulic jumps in parabolicshaped channel after sluice gate, the first derivative of the conjugate depths was obtained and defined to be equal to zero for calculating the critical depth. A dimensionless conjugate depths formula was proposed by means of two ratios of the depth before water jump and the critical depth, as well as the critical depth and the depth after water jump. Then the iterative functions of the depths before and after the jump were derived in terms of energy characteristics of upstream and downstream flow. To accelerate the convergence speed, applying the maximum product term of dimensionless depths before and after water jump, namely the true solution of the slowest convergence point, appropriate initial values were calculated. As a result, an explicit calculation equation with higher accuracy was obtained with only one iteration. Error analyses indicate that the maximum relative errors of the upstream and downstream depths, calculated by the explicit calculation equations, are 047％ and 055％ respectively. The proposed explicit calculation equations are simple, accurate and widely applicable.
冷畅俭, 王羿, 王正中. 抛物线形断面渠道共轭水深的直接计算公式[J]. 排灌机械工程学报, 2013, 31(2): 132-136.
LENG Chang-Jian, WANG Yi, WANG Zheng-Zhong. Explicit calculation equations for conjugate depths of channels in parabolicshaped crosssection. Journal of Drainage and Irrigation Machinery Engin, 2013, 31(2): 132-136.
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