A simplified solution of the conjugated depth of abruptly expanding hydraulic jump
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Abstract:
The simplified solution of the hydraulic jump equation is provided by analyzing the hydraulic characteristics of a hydraulic jump in an abruptly expanding channel. Based on analyzing the flow pattern of a hydraulic jump in an abruptly expanding channel, a hypothesis is made for the depth in the back-flow region considering the effect of the abruptly expanding ratioon the depth in the back-flow region. The law of momentum conserv ation is used to est ablish the hydraulic jump equation in an abruptly expanding channel. Through the a pproximate treatment, the explicit simplified solution of the hydraulic jump equation in an abruptly expanding channel is derived. An empirical formula for the related parameters is given. The averageerr or between the simplified solution and the experimental result is 1.924% at an abruptly expanding ratio when β= 1.0. The error between the classical solution and the simplified solution in the range of 3.0< Fr 1 < 9.0 decreases with the increase of the flow Froude number and the max imum error is less than 3.001 % . The sim plified solution well agrees with the experiment and the classical solution of 2D hydraulic jump. The average error of the simplified solution and the experimental result under different abrupt expanding ratio is 5.511% , indicating good accuracy. Therefore, it can be applied to carry out the hydraulic calculation in the downstream of the outlet structure.
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