포물선형 개수로에서 공액수심의 양해적 해석
Explicit Solution for the Conjugate Depth Ratio in Parabolic Open Channels
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초록
This study derived a non-linear specific force equation for parabolic open channel flows. In addition, an explicit method is presented for obtaining accurately a solution to the specific force equation. The Newton-Raphson method, which has 2nd-order accuracy, was used to obtain the solution of the derived equation. The initial value of the calculation was obtained from recent research results in the form of a regression equation. The maximum relative error is about 0.33% when the conjugate depth ratio is calculated using the existing regression equation, but it is 0.07% using the results of this study, even in the extreme case where the Froude number is around 1.0. That is, the conjugate depth ratio of the parabolic channel can be calculated accurately and easily by using the explicit method presented in this study.
Abstract
This study derived a non-linear specific force equation for parabolic open channel flows. In addition, an explicit method is presented for obtaining accurately a solution to the specific force equation. The Newton-Raphson method, which has 2nd-order accuracy, was used to obtain the solution of the derived equation. The initial value of the calculation was obtained from recent research results in the form of a regression equation. The maximum relative error is about 0.33% when the conjugate depth ratio is calculated using the existing regression equation, but it is 0.07% using the results of this study, even in the extreme case where the Froude number is around 1.0. That is, the conjugate depth ratio of the parabolic channel can be calculated accurately and easily by using the explicit method presented in this study.
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