양해법을 이용한 사각형 및 사다리꼴 단면 개수로에서 한계수심과 등류수심의 산정
Explicit Solutions for Critical and Normal Depths in Rectangular and Trapezoidal Open Channels
1
조회
0
다운로드
2
인용
0
참고문헌
키워드
초록
본 연구에는 사각형과 사다리꼴 단면에 대해 한계수심과 등류수심을 정확히 구할 수 있는 양해법을 제시하였다. 이를 위해 사각형 단면의 등류수심과 사다리꼴 단면의 한계수심 및 등류수심을 지배하는 비선형 무차원방정식을 유도하였다. 유도된 비선형방정식의 해법은 2차의 정밀도를 가지는 Newton- Raphson 방법을 이용하여 해를 구하였다. 계산에 필요한 초기값을 구하기 위하여, Matlab의 비선형방정식의 해를 구하는 함수인 fzero를 이용하여 앞에서 유도한 무차원방정식의 정확해를 구했으며, 이의 회귀식을 구하고, 그 회귀식으로 산정한 결과를 초기값으로 사용하였다. 이러한 방법론을 적용하여 한계수심과 등류수심을 실제로 계산해 본 결과, 정확해와 거의 일치하는 좋은 결과를 얻을 수 있었다.
Abstract
This study suggests an explicit method to obtain accurate critical and normal depths in the rectangular and trapezoidal sections. To this end, this study derived a nonlinear non-dimensional equations that govern the normal depth in the rectangular section and the critical and normal depth in the trapezoidal section. The solution for this nonlinear equation was obtained by using the Newton-Raphson method, which has second-order accuracy. In order to obtain initial values necessary for calculation, the exact value of the non-dimensional equation derived earlier was obtained by using Matlab fzero, a function to obtain a solution of nonlinear equations. A regression equation was then drawn, and the result calculated from this equation was used as the initial value. This study used this methodology to calculate the critical and normal depth and obtained results that coincided closely with the exact values.
참고문헌 (11)
- Swamee, P. K., "Critical depth equations for irrigation canals", J. of Irrigation and Drainage Engineering, 119(2), pp.400~409 (1993), ASCE
- Swamee, P. K., "Normal depth equations for irrigation canals", J. of Irrigation and Drainage Engineering, 120(5), pp.942~948 (1994), ASCE
- Wang, Z. Z., "Formular for calculating critical depth of trapezoidal open channel", J. of Hydraulic Engineering, 129(4), pp.253~259 (2003), ASCE
- Swamee, P. K., "Exact solution for normal depth problem", J. of Hydraulic Research, 42(5), pp.541~547 (2004), IAHR
- Swamee, P. K., "Exact solution for critical depth in a trapezoidal canal", J. of Irrigation and Drainage Engineering, 131(5), pp.474~476 (2005), ASCE
- Das, A., "Flooding probability constrained optimal design of trapezoidal channels", J. of Irrigation and Drainage Engineering, 133(1), pp.53~60 (2007), ASCE
- Vatankhan, A. R., "Simplified accurate solution for design of erodible trapezoidal channels", J. of Hydrologic Engineering, 16(11), pp.960~965 (2011), ASCE
- Vatankhan, A. R., "Explicit solutions for critical and normal depths in channels with different shapes", Flow Measurement and Instrumentation, 22, pp.43~49 (2011)
- Vatankhan, A. R., "Explicit solutions for critical and normal depths in trapezoidal and parabolic open channels", Ain Shams Engineering Journal, 4, pp.17~23 (2013)
- Chow, V. T., "Open-Channel Hydraulics", pp.63~99 (1959), McGraw-Hill
- Kreyszig, E., "Advanced Engineering Mathematics", pp.790~794 (2006), John Wiley & Sons