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Analytical Solutions for Specific Energy and Specific Force Equations in Rectangular Open Channels
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In specific energy/specific force equations for a rectangular open channel flow, characteristic equations for obtaining alternate depths/conjugate depths were derived and their analytic solutions were presented. The characteristic equations were in the form of cubic equations for dimensionless alternate depths/conjugate depths, and the solutions to these characteristic equations had three real roots. Out of the three real roots, the first was a negative solution without any physical significance, the second was a solution located in the subcritical flow zone, and the third was a solution located in the supercritical flow zone. Consequently, under critical flow conditions, the solutions for the subcritical flow zone and the supercritical flow zone had identical multiple roots. In addition, it was demonstrated that the analytic solutions presented in this study are readily applicable to the analysis of water level changes and hydraulic jumps according to the channel transition.
Abstract
In specific energy/specific force equations for a rectangular open channel flow, characteristic equations for obtaining alternate depths/conjugate depths were derived and their analytic solutions were presented. The characteristic equations were in the form of cubic equations for dimensionless alternate depths/conjugate depths, and the solutions to these characteristic equations had three real roots. Out of the three real roots, the first was a negative solution without any physical significance, the second was a solution located in the subcritical flow zone, and the third was a solution located in the supercritical flow zone. Consequently, under critical flow conditions, the solutions for the subcritical flow zone and the supercritical flow zone had identical multiple roots. In addition, it was demonstrated that the analytic solutions presented in this study are readily applicable to the analysis of water level changes and hydraulic jumps according to the channel transition.
참고문헌 (6)
- Chow, V.T., "Open channel hydraulics" (1959), McGraw- Hill
- Lee, J.S., "Hydraulics" (2007), Goomibook
- Henderson, F.M., "Open channel flow" (1966), Macmillan Series in Civil Engineering
- Abdulrahman, A., , J. of Irrigation and Drainage Engineering, 134(4), pp.533~537 (2008)
- Sing, S.K., , J. of Irrigation and Drainage Engineering, pp.0401406-1-~ (2015)
- Spiegel, M.R., "Mathematical handbook of formulas and tables" (1968), McGraw-Hill