Research Article
Sep 1980
Minimum Stream Power: Theory
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VIEW THE REPLYPublication: Journal of the Hydraulics Division
Volume 106, Issue 9
Abstract
Variational formulations of the equations of motion applicable to irrotational, nonaccelerating, as well as gradually varied open channel flows are presented. It is shown that there exists a suitable functional, J, from which the equation of motion can be obtained as the condition of minimization with respect to the velocity profile. Minimization of J is shown to be equivalent to the minimization of the total rate of energy loss, E, providing that the discharge, Q, and the total head, H, at upstream and downstream ends of the river is known. Furthermore, if the speed of the movement of the river bed is small, then the total rate of energy loss is shown to be equal to the total stream power. Thus, under certain restrictive conditions the hydraulic problem reduces to the problem of minimizing total stream power. The minimization theory presented here is somewhat similar to the second writer's theory of minimum unit stream power.
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Published In
Journal of the Hydraulics Division
Volume 106 • Issue 9 • September 1980
Pages: 1477 - 1487
Copyright
© 1980 American Society of Civil Engineers.
History
Published in print: Sep 1980
Published online: Feb 3, 2021
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Authors
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Charles C. S. Song, M.ASCE
Prof. of Civ. Engrg., St. Anthony Falls Hydr. Lab., Univ. of Minnesota, Minneapolis, Minn.
Chih Ted Yang, M.ASCE
Civ. Engr., U.S. Dept. of the Interior, Water and Power Resources Service, Engrg. and Research Center, Denver, Colo.
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