RECTANGULAR channel for a given area, perimeter(P) should be minimum.Calculation:Width of rectangular channel is b and depth of rectangular channel is yThan Area, A = byPerimeter, P = b + 2yP = (A/y) + 2yFor P to be minimum, dP/dy = 0(-A/y2) + 2 = 0A = 2y2by = 2y2b/y = 2Rectangular channel sectionTrapezoidal channel sectionR = y / 2A = 2y2 T = B = 2yP = 4yD = yR = y / 2\(A = \SQRT 3 {y^2}\)\(T = \frac{{4Y}}{{\sqrt 3 }}\)\(P = \frac{{2y}}{{\sqrt 3 }}\) D = 3y / 4

"> RECTANGULAR channel for a given area, perimeter(P) should be minimum.Calculation:Width of rectangular channel is b and depth of rectangular channel is yThan Area, A = byPerimeter, P = b + 2yP = (A/y) + 2yFor P to be minimum, dP/dy = 0(-A/y2) + 2 = 0A = 2y2by = 2y2b/y = 2Rectangular channel sectionTrapezoidal channel sectionR = y / 2A = 2y2 T = B = 2yP = 4yD = yR = y / 2\(A = \SQRT 3 {y^2}\)\(T = \frac{{4Y}}{{\sqrt 3 }}\)\(P = \frac{{2y}}{{\sqrt 3 }}\) D = 3y / 4

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In an open channel flow, for best efficiency of a rectangular section channel, ratio of bottom width to depth shall be:

Fluid Mechanics Open Channel Flow in Fluid Mechanics . 6 months ago

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Concept:For hydraulic efficient RECTANGULAR channel for a given area, perimeter(P) should be minimum.Calculation:Width of rectangular channel is b and depth of rectangular channel is yThan Area, A = byPerimeter, P = b + 2yP = (A/y) + 2yFor P to be minimum, dP/dy = 0(-A/y2) + 2 = 0A = 2y2by = 2y2b/y = 2Rectangular channel sectionTrapezoidal channel sectionR = y / 2A = 2y2 T = B = 2yP = 4yD = yR = y / 2\(A = \SQRT 3 {y^2}\)\(T = \frac{{4Y}}{{\sqrt 3 }}\)\(P = \frac{{2y}}{{\sqrt 3 }}\) D = 3y / 4

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Posted on 19 Nov 2024, this text provides information on Fluid Mechanics related to Open Channel Flow in Fluid Mechanics. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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