New formula for calculating the depth of a rectangular expanding deep excavation energy dissipation basin with a flat bottom
To address the inconsistency between the traditional formula for calculating the depth of a flat-bottom rectangular ex-panding deep excavation energy dissipation basin and the formula for calculating the depth of an equal-width rectangular section energy dissipation basin,a new formula for calculating the depth of an expanding rectangular section deep excavation energy dis-sipation basin has been derived.This derivation involves establishing equations for the contraction section water depth,hydraulic jump,basin outflow drop,and the geometric relationship at the end of the energy dissipation basin.Analysis suggests that the tra-ditional formula for calculating the depth of the energy dissipation basin often yields results smaller than those obtained using the new formula.Using the depth calculated by the traditional formula as a design basis may not fully ensure the formation of a sub-merged hydraulic jump with a determined submergence coefficient.This could lead to significant downstream riverbed erosion and fail to meet energy dissipation design requirements.When the widths at the beginning and end of the energy dissipation basin are equal,the new formula coincides with the formula for calculating the depth of an equal-width rectangular section energy dis-sipation basin.The new formula,with its clear physical concept,provides a more reliable basis for engineering design.
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