| The heteromorphic ellipse cross-section is a new kind of hydraulic tunnel section with two-parameter curve,and its standard type section has a high degree of agreement with the existing horseshoe-shaped and egg-shaped sections.Calculations of characteristic depths and water surface profile for this new type of cross-section involve higher-order implicit function equation and complicated function integral operation,which cannot get analytical solutions.In this paper,the hydraulic characteristics and hydraulic calculations in free surface flow of standard type heteromorphic elliptic crosssection are systematically studied.The main results are as follows:(1)Based on Wu's two-parameter curve,the basic equation of the standard type heteromorphic elliptic section was derived,and the calculation formula of hydraulic elements of this new type of cross-section was given.Collated and deduced the hydraulic elements calculation formulas of four types of horseshoe-shaped section,including the standard kind and the chamfer kind.The results of geometric features and hydraulic elements comparative analysis show that the hydraulic characteristics curves of standard type heteromorphic elliptic cross-section and horseshoe cross-section are very close.This new type of cross-section with smooth and continuous shape has obvious advantages on relative water area and flow capacity in the range of medium and low water depths,and is beneficial to improving the flow conditions.(2)On the basis of the open channel uniform flow and critical flow basic equation,combined with the calculation formula of hydraulic elements of the cross-section,by introducing dimensionless parameter and MATLAB optimization curve fitting,the explicit formulas of normal depth and critical depth in free surface flow of this new type of cross-section were put forward.The absolute values of relative error were less than 0.362% and 0.288% respectively.(3)Based on the basic differential equation of the non-uniform gradient flow in open channel,the piecewise trial calculation method of the surface line in free surface flow for this new type of cross-section was derived.Using the function substitution method,the simplified integral calculation method of the water surface profile and the direct calculation formula were given.The error of the calculation example is 0.049% and 0.324% respectively.(4)Based on the basic equation of hydraulic jump and the contraction cross-section in open channel,through parametric function fitting,the explicit solution method of the conjugate depth and contraction depth in the form of monobasic high power equation for standard type heteromorphic elliptic cross-section were given.The error of the calculation example is-0.477% and-0.462% respectively.The direct calculation methods for characteristics depth and water surface profile in free surface flow of standard type heteromorphic elliptic cross-section presented in this paper are simple in form and have strong generality.The applicable scope and accuracy can meet the requirements of practical engineering calculation,which can provide theoretical reference for the popularization,application and engineering design of this new type of cross-section. |
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