Research On The Calculation Method Of Characteristic Depths Of Open Channels

Characteristic water depth of open channel is an important hydraulic parameter for channel engineering analysis and design,channel operation and management,channel energy dissipation and scour prevention,including normal water depth,critical water depth,conjugate water depth and shrinkage water depth.Its basic control equations are implicit transcendental equations,and some complex sections are even piecewise high-order functions,which can not be solved directly in theory.Traditional calculation methods such as trial algorithm,iteration method and chart method can get results,but there are various drawbacks,such as trial algorithm workload is large,calculation is tedious,the advantages and disadvantages of iteration depend on the selection of initial iteration values.Chart method needs special charts,which is extremely inconvenient to use,and can not meet the needs of today's production practice.Therefore,a simple,universal and accurate method for calculating the characteristic depth of open channel is proposed,which not only can further improve the theoretical system of hydraulic calculation,but also has a very important significance for solving the practical problems of channel engineering.This paper summarizes the formulas for calculating the normal and critical depth of open channel sections proposed by domestic and foreign scholars in recent years by means of regression analysis,binary optimization fitting,least squares fitting,genetic algorithm and neural network.A series of typical calculating methods are optimized through error analysis and case calculation.On the basis of previous studies,the basic governing equations of normal and critical water depth of circular section,ordinary gate-shaped section and egg-shaped section are mathematically transformed.Dimensionless parameters are introduced to simplify the governing equation,the calculation model is established by using limit principle,and the improved particle swarm optimization algorithm is realized by using MATLAB software programming.The calculation model parameters are obtained by uniform optimization,respectively.The direct formulas for calculating the normal and critical water depths of circular section,ordinary gate-shaped section and egg-shaped section are established.Error analysis and example calculation show that the maximum relative error of normal water depth formula for circular section is less than0.07% and that of critical water depth formula is less than 0.18%.The maximum relative error of normal water depth formula for Chengmen cave section is less than 0.04% and that of critical water depth formula is less than 0.06%.The maximum relative error of water depth formula is 0.07%,and the maximum relative error of critical water depth formula is 0.17%.In addition,fast formulas for calculating the water depth of the ordinary city gate section and theegg shaped section are proposed.Ten sets of formulas are simple in form,high in accuracy and versatility.By optimizing fitting,the solution of normal and critical water depths of ordinary gate-shaped section and egg-shaped section can avoid the calculation between zones caused by geometric shape change,which makes the calculation more simple and can provide useful reference value for channel engineering analysis,design and operation management.