A shear velocity model for open channel flow with bed forms
Einstein's method,namely,the bed hydraulic radius is the sum of two hydraulic radii corresponding to grain resistance R'b and bed form resistance R''b,was usually used in engineering for open channel flow with bed forms.A wide range of ks values have been suggested by different researchers when they use the logarithmic equation to calculate R'b.348 data sets of plane bed data were used for verifying the grain roughness ks,the results showed that the error is minimum when ks =d50 ; Einstein introduced a correction factorx into the logarithmic velocity equation to obtain the velocity in the transitional regimes,by analyzing Nikuradse's pipe flow data,consequently a uniform formula was developed to compute the correction factorx.The bed form resistance related to R''b,resulting from resistance to flow due to the bed configuration.By analyzing the measured data,the area of movable and stationary flat bed were distinguished to solve the problem that the Einstein's method could not solve.An empirical equation for the bed form resistance related radius Rb'' has been developed by analyzing the measured data.Finally,the model for calculating shear velocity was tested against a wide range of measured data and compared with original Einstein model; the results showed that present model got a lower error.Furthermore,the present model was more acceptable physically because R''b was zero for upper and lower plane bed regimes compared with the original Einstein model.
bed formgrain resistancebed form resistancecorrection factorhydraulic radius
国家科技期刊平台
NSTL
万方数据
维普
