Study On Relative Hydraulic Parameters Law Of Stepped Spillway

Stepped spillway is common in flood energy dissipating body of water conservancy projects, it is known that stepped spillway has higher energy dissipation, and it is more convenient for construction than smooth stepped spillway in engineering projects. It can overcome cavitation damage existed in smooth spillway. Nowadays the study on stepped spillway flow rule is a hot issue, however, there is no convenient research results for engineering applications because of the complex affected factors of stepped spillway; the relative hydraulic parameters is proposed as a new idea in our school: it puts forward the definition of the relative hydraulic parameters after comparing the difference of hydraulic parameters of stepped spillway and smooth spillway, and then study the flow law of stepped spillway on the basic of smooth spillway.Four new hydraulic parameters are defined in this paper in order to make research on stepped spillway: the relative energy dissipation ratio is the difference of energy dissipation between stepped spillway and corresponding smooth spillway; relative Froude number is the difference of Froude number between smooth spillway and corresponding stepped spillway; relative energy dissipation head is the difference of energy dissipation head between stepped spillway and corresponding smooth spillway; relative velocity is the difference of velocity between smooth spillway and corresponding stepped spillway. 21 groups tests with 26.57°, 32.01°, 33.69°, 38.66°, 51.3° slopes, 1.43~6.67 cm different step heights have been made, this paper study the relation between the relative hydraulic parameters and the length of the spillway, unit width discharge, step height, slope systemly. The results show that there is good law between them, which exist in the following several aspects:(1) It is obvious in non-uniform flow that the straight slope of relative velocity decreases while the unit width discharge increases, and increases while the stepped height and the slope of stepped spillway increase, and the correlation coefficient is high.(2) In non-uniform flow the relative Froude number increases while the unit width discharge decreases, stepped height and slope increase, and the correlation coefficient is well performed.(3) In non-uniform flow the relative energy dissipation ratio do not changes nearly while the unit width diascharge and stepped height change, but it increases first and then keep still while the slope of stepped spillway increases, and the correlation coefficient is good.(4) The relative energy dissipation head has the same law with the relative energy dissipation ratio.The papaer also study the relation between relative velocity, relative Froude number, relative dissipation ratio, relative dissipation head in different length of the spillway, unit width discharge, step height, slope. The results show that there is good law between them, which exists in the following several aspects:(1) the relative velocity and relative Froude number keep linear relation along the flow, and the correlation coefficient is well performed, theoretical analysis proves its inevitability.(2) the relative Froude number and the energy dissipation ratio also keep linear relation along the flow, and the correlation coefficient is good.(3) the relative velocity and the relative energy dissipation ratio keep relation along the flow, and the correlation coefficient is good.The existence of the linear relationship provides a basis for the calculation of stepped spillway hydraulic parameters. We can solve the relative hydraulic parameters in the areated point after calculating the mixture height and mean velocity of stepped spillway and the results calculated results of corresponding smooth spillway. According to linear relation of the relative hydraulic parameters, we can decide hydraulic parameters of stepped spillway based on the results of corresponding smooth spillway, such as energy dissipation, the mean depth and energy dissipation ratio in the flow cross section.The innovation of this paper is:(1) the paper study the relative flow law of stepped spillway systematically, and gained clear law: in non-uniform flow the relative flow parameters keeps good linear relation along the chutea, the linear correlation coefficient is good.(2) the paper study the relation between two relative flow parameters in the whole flow, the linear relation also exists, and the linear correlation coefficient is good.(3) the results of this study have a wide use, it can be applied for the slope 26.57 °~ 51.3°,and it has a good performation.(4) the method calculation of hydraulic parameters of stepped spillway using relative flow law does not introduce the empirical formula, and also overcomes the specialized requirements of numerical simulation for engineering applications. It meets the engineering requirements. The maximum error of calculation results of mean depth of stepped spillway is small, for example.