Study On The Variation Law Of The Stepped Spillway Relative To The Frude Number

The stepped spillway has been widely used in water conservancy projects in recent years because of its functions of both water discharge and energy dissipation.The research on the stepped spillway mainly focuses on the hydraulic characteristics.By introducing the concept of relative Froude number,predecessors studied the variation law of the stepped spillway relative Froude number under the influence of dimensional factors along the spillway.Based on the previous research,the dimensionality of the relative Froude number is analyzed.This paper defines the dimensionless number related to relative Froude number:relative critical water depth,dimensionless number of section position,slope.42 groups tests with five different slope of 26.6°,32°,38.6°,48°,51.3°,seven different step heights of 0.014m?0.067 m have been made.This paper analyzes the functional relationship between the relative Froude number and the dimensionless number.At the same time,the relationship between the relative Froude number and dimensionless hydraulic parameters is studied,and the relevant laws are summarized and applied.The main conclusions are as follows:(1)The relative Froude number has a linear increasing relationship with the dimensionless number of section position,and the straight lines pass through the origin,with good correlation.The relative Froude number and dimensionless number of section position always keep a high correlation regardless of the change of relative critical water depth and slope.The slope of the linear relationship decreases with the relative critical water depth as a power function,which indicates that the greater the relative critical water depth is,the smaller the obstruction of the step to the flow is.The slope relationship increases with the slope,which indicates that the greater the slope is,the greater the obstruction of the step to the flow is.It is more advantageous to increase the height and slope of the step for energy dissipation,and it is more necessary to use the stepped spillway when the flow of small unit width and the slope is steep.In this paper,the empirical formula of slope with respect to relative critical depth and slope is obtained by surface fitting,and the water surface profile is calculated with good result by using this formula.It is obvious that the dimensionless results are more universal.(2)The dimensionless relative velocity is obtained from the relative velocity: the relative step velocity.The relationship between the relative Froude number and the dimensionless and dimensionless relative velocity is obtained by analyzing the experimental data.The relative Froude number has a linear increasing relationship with the relative velocity,but the slope reflected by the dimensional relative velocity is not strong and difficult to be applied.There is a good linear relationship between the relative Froude number and the relative step velocity,and the slope relationship is exponentially decreasing with the relative critical water depth and linearly decreasing with the slope.The empirical formula of slope on relative critical water depth and slope is obtained by surface fitting,and the calculation results are good.Obviously,the dimensionless result is more general.(3)The dimensionless relative velocity head is obtained from the relative velocity head:the relative step velocity head.The relationship between the relative Froude number and the dimensionless and dimensionless relative velocity head is obtained by analyzing the experimental data.The relative Froude number increases linearly with the head of relative velocity,but the slope of the head of dimensional relative velocity is not very regular,so it is difficult to analyze and apply.There is a good linear relationship between the relative Froude number and the relative step velocity head.The slope of the linear relationship has a power function decreasing relationship with the relative critical water depth and a linear decreasing relationship with the slope.The empirical formula of slope on relative critical water depth and slope is obtained by surface fitting,and the calculation results are good.Obviously,the dimensionless result is more general.(4)The dimensionless relative specific energy is obtained from the relative specific energy:the relative step specific energy.The relation between the relative Froude number and the dimensionless and dimensionless relative specific energy is obtained by analyzing the experimental data.The relative Froude number increases linearly with the relative specific energy,but the slope reflected by the dimensional relative specific energy is not very regular and difficult to be applied.The relative Froude number increases linearly with the relative step specific energy,and the slope decreases exponentially with the relative critical water depth and linearly with the slope.As the slope law reflected in this chapter is not ideal,more data are needed to verify.it is obvious that the dimensionless relative specific energy law is more general.(5)The dimensionless relative water depth is obtained from the relative water depth: the relative step water depth.Combined with the experimental data,it is found that the relative Froude number has an increasing relationship with both dimensionless and dimensionless relative water depth,but the rules are complicated and inconvenient to apply.