青岛市老排水涵管德式蛋形断面的水力学分析

Hydraulics Analysis of German Egg-shaped Cross-section of Qingdao Old Drainage Culvert Pipe

以青岛市老排水涵管的实物为基础,通过断面尺寸的测量、曲线拟合和几何学分析计算,给出了该断面是由底部、左右两侧和顶部半径比为0.5∶3.0∶3.0∶1.0四段圆弧相切组成的设计复原图及其参数关系;以德式蛋形断面的最大宽度和圆心角为自变量参数,全面给出了各水力要素的理论计算公式。系统比较了德式蛋形与等效圆形断面的水力学特性,结果表明等效圆形比德式蛋形断面多占地约20%;在小充满度条件下,德式蛋形断面比圆形断面的流速大,水力学条件更加优越;在圆形断面设计充满度为0.75时对应的自由水面以上净空高度相等的条件下,德式蛋形断面的充满度约为0.80,其过水流量大于满管流量相等的等效圆形断面的过水流量。以量纲一的数提出的德式蛋形断面在不满管流与满管流时流速比和流量比的理论计算公式及曲线图,适用于各种规格的断面尺寸、管材粗糙系数和涵管底坡,简单、快捷、方便、实用,为该断面的水力设计提供了理论依据。

Based on the Qingdao City old drainage culvert pipe and through the cross-section size measurement, curve fitting and geometric analysis and calculation, the cross-section＇ s restored diagram consisting of four tangential arcs and its parametric relations were obtained. The radius ratios of the bottom, left side, right side and top arcs were 0.5 ： 3.0 ： 3.0 ： 1.0. Taking the German egg-shaped crosssection＇s maximum width and central angle as the independent variable parameters, the theoretical calculation formulas of hydraulic factors were given. The systematic comparison of hydraulic characteristics between the German egg-shaped cross-section and an equivalent circular cross-section was performed, indicating that the area of the latter was 20% larger than that of the former. In the condition of small fullness, the flow velocity in the German egg-shaped cross-section was larger than that in the circular crosssection, and the hydraulic condition of the former was more favorable. When the flow filled 0.75 of the design fullness of circular cross-section, and the free space above the free surface of the two sections was equal, the fullness of German egg-shaped cross-section was O. 80 and its flow rate was higher than that of the circular cross-section whose flow rate was the same when pipe was full. The theoretical calculations and graphs of the flow ratio and velocity ratio under the condition of partial and full pipe flow configurations were presented by dimensionless variables. The formulas are suitable for several cross-section sizes, pipe roughness coefficients and pipe bottom slopes. They are simple and efficient, convenient and practical, providing a theoretical basis for the hydraulic design of the cross-section.