矩形断面收缩水深简捷计算公式

根据矩表断面收缩水深的基本方程得出计算收缩水深的递推公式，并结合收缩水深的特点，将该递推公式马克劳林级数展开成级数和，应用求和公式及统计计算得出了矩形收缩水深的直接计算公式。误差分析及算例表明，该公式简便，在工程实用范围内，其最大相对误差的绝对值不超过０．４３％，可以满足精度要求子以和查图查表及试算迭代法的缺点。

A Formula for quickly calculating water depth at vena contraction in rectangular channel flow

A recurrence formula for computing water depth at vena contraction is derived from the basic equation of water depth at vena contraction in rectangular channels. With the water depth at vena contraction much less than the specific energy of the flow at the section before dam,the recurrence formula is expanded into Maclaurin series,then the summation formula and statistical calculation are used to obtain the final formula for directly computing water depth at vena contraction in rectangular channels. Error analysis and a case history computed by using the formula indicate that the formula is simple and convenient,and needs no graphic chart,trial computation and iteration. As far as the engineering practice is concerned,the absolute value of the maximum relative error of the water depth computed by using the formula is not greater than 0. 43 percent,and can meet the requirement for accuracy.