通过对圆形断面临界流公式的数学变换,得到其临界水深的牛顿迭代公式,应用最优一致逼近法得到了临界水深中心角θ的近似计算式,并以此近似算式为初值函数,代入迭代方程获得了圆形断面临界水深的直接计算公式。实例计算及误差分析结果表明,在工程实用范围内该方法最大相对误差为0.03%,若用该近似结果再迭代一次,精度则高出104倍。 Through the mathematical transformation of the circular section critical flow formula, the Newton iteration formula of its critical water depth is obtained, and the approximate calculation formula of the critical depth center angle θ is obtained by using the optimal uniform approximation method. Based on this approximate formula as the initial value function, The iterative equation obtained the direct calculation formula of the critical depth of circular section. The results of example calculation and error analysis show that the maximum relative error of this method is 0.03% within the engineering practical range. If the approximation result is iterated again, the precision is 104 times higher.