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本文首先根据习认为的泥沙粒径的对数值1nd服从正态分布的假设,导出粒径d的对数正态分布式及其相应的均值和方差计算式,与此同时,从理论上指出天然沙的平均粒径d_(pj)恒大于其中值粒径d_(50);其次,给出一种确定混合沙全沙代表粒径d_j以及任意粒径组泥沙的代表粒径(中值粒径)d_(j50)的方法和计算公式;最后,从数学上证明并指出目前有些河流动力学教科书中关于与正态分布有关的诸如平均粒径d_(pj)、几何平均粒径d_(?)、均方差σ或σ_d以及四分差σ_q等几个表达式的正误。
Based on the assumption that the logarithm of sediment particle size logarithm 1nd obeys normal distribution, this paper derives the logarithm normal distribution of particle size d and its corresponding mean and variance calculation formulas. At the same time, it points out theoretically The mean particle size d_ (pj) of natural sand is always greater than its median particle size d_ (50). Secondly, a representative particle size of sediment with median particle size d_j Particle size) d_ (j50). Finally, it is proved and pointed out mathematically that some current textbooks on river dynamics such as average particle size d_ (pj), geometric mean particle size d_ ?), Mean square deviation σ or σ_d and quartile difference σ_q and so on several positive and false expressions.