An Empirical Formula which Predicts the Critical Parameters of a Planar Array of Uranium-Solution-Filled Cylinders

An empirical formula has been developed for determining the individual diameter of essentially unreflected cylinders in a critical planar array. The formula is. The independent variables are N, the number of cylinders in the array; S, the edge-to-edge spacing between adjacent cylinders; H, the solution height in the array; C, the concentration of the solution [U ∼93 wt% ²³⁵U]; G, the geometry factor determined by the shape of the array; and k_i (i = 1, 2, ... , 8), the constants determined by the type of solution, either uranyl nitrate or uranyl fluoride. These independent variables, the formula ranges, and approximations are discussed. The critical cylinder diameter, calculated by this formula, is within ±8% of the experimentally measured diameter for 112 experimental data points. Therefore, the formula can be used as a guideline for nuclear criticality safety.