Explain the Normal Depth Equation

The equation is derived from the Chezy-Manning equation. As written below it determines the diameter of a circular storm or sanitary sewer when the Q_full, roughness coefficient (n) and slope (s) are known.   

      D = 1.335 (n Q_full /(s) 0.5) 0.375  

Rearranged, the equation can determine Q_full when the inside diameter, roughness coefficient and slope are known.

Q_full ^0.375 = (D (s)^0.188)/(1.335 (n)^0.375)

Rearranged, the equation can determine the slope of a sewer installation if Q_full, roughness coefficient and diameter are known.

      (s)^0.5 = (n Q_full)/(D/1.335)^2.67