The Limerinos equation computes bed roughness based on grain roughness. It is primarily applicable to channels without active bed forms, where grain roughness is the primary source of bed roughness. It is the simplest equation, computing bed roughness as a function of the hydraulic radiI(R) of the channel and the d84 particle size (the partial size diameter two standard deviations above the mean):
n = \frac{0.0926R^{1/6}} {1.16+2.0log \left( \frac{R}{d_8_4} \right)}