Q. Evlaute width and depth for stable alluvial canals?

Lacey originally evolved width and depth formulae for stable alluvial canals. These were the following. 

P = 4.836 Q^1/2

R = 0.473 (Q/f)^1/3

wherein P is wetted perimeter in m, Q is discharge in m³/s, R is hydraulic mean radius in m and f is the silt factor which is given as 1.76 m^1/2, m being weighted mean diameter of bed material in mm. On the basis of data of a few rivers, Lacey showed that his P:Q relationship is valid not only for canals but also for alluvial rivers. Since river sections are much wider than canals, P and R can be replaced by W and D, namely width and depth respectively.