q evlaute width and depth for stable alluvial

Question

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.