This is sometimes called section factor (See Ricahrd French Book or ASCE book by Segio Montes) That is the P (Wetted perimeter) over y (Depth) nothing special.
PS: Those analytical developments in Open Channel Flow are absolutely lame and part of history today. All people solve 1D Saint Venant and find the free surface and most of the time your channel is not prismatic any more. Also solving an even very large network of 1D channels with more than 50000 nodes is very fast and efficient those days