Somewhere in the Alps, a mountain lake discharges into a 8-m wide stream with boulders across the bottom and gravel along its sides, thus having a Manning coefficient n = 0.041. At the starting point on the edge of the lake, the stream bottom lies 0.90 m below the open water level in the lake and, downstream of that point, the bottom slope is uniform at S = 0.005.
(a) What is the volumetric discharge of the lake into the stream? And, for this discharge, can the bottom slope be considered mild or steep?
(b) What are the water depth and velocity at the head of the stream? And,what are they far downstream (assuming no change in slope, width or bottom