Consider gradually varied flow of water in a wide rectangular irrigation channel with a per-unit- width flow rate of 5m³/s·m, a slope of 0.01, and a Manning coefficient of 0.02. The flow is initially at uniform depth. At a given location, x = 0, the flow enters a 200m length of channel where lack of maintenance has resulted in a channel roughness of 0.03. Following this stretch of channel, the roughness returns to the initial (maintained) value.

(a) Calculate the normal and critical depths of the flow for the two distinct segments. 

(b) Numerically solve the gradually varied flow equation over the range 0 ≤ x ≤ 400 m. Plot your solution (i.e., y vs. x) and comment about the behavior of the water surface.

FIGURE P13–95

Transcribed Image Text:

0 X Rough surface 200 m Smoother surface 200 m