Question

A ditch was channelized to augment its capacity to convey water from a lake to a detention pond. The channel is straight, and it has a trapezoidal cross-section with side slope 4:1 and bottom width 14 feet. The bottom elevation of the channel is 715.50 feet where it is connected to the lake, and 708.35 feet at the end of the channel where it joins the detention pond. The channel length is 950 feet, and it is lined with concrete with gravel on the bottom. (a) Use Manning’s equation to compute a rating curve for the channel cross section, at a location where channel bottom elevation is 709.27 feet. That is, construct a plot of stage (ft) versus discharge (ft3/s). For these computations, assume the value of the Manning roughness coefficient (n) equals 0.02. (b) At what flow discharge will the channel overflow its banks and cause flooding to occur? (c) Consider the hypothetical case in which the channel is simply excavated and not maintained, resulting in dense weeds as high as the flow depth. Assume a Manning’s n value equal to 0.08 in this case. For what flow discharge will the channel overflow its banks? How does this compare with the value computed in part (b)? (d) For the discharges that cause overflow in parts (b) and (c), is the flow super- or subcritical? What are the critical depths for those discharges?

Answer 1

a) For this questions, first of all we must draw the cross section of channel indicating top width of flow, bottom width , water depth and side slopes.

Repeat the trial and error method by substituting values ranging between 708.35ft and 715.5ft and draw the rating curve between stage(ft) in x axis and discharge in y axis (take any 5 values for drawing the curve). Also specifically find Q corresponding to 709.27ft.

b) At flow discharge corresponding to 715.5ft, flooding may occur as that is the maximum elevation of channel available.

c)Since there is presence of dense weeds in the entire channel depth the discharge at which flooding occurs at 715.5ft will be lesser than that in case (b) though its hypothetical.

d) First find out the Froude number, if its less than one the flow is sub critical and if its above one flow is super critical.Use critical depth equation for a trapezoidal section to find out critical depth.

For additional inputs, students can refer to any of fluid mechanics books dealing with open channel flow.

Similarly find discharges for each value of mean depth y