Problem 3. The approximate profile of a stream channel is given in the graph below. The depth is modeled using the equation d(w) = = -20- -1-0- 0 8 (w4-20w3+141w² - 406w) +51 width (ft) 10 (a) The stream is deep, but not so wide. 1. (***) At pre-flood stage, the water depth is 20 ft (the green line), and the edge of the stream spans from w = .8 ft to w = 9 ft. Calculate the cubic feet per second if the water is moving at 9 feet per second. Repeat this process for "typical" early summer flows (10 ft depth marked in purple) when the river spans from w = 1.3 ft to w = 8.5 ft, and the water moving at 5 feet per second. 2. (**) You can see from the profile that the stream depth is not uniform. Calculate the average depth at "typical" early summer flow. Draw a picture showing the simplified stream profile. Use your simplified stream depth model to create an equation that gives the cubic feet per second which relies only on stream speed v. What are the limitations of your model?

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