### Sample RiverNet Problem Project of the Month III

Math and science lessons often focus on facts and techniques. In practice, mathematics provides a collection of tools for answering questions and science is the result of our attempts to understand the world around us. Projects like Bridgewater State College's RiverNet Watershed Access Lab and TERC's Global Lab provide students with a chance to partipate in a real science experiment, gathering information from the world around them and using mathematical tools to interpret it, then reporting their results to the public. The following story problem is based on a real report on the Quequechan River and is designed to give you a taste of the mathematics involved in a project like this; hopefully you will someday experience the data collection and comparison, collaboration and reporting involved in such a project with your own students.

At Murdock Street in Middleboro, the Nemasket River is 32 feet wide. Someone waded into it and measured its depth at the ends and center of each two foot interval (approximately 32 measurements). At each two foot interval they also took three measurements of the flow of the river -- its speed measured in feet per second (a total of 48 measurements). The data is displayed in the table below. (Distances are measured in feet, flow is measured in feet per second.)

 Width Seg. Seg. Mid Point Discharge Seg. # d (Dist.) Depth a Depth b Depth Area Flow 0.6 Avg. Flow (CFS) 1 2.00 2.70 3.00 2.80 1.30 #VALUE! 1.17 1.20 2 2.00 3.00 3.55 3.10 1.68 #VALUE! 1.73 1.80 3 2.00 3.55 3.60 3.68 1.61 #VALUE! 1.58 1.61 4 2.00 3.60 3.70 3.60 1.61 #VALUE! 1.98 1.79 5 2.00 3.70 3.50 3.50 2.12 #VALUE! 1.78 1.66 6 2.00 3.50 3.55 3.60 1.49 #VALUE! 1.73 1.58 7 2.00 3.55 3.20 3.20 1.76 #VALUE! 1.61 1.68 8 2.00 3.20 3.00 3.15 1.99 #VALUE! 1.64 1.77 9 2.00 3.00 3.00 3.00 1.71 #VALUE! 1.84 1.88 10 2.00 3.00 2.75 2.80 1.42 #VALUE! 1.51 1.41 11 2.00 2.75 2.75 2.87 1.31 #VALUE! 1.36 1.63 12 2.00 2.75 2.85 2.90 1.70 #VALUE! 1.50 1.41 13 2.00 2.85 2.93 2.90 1.39 #VALUE! 1.31 1.27 14 2.00 2.93 2.95 2.80 1.39 #VALUE! 1.37 1.26 15 2.00 2.95 3.10 3.10 1.27 #VALUE! 0.89 1.29 16 2.00 3.10 2.30 2.55 1.06 #VALUE! 1.17 1.11

Question 1: Approximately how many cubic feet of water per second go through the river at this point?

Now suppose you take a sample of river water to a chemistry lab and dtermine that it contains .04 mg/L of nitrogen.

Question 2: If the concentration of nitrogen is the same for all the water in the river, how much nitrogen (in grams) flows down this river per second?

Sample Solution

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