Purpose of the project: Apply numeric integration techniques to a real-world problem.
How do you measure streamflow? The basic idea is simple: it is area times velocity. For example, suppose you had a river that was [latex]20[/latex] feet wide, [latex]3[/latex] feet deep, and had water moving at [latex]2[/latex] feet per second. Then we multiply the [latex]20[/latex] and the [latex]3[/latex] to get an area of [latex]60[/latex] ft[latex]^2[/latex], and the multiply by the [latex]2[/latex] ft per second to get [latex]120[/latex] ft[latex]^3[/latex] per second. This works great if you have a rectangular river where the water moves at a constant velocity. But what if the river is not a rectangle? What if the velocity changes depending on where in the river you are? How can you find the streamflow? And what does this have to do with numeric integration techniques?
- Come up with two different ways to find streamflow in a river. Why do they work? And how do they relate to the numeric integration techniques we studied?
- Try both methods on the virtual river (link). I recommend using a spreadsheet to record your data and to automatically do the calculations for you.
- If you have access to a flow meter or some method of calculating water velocity, try out both methods in a real river. Which method do you feel worked better? Why?