Treebeard's Stumper Answer

Rollin' on the River
I took the Dunn Middle School 8th grade to the Santa Ynez River last week with the assignment to measure the flow in gallons per second. With three dams upstream and our usual 6 month summer drought, the river is not large, only about 30 feet across and a foot deep. That's a far cry from last year's floods! Part of the assignment was to devise a method for the task. But first, the kids had to decide where to measure the flow. One section of the river was deep and barely moving. Another place was narrow and swift. Would that make a difference?
DMS 8th graders measured a crosssection of the river and timed a floating object to get the speed and flow. It shouldn't matter where you measure a river. Except for new tributaries, there must be the same amount of water moving in slow and fast places or the river would back up on itself. But our local rivers often flow "upside down," with the rocks on top and the water beneath. The river might go dry just around the bend, though it's still moving through the rocks. The total flow is constant, but the measurable flow can vary a lot.Note: Despite the uncertainties of our homebrew methods, the kids' estimates of the river flow were fairly close. Working in different places with slightly diffferent methods, the kids measured between 60 and 250 gallons per second, at least in the same ballpark. One group started worrying about their methods when they noticed a leaf floating upstream blown by the wind! The same river peaked at 20,000 cubic feet per second (cfs) during last year's El Niño floods.
A few years ago, we were at the end of an extended drought here in Central California. Cachuma Lake is the largest reservoir on the Santa Ynez River. It was 60 feet down, so low that you could see the original river channel. At only about 30% of capacity, there was serious concern about our future water supply. Then the rains came. We tried to sneak in below the dam to watch it spill, but we were rousted by the authorities. The dam spilled for the first time in a decade that night. I missed the actual event, but I still wonder what happened. With 10,000+ cfs of water coming into the lake from above, there must be a sudden flow of 10,000+ cfs of water spilling over the dam. Would that huge wall of water run all the way to the ocean? Thinking about my answer above, I think not, but I'll leave it as an open question.
Graybear sent a detailed account of how to measure stream flow:
I'll tell you how we did it in engineering school. Rate of flow is comprised of two parts  the crosssectional area of the river and the velocity at which it's moving. To compute the area, we pulled a tape measure across the river and measured the depth at each foot along the tape. The area is then the sum of the areas of the various triangles and trapezoids. (Actually, if you measure the depth in feet, the area in square feet will the the sum of the depths.) To compute the velocity, we stretched two parallel strings across the river, several feet apart (farther apart for faster moving rivers). A small piece of wood would be dropped in the river upstream from the first string. We used a stopwatch to measure the time that elapsed between the wood crossing the first and second string. We repeated this process many times and from several points across the breadth of the river. The distance between the strings in feet divided by the average time in seconds gives the velocity. The flow rate, in cubic feet per second, is the product of the area and the velocity. To convert to gallons per second, multiply by 1728 (# of cubic inches/cubic foot), then divide by 231 (# of cubic inches/gallon).This method is obviously an approximation, but it is how most field engineers without sophisticated equipment would do it. Water flows faster on the surface than on the bottom, so the answer is larger than it should be.
As far as the difference between the fast and slow portions of the river, if we can assume that no water is lost or gained to/from groundwater, then the answer *should* be the same  it's a closed system. However, very fast sections usually have rapids, turbulence, large rocks, and uneven bottoms which make measuring the area very difficult, to say the least. Measuring the average velocity is no picnic either  rapids have eddies that can hold your float for hours, and underwater, the current can be flowing in a negative direction.
We have a small river in Virginia called Sinking Creek, so named because at several points along its course it flows underground. It is large enough to canoe/kayak, but as you float along the river it suddenly dries up and you must portage several hundred yards down the rocky bed to find flowing water again. Where you decide to measure its flow makes a big difference!
Thanks, Graybear. You helped me (again!) understand the situation.
The early Greek philosopher Heraklitus wrote that you can't step in the same river twice. In all the swirl of change that is a real river, it's a relief to realize that something must stay the same.
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