Maddenation
Measuring streams
This is for David, but anyone in the family (or the world) can feel free to be interested. I was reading the recent issue of Volunteer Monitor, the national newsletter of volunteer watershed monitoring (right up there with Hazardous Waste Digest, which is NOT, by the way, about eating hazardous materials) and ran accross a description of the “Head Rod” method for determining stream flow. I love these things. Somebody takes a simplified version of the Bernoulli equation and develops a method for measuring flow in small rivers and streams. It goes like this.
Take a meter stick or other suitable measuring rod that has a thin edge and a wide edge. (Maybe you should affix a flat disk to the bottom end to prevent it from sinking into the mud during use.) At a given point in the stream, measure the depth of the water with the thin edge facing the current. This measurement will be used for determing the depth profile in the stream. Then turn the stick sideways and measure the increase in depth due to the water “piling up” against the side of the ruler. This is a crude measurement of the “velocity head” of the water as it converts the kinetic energy of flow into the potential energy of static head. At each point, the velocity of the water can be calculated by taking the square root of 2gh, where h is the increase in depth and g is the gravitational constant. (Use the right units, children.) What’s really neat is that, if there are variations in the vertical velocity profile, this method ought to provide a “physically” averaged result.
The total flow can be determined by integrating the flow over the cross-sectional area of the stream. Assuming measurements are at equal distances across the width of the stream, each flow will represent an area proportional to the depth measured at that point. So the average stream velocity will be the depth-weighted average of the individual velocities. The cross-sectional area of the stream is determined based on the width of the steam and the average of the depths measured.
For more information, see this Waterwatch Australia website.
Maybe you could take your students on a field trip to a nearby stream (the Chicago river? no, I guess not) and measure the flow. We should definitely measure the Whippany river when you’re home for Easter. Then we can check our result vs. actual flow measurements by the State. I have the perfect ruler to use, a stainless steel 4 ft “yard” stick. I can’t wait to try it.
Dad • Ideas • 04/02/04 • 7 comments
Comments
Dad • 12/09/04 • 11:17 PM:Not only didn’t we try this, but I can’t find the stainless steel ruler! I’m sure I took it out to get ready for the measurements, and then lost track of it! It’s your fault, David.
David • 12/10/04 • 8:20 PM:Had you done it then, and done it quickly, none of this would’ve happened. I was hoping and waiting.
PS. You’ll find the ruler with your shoelaces.
Dad • 01/02/05 • 7:50 PM:Hey! You’ll be happy to know I found the ruler. But I’m still missing those shoelaces.
Dad • 04/17/06 • 7:55 PM:On Saturday, over two years after the original posting, Dave and I finally measured the Whippany river. We didn’t do the full cross-section, as you would do if you really wanted accuracy, but we did a few single point measurements along the southern shore.
Dave had visited the area a couple days earlier while walking to the Brookside diner. No doubt you will hear about his adventures that day in another posting. Suffice to say, he wanted to show me where he’d been, so before walking over, I grabbed my walking stick and the famed 4-foot steel ruler.
As we approached the river, we noticed many large rocks partially submerged along the river’s edge. These made excellent standing points from which to slip the ruler into the flowing water. The water’s depth was generally in the range of 20-22 inches, while the increase in depth with the ruler turned sideways (see above) was between 1 and 2 inches. That’s it! We can now estimate the river’s flow.
If we take 1.5” increased depth (h), the velocity is equal to the square root of 2gh, which is about 2.8 ft/sec. If we assume a river width of 20 feet and an average depth of 21 inches, then the cross-sectional area of the river is about 35 sq ft. So that velocity amounts to almost 100 cubic feet per second, which is something like 45,000 gallons per minute. That’s a pretty large flow. About twice as large as the flow recorded in Morristown for the Whippany river. Oh well. To be accurate, we really needed to do measurements across the whole river, and this would have involved getting wet.
Patrick • 04/21/06 • 4:12 PM:OK. I don’t entirely get this: “Then turn the stick sideways and measure the increase in depth due to the water “piling up” against the side of the ruler.” Do you mean that the water hitting the broad side of the ruler tunnels down and pushes away some of the river bottom, thus letting the yard stick stick lower? Or do you mean that you’ve got the yard stick at an angle when its broad side gets hit by the water?
Dad • 04/21/06 • 11:21 PM:This link shows a diagram of the “head rod” method. The description isn’t that good (the formula should be H = D2 - D1), but maybe the picture will help. No “pushing away of the river bottom” is involved. When you turn the stick sideways, you are stopping a 2” wide column of water, which then has to flow around the ruler. This causes an increase in the height of the water that is proportional to the flow rate.
By the way, the example they give, where h is a half meter, is a little unreasonable. That would represent a very fast stream, which would likely be very dangerous to wade in for the purpose of getting the flow rate. The force required to hold the ruler steady in the stream would be very high.
Patrick • 04/23/06 • 10:40 PM:Ah. That makes sense. Not to be too critical, but you could have explained it a little better.
Anyway, I love that you actually did this, but it would have been a bit cooler if you had waded into the water, especially above the dam!
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