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Name: Meredith B.
Status: Educator
Age: 30s
Location: N/A
Country: N/A
Date: June 2002


Question:
I teach physics, and my student posed this real life problem: Their summer house is on a lake. The lake level is too low so they would like to raise it up. They want to propose that the town throw rocks (approximately 2 ft large) in the outlet stream of the lake to raise the lake level. I said this would work and gave the analogy of putting a crack in a Polystyrene foam cup full of water and then pouring water into the cup from an outside source. All the water going in eventually has to come out, the higher up the crack is, the higher the level of the water before the water reaches steady flow out.

The student (and her parents) insist that the size and shape of the outlet (about 20 feet across and maybe 5 feet deep now) need to be carefully considered. I think that in reality you cannot really place rocks that carefully and if you did go through and account for the fact that as the lake level rises its surface area increases slightly and that the outlet has a ragged bottom and sloping sides and is 3 d not 2 d you would not drastically change the results - if you raised the bottom of the outlet by about 2 feet you would raise the level of the lake in approximately the same proportion. I have been wrong before, please help. Thanks!



Replies:
Meredith,

Without seeing and taking measurements and evaluating things like where the input water to the lake comes from and at what height, this becomes a theoretical problem. In reality all sorts of things would influence the result of "throwing stones". For example, if the water input to the lake is just above the current water surface of the lake, raising the water surface height could interfere with the water input to the lake, unless of course topography was feeding the lake with water from a high enough level to overcome the level change. Again, all this depends on the actual setting.

Has the weather been drier in your area over the last several years? They may be witnessing a lower water table due to drought. This situation could fix itself naturally, if it is the case.

I would close with what could be a simple solution which I saw in practice a few years back in eastern Montana when I worked for the US Forest Service. We worked in fire fighting and were always anxious about where we might get water in the event we needed a good supply of water quickly. One of the local's solutions was a neat one.....he trapped a couple local beavers and transported them to live adjacent to a tiny stream in the area. Soon we had a functioning dam and a good water reservoir above the dam from which we could draw emergency water. Again, naturally, the topography of your area would be a major consideration, but it might be possible to construct a dam near the lake outlet to the stream to cause the water to accumulate to a higher level before spillover. This would need to be substantial enough to endure the possible occasional high water flooding situations you might experience over a 10-20 or even 50 year period. (You do not want to see your efforts wash away.) Again, any change in the lake height could have other effects... it can prevent the water in the lake from becoming as warm, could support or wipe out other plant/fish/other animal species than tolerated the original depth/water temperature.
Bottom line...this is possible and perhaps worth doing, but to reduce a water level adjustment to apurely physics theory problem would be to miss a large part of how we and the lake flora/fauna interact with the environment.

Thanks for using NEWTON!

Ric Rupnik


Meredith,

If they wish to raise the level of the lake, 5 feet than they need to raise the level of the discharge stream by 5 feet. But throwing boulders in the way is not necessarily going to accomplish this. Water will still find its way past these large boulders. The outlet area would need to be filled with boulders as well as back filled with dirt and smaller sized material to completely dam up the water, to that new level. Yes the lakes surface area does rise with elevation but that will only affect the rate at which the lake fills. The lake level will rise to the new higher level provided that

1.) there is a constant inflow of water to the lake
2.) the boulders / dirt / etc.... added to the outlet stream block the water such that water is coming in faster than it is leaving the lake.

Another point: I do not know the topography or the population of the lake, so I will say this: If these people wish to raise the level from 1250 feet to 1255 they may want to check with all other inhabitants of the lake. Obviously, all land that is in contact with the lake at 1250 feet will now be under 5 feet of water.

Better yet, you should instruct your students parents to purchase a USGS topographic map (7.5 minute series) of the quadrangle in question. These maps are usually found in a good map store. They should look at the contours around the lake and the surrounding land to see what type of impact this would have (who is going to need a boat to leave their house?).

-Darin Wagner


If there is a significant amount of water coming into the lake, then damming the exit will raise the height of the water until it reaches the height of the dam, and impeding the exit water with an incomplete dam will raise the lake by an amount that is hard to guess at without detailed information.

If the incoming water is not all that significant compared to the amount of water already in the lake, then the lake level represents the level of water in the ground, and damming will not raise it.

Tim Mooney


Well, like many real world problems, the answer to this question is not necessarily straightforward. How well piling rocks (referred to as rip-rap) in the stream bed would restrict flow would depend on the specific rate of flow. When an obstruction, such as a boulder, is placed in a flowing stream, the water is forced to flow around it. This extra change of direction absorbs some portion of the kinetic energy inherent in the flow, thus reducing the velocity of the stream.

The absorbed kinetic energy is primarily converted into potential energy since water will build up behind the obstruction, increasing the depth. But the amount of buildup will depend on the amount of kinetic energy the water has in the first place. If the water is just barely oozing along, the buildup will be negligible unless the obstruction is nearly total. If the stream is raging whitewater, the buildup can be larger and the obstruction must be capable of withstanding substantial forces.

Since the piled rocks will not be impermeable, a similar effect will occur. If this is a very slow-moving stream, then the depth increase will not be that big. The physics of open channel flow are complex and, to some extent, empirically modeled. To determine the exact effect will require the services of a hydrologist, who is typically an licensed professional engineer specializing in management of surface water and runoff. I would urge EXTREME caution in this type of do-it-yourself endeavor because an improperly constructed structure can fail suddenly during periods of high flow. This could cause potentially dangerous flooding downstream. For this reason, dams, even little ones, are typically regulated by state and federal agencies to ensure public safety.

However, if you would like more information on how to construct this type of thing, check out this web site hosted by Mississippi State University on how to construct weirs from logs and boulders.

http://www.abe.msstate.edu/csd/NRCS-BMPs/pdf/streams/habitat/boulderweir.pdf

Andy Johnson, Ph.D., P.E.


Meredith,

If they wish to raise the level of the lake, 5 feet than they need to raise the level of the discharge stream by 5 feet. But throwing boulders in the way is not necessarily going to accomplish this. Water will still find its way past these large boulders. The outlet area would need to be filled with boulders as well as back filled with dirt and smaller sized material to completely dam up the water, to that new level. Yes the lakes surface area does rise with elevation but that will only affect the rate at which the lake fills. The lake level will rise to the new higher level provided that

1.) there is a constant inflow of water to the lake
2.) the boulders / dirt / etc.... added to the outlet stream block the water such that water is coming in faster than it is leaving the lake.

Another point: I do not know the topography or the population of the lake, so I will say this: If these people wish to raise the level from 1250 feet to 1255 they may want to check with all other inhabitants of the lake. Obviously, all land that is in contact with the lake at 1250 feet will now be under 5 feet of water.

Better yet, you should instruct your students parents to purchase a USGS topographic map (7.5 minute series) of the quadrangle in question. These maps are usually found in a good map store. They should look at the contours around the lake and the surrounding land to see what type of impact this would have (who is going to need a boat to leave their house?).

-Darin Wagner


My analysis would be: Lake level = Volume of the lake + Volume of water added to lake (by rain fall, underground springs, etc.) - Volume of water leaving the lake (through evaporation, soil absorption, and the proposed dam. All of these could vary with conditions and time. Your analogy of a crack in a Polystyrene foam cup assumes a single exit. As I understand the proposed solution of dumping rocks into the outlet, the analogy would be more like a Polystyrene foam cup with a bunch of punctures with a pin or nail at varying heights in the wall of the cup. Only when the lake level decreases below the height of a hole will that hole stop draining water from the cup (or the lake). So filling the exit of the lake with rocks will slow, but not stop the drainage. Just how effective this would be depends upon how the rocks pack together.

I am not an engineer but the local department of natural resources might have some ideas of how to do this better. They should be contacted anyway because there probably are state laws and regulations about constructing dams on lakes, depending upon the state. In the event of heavy rains or a rapid ice melt in the spring, the lake may backup and damage summer cottages etc. So the size of the lake's flood plane has to be taken into account. This does not sound like a job for non-specialists.

Vince Calder



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