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Raising Lake Depth
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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