I should know this dam principle...

[charliealphabravo]

So you have a dam that is say 10 feet high and 1 foot wide that is retaining water over the full height.

Integrating the water pressure over the height of the dam gives a horizontal force component of 3120 pounds acting on the back of the dam.

So far so good.

Now suppose you construct an identical dam 1 foot behind the first dam so that they are oriented back to back and supporting a column of water that is 1 square foot by 10 feet high. Without thinking too much about it I would say that the calculation of pressure and force on the back of the first dam is unchanged. But I am thinking too much about it. And after thinking about it I realized that I couldn't explain intuitively how a column of water weighting 624 pounds would exert 3120 pounds of force on the first dam.

I'm embarrassed to be drawing a blank here but it has been too long since I thought about this. Can someone point out the blind spot in my thought experiment?

Thanks in advance.

 

[paddingtongreen]

Accept the mathematics. If you work the other way, hydraulics would disappear.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[Compositepro]

The 624 pounds is acting on the one sq.ft. under the column. There are ten sq.ft. of wall being exposed to pressure. Also, realize that if the wall moved one inch the column of water would fall 10 inches.

 

[rb1957]

pressure is rho*g*h = p
weight is rho*g*h*A = P*l*b
hydrostatic load on the wall is 1/2*(rho*g*h)*Adam = 1/2*p*(h*b)

Quando Omni Flunkus Moritati

 

[Once20036]

I`ll take a crack at this... though hydraulics was a long time ago.
Water weigh 62.4 pcf.
The retained width doesn't matter (1' in your example), so it exerts 62.4 psf.
We`ll look at a strip 1' wide, so we have 62.4 plf.
I`m going to look at 1' depth increments, so we have 62.4 lb. Obviously this creates some significant rounding errors, but let's ignore those.

The first cubic foot of water weighs 62.4lb, and exerts 62.4lb lb on each face.

The second cubic foot of water is pushed down with 62.4lb on the top, from the first cubic foot of water. This weight transfers out to each face. Thus, horizontally on this face we have 62.4lb (from above) and 62.4lb (from this cube). We have 124.8lb on this face, plus the 62.4lb on the face above gives 187.2lb total

The third foot has 124.8lb from above (on each face) + 62.4 lb from this cube. We have 187.2 lb outward on this face. Total, we have 187.2 lb on this face + 187.2 lb above, 374.4 lb.

Keep going for the next 7 feet and you`ll have 3432lb - Itegrate better than my 10 cubes, and I bet that will head down to 3120lb.

 

[Archie264]

Shoot, I was hoping this is what you were referring to:

STATE OF MICHIGAN
Reply to: GRAND RAPIDS DISTRICT OFFICE STATE OFFICE BUILDING 6TH FLOOR
350 OTTAWA NW GRAND RAPIDS MI 49503-2341
JOHN ENGLER, Governor
DEPARTMENT OF ENVIRONMENTAL QUALITY
HOLLISTER BUILDING, PO BOX 30473, LANSING MI 48909-7973
INTERNET:

http://www.deq.state.mi

RUSSELL J. HARDING, Director

December 17, 1997

CERTIFIED

Mr. Ryan DeVries 2088 Dagget Pierson, MI 49339

Dear Mr. DeVries:

SUBJECT: DEQ File No. 97-59-0023-1 T11N, R10W, Sec. 20, Montcalm County

It has come to the attention of the Department of Environmental Quality that there has been recent unauthorized activity on the above referenced parcel of property. You have been certified as the legal landowner and/or contractor who did the following unauthorized activity:

Construction and maintenance of two wood debris dams across the outlet stream of Spring Pond. A permit must be issued prior to the start of this type of activity. A review of the Department's files show that no permits have been issued.

Therefore, the Department has determined that this activity is in violation of Part 301, Inland Lakes and Streams, of the Natural Resource and Environmental Protection Act, Act 451 of the Public Acts of 1994, being sections 324.30101 to 324.30113 of the Michigan Compiled Laws annotated. The Department has been informed that one or both of the dams partially failed during a recent rain event, causing debris dams and flooding at downstream locations. We find that dams of this nature are inherently hazardous and cannot be permitted. The Department therefore orders you to cease and desist all unauthorized activities at this location, and to restore the stream to a free-flow condition by removing all wood and brush forming the dams from the strewn channel. All restoration work shall be completed no later than January 31, 1998. Please notify this office when the restoration has been completed so that a follow-up site inspection may be scheduled by our staff. Failure to comply with this request, or any further unauthorized activity on the site, may result in this case being referred for elevated enforcement action. We anticipate and would appreciate your full cooperation in this matter.

Please feel free to contact me at this office if you have any questions.

Sincerely,

David L. Price
District Representative Land and Water Management Division

________________________________________

Dear Mr. Price:
Re: DEQ File No. 97-59-0023; T11N, R10W, Sec 20; Montcalm County

Your certified letter dated 12/17/97 has been handed to me to respond to. You sent out a great deal of carbon copies to a lot of people, but you neglected to include their addresses. You will, therefore, have to send them a copy of my response.

First of all, Mr. Ryan DeVries is not the legal landowner and/or contractor at 2088 Dagget, Pierson, Michigan — I am the legal owner and a couple of beavers are in the (State unauthorized) process of constructing and maintaining two wood "debris" dams across the outlet stream of my Spring Pond. While I did not pay for, nor authorize, their dam project, I think they would be highly offended you call their skillful use of natural building materials "debris." I would like to challenge you to attempt to emulate their dam project any dam time and/or any dam place you choose. I believe I can safely state there is no dam way you could ever match their dam skills, their dam resourcefulness, their dam ingenuity, their dam persistence, their dam determination and/or their dam work ethic.

As to your dam request the beavers first must fill out a dam permit prior to the start of this type of dam activity, my first dam question to you is: are you trying to discriminate against my Spring Pond Beavers or do you require all dam beavers throughout this State to conform to said dam request? If you are not discriminating against these particular beavers, please send me completed copies of all those other applicable beaver dam permits. Perhaps we will see if there really is a dam violation of Part 301, Inland Lakes and Streams, of the Natural Resource and Environmental Protection Act, Act 451 of the Public Acts of 1994, being sections 324.30101 to 324.30113 of the Michigan Compiled Laws annotated.

My first concern is — aren't the dam beavers entitled to dam legal representation? The Spring Pond Beavers are financially destitute and are unable to pay for said dam representation — so the State will have to provide them with a dam lawyer. The Department's dam concern

that either one or both of the dams failed during a recent rain event causing dam flooding is proof we should leave the dam Spring Pond Beavers alone rather than harassing them and calling them dam names. If you want the dam stream "restored" to a dam free-flow condition — contact the dam beavers — but if you are going to arrest them (they obviously did not pay any dam attention to your dam letter-being unable to read English) — be sure you read them their dam Miranda rights first.

As for me, I am not going to cause more dam flooding or dam debris jams by interfering with these dam builders. If you want to hurt these dam beavers — be aware I am sending a copy of your dam letter and this response to PETA. If your dam Department seriously finds all dams of this nature inherently hazardous and truly will not permit their existence in this dam State — I seriously hope you are not selectively enforcing this dam policy, or once again both I and the Spring Pond Beavers will scream prejudice!

In my humble opinion, the Spring Pond Beavers have a right to build their dam unauthorized dams as long as the sky is blue, the grass is green, and water flows downstream. They have more dam right than I to live and enjoy Spring Pond. So, as far as I and the beavers are concerned, this dam case can be referred for more dam elevated enforcement action now. Why wait until 1/31/98? The Spring Pond Beavers may be under the dam ice then, and there will be no dam way for you or your dam staff to contact/harass them then. In conclusion, I would like to bring to your attention a real environmental quality (health) problem: bears are actually defecating in our woods. I definitely believe you should be persecuting the defecating bears and leave the dam beavers alone. If you are going to investigate the beaver dam, watch your step! (The bears are not careful where they dump!) Being unable to comply with your dam request, and being unable to contact you on your dam answering machine, I am sending this response to your dam office.

Sincerely,
Stephen L. Tvedten

 

[DamsInc]

Not sure I understand the second part of the thought exercise with the second dam. But just to add to the answers in this thread, I believe one critical concept to remember is that pressure acts in all directions normal to the surface. The 624lbs of water is only acting in the downwards direction which is what causes the conceptual dissonance between the 624lbs and 3120lbs. The water column is pushing downwards with 624lbs of force, but it is also pushing horizontally with 624lbs at the base only. Like composite pro said, 624lbs is on one square foot which could be the bottom of the lake or the one square foot at the base of the dam (assuming 1ft intervals).

Archie264, is that a real letter or a piece of creative writing? Either way thanks for the laugh! Beaver dams can cause a lot of serious problems, but a governing authority should be able to tell the difference between a man-made and beaver-made dam!

 

[fromtherafters]

I believe the OP is referring to load transfer between two concrete walls cast against each other.

If this is the case and assuming the walls are not doweled together, the second wall is designed for the full load of the retained water, there are no issues with the footing design, and there is no compressible material, soil or water between the two walls, then I believe the load on the original wall will be a result of the deflection of the second wall; creating a new pressure diagram.

 

[Archie264]

DamsInc,

That letter is supposed to be real. I first read it back in the 90's in the Wall Street Journal, which isn't generally known for passing around hoaxes. Snopes says it's true, but I don't trust Snopes so that doesn't hold (wait for it) water with me.

 

[paddingtongreen]

If, instead of the column being the same width, consider only a one foot cube at the bottom with a small pipe column up to ten feet above, all filled with water. The pressures in the pipe and the void at the bottom would be the same as in your example.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[charliealphabravo]

Well I think PG has put me on the right track. My thought experiment is basically an application of Pascal's law. I guess I just never thought of how bizarre and non-intuitive it seems in the extreme case.

 

[BAretired]

Dam good story, Archie.

BA

 

[Triangled]

archie,
perhaps my all time fav
I read also that it's a true story.

 

[Triangled]

Archie,
my verification source, a nice site.....

http://www.truthorfiction.com/rumors/b/beaverdam.htm#.U2QvhfldWSo

 

[dicksewerrat]

I want to know if the bears were arrested.

Richard A. Cornelius, P.E.

http://WWW.amlinereast.com

 

[chicopee]

Not only will water exert 3120 lbs of force on the first dam,it will also exert 3120lbs of force on the "mirror" dam when water is trapped between the two dams.

 

[RFreund]

I hate thinking about this problem, it is very counterintuitive to me for some reason.

I like the explanation by Once20036 but lets say you have 3" between the walls...
wait does the force decrease then, damnit I confused myself again



EIT

http://www.HowToEngineer.com

 

[slickdeals]

It definitely is counter intuitive. Take a look at this video. It is similar to concrete formwork pressures, pressure is the same regardless of whether you are pouring a 36" thick wall or a 6" thick wall.

http://www.gatesconcreteforms.com/water.html

 

[Ron]

Let's look at two interpretations of your problem statement.

First, if you build as described and assume you have only trapped a column of water between the two dams and there is no water outside either dam boundary then the pressure is the same on either dam.

If; however, you build the 2nd dam and it traps a column of water between the two dams but there is still the water behind dam 2 that was originally retained by dam 1, you now have equal and opposite pressure on dam 2 and the original pressure on dam 1.

 

[MJB315]

I remember seeing a case study where water penetrated between an existing structure and some form work. The space was less than a 1/4" wide...but it was 20+ feet tall. Needless to say, the pressure blew out the formwork. 20' of head is 20' of head, regardless of the width!

"We shape our buildings, thereafter they shape us." -WSC