Water flow in a lake... 1

[Hoot60]

New engineer here. This is what happens when the fish are not bitting. If a dam gate is open and water starts flowing thru the dam, how long does it take for a boat 10 miles away to start floating towards the dam? For numbers, let's say the gate is 20ft X 20ft and is 60ft below the water level. The lake is 30ft deep and is 600 feet across. I can calculate the flow thru the gate and the volumme of water in the lake to the boat and divide, but I don't think this is how to work this problem. Any formulas and help is appreciated.

Hoot60

 

[cvg]

typically this would be done using two-dimensional hydraulic modeling. divide the reservoir into grid cells and compute a mass balance at time steps across the grid. realistically, the boat starts floating towards the dam when the wind starts blowing that direction

 

[3DDave]

Speed of sound in water is the limiting factor for how long it takes a step input to traverse the length of the lake. It also depends on the time of year as winter ice may delay the movement of the boat.

 

[bimr]

Such a situation is a negative surge, a retreating wave moving upstream. Negative surges are unstable and quickly disperse because the deep water end of the profile travels faster than the shallow end.

Link

 

[Artisi]

Don't forget wind effect assisting as well as hindering.
Actually sounds like a "how long is the string" question to me.

It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts. (Sherlock Holmes - A Scandal in Bohemia.)

 

[MikeHalloran]

<tangent>
Recalled from an Electrical Engineer's Handbook dating to about 1900, which included details about designing hydro dams:

If the gate opening is in a horizontal plane, such that the flow is generally downward, fish will be drawn into the gate and discharged through the spillway.

If the gate opening is in a vertical plane, such that the flow is generally horizontal, and the flow velocity does not exceed their speed capability, the fish will swim away from the gate and not be sucked into it.

Fish are extraordinarily sensitive to lateral pressure, demonstrated by near simultaneous turns of entire schools. They are much less sensitive to up/down pressure, so will be sucked into a vertical flow, as in a simple drain.

This is why the racks at hydro volute entrances are called 'trash racks' and not 'fish racks'.

</tangent>

Mike Halloran
Pembroke Pines, FL, USA

 

[BigInch]

Proof that engineers should not go fishing, or if they do, they should first learn to think like fish.

 

[LittleInch]

That far away and at that flow, your boat will just slowly go down with the water level until the lake is essentially dry when it will ground on the bottom. Now if it was 300 feet away it would be a different story.....

BTW how is the gate 60ft below the water level when the lake is only 30 ft deep?? Is it horizontal gate or vertical gate? It will make a difference. What is your flow rate? You can only calculate this if you know what is on the other side of the gate. Too many unknown variables! How long is the lake?

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[BigInch]

With the 10 mi length and 600 ft width, it's a ratio of 88:1, and you have a relatively shallow depth, so I think you should treat this a long open channel flow problem. There are numerous resources online for these types of problems, search "open channel flow" and for "river and stream channel flow".

And if the boat is in the center of the channel, current will be quite a bit faster (30% more than average, or so) than if drifting along the edges.

 

[Artisi]

And if the prevailing wind is from the direction of the dam - what then?
Besides, being such a nonsense question, it's an odds on bet it's student homework.

It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts. (Sherlock Holmes - A Scandal in Bohemia.)

 

[BigInch]

Possibly.
Just answering the question as asked.

 

[Hoot60]

This is not a homework question. I am a 60 year old ME in North Alabama. Myself and another friend were floating and fishing on the Tennessee River when this topic came up. The river flows towards Florence Alabama and thru Wheeler Dam. Interesting to read the comments I'm getting. Thanks BigInch for your suggestions.

 

[IRstuff]

10 miles upstream; it's moored, and won't move downstream at all ;-)

TTFN
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[LittleInch]

If there's a river coming into the lake at the top end that this is a different question / solution compared to a fixed volume of water with , say, multiple small streams coming in at the sides.

wind is going to have to be discounted as this will have more effect than anything else.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[1gibson]

The real problem here is that on fishing trips you should only talk about fishing, the weather, and maybe beer (limited to "pass me one.")

 

[BigInch]

"Fish weren't biting." If that's the case, you can talk about anything.

 

[racookpe1978]

Robt will put rubber ducky as experimental floating object in bathtub at hotel tomorrow night as experiment.

Suspect the "boat grounds on bottom of lake" is correct answer if lake is long and has a shallow contour of the original bottom. Been across that lake, but not on it.

 

[BigInch]

The basic boundary condition of having a lake to begin with is that water outflow cannot be greater than water inflow, thus grounding is not possible, except in cases of poor navigation.

 

[Hoot60]

for this problem, let's assume that the lake does not go dry, we are not anchored,and there is no wind blowing....i found this equation for large apature gates and flow: flow = .66 X Cd X width of gate X (2G)^1/2 X (D1^3/2 -D2^3/2). I set Cd to .97 as the flow coefficient, D1 is the bottom of the gate and D2 is the top of the gate (ignore the 60 feet, wrong input). D1 is 30 and D2 is 10. So we open this gate and we have 13521 cuft per second flowing thru the gate. The volume of water to the boat is 950,400,000 cu ft. Dividing gives you 19 hours. I know this is not the way to approach this problem. Must be some caluclus or differental equation involved, maybe ecomputer modeling. Be interested in racookpe1978's experiment. And I have been out of school too long to know what grid cells and mass balances are...

 

[cvg]

well, 13,521 might be the "initial" flow through a gate, but as the water level drops, so does the flow rate throught the gate. It would take a lot longer than 19 hours. Generally, dams of this size would have a much smaller low level outlet. 20'x20' is enormous, 36-inch diameter pipe is more typical. So a more typical flow rate out of the lake might be 200 cfs and draw down is measured in weeks or months. In that case, I stand by my original estimate that you will begin moving when the wind blows