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Math formula for "flow system" problem for a river

10/17/2007 1:14 PM

Assuming 10kg of a pesticide is sipping in a river with a leaking rate of 10 mg/sec. River flow 20L/sec, speed 10km/hr, River volume 20x10^6 L. at what distance the pesticide concentration will still 1ppm?

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Guru
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#1

Re: Math formula for "flow system" problem for a river

10/17/2007 2:52 PM

Assuming it is completely soluble in water....

The best I can figure out without dispersion rates, settling rates, or solubility etc. is this;

10,000 grams / .01 gram per second = 1,000,000 sec ~=278 hours

~278 hours X 10 km per hour = 2777.8 km

20 liters per hour / 20 X 106liters ~= 278 hours. therefore the whole river is also replenished in 278 hours

10000 grams / 20 X 106 = 500 parts per million

The river will become contaminated for a distance of 2777.8 km at a concentration of 500 parts per million.

The pesticide will stop entering the river after 11.5 days. 11.5 days later the river will be completely replaced with fresh water. the 2777.8 Km of contamination will have travelled another 2777.8, km or until it hits a larger body of water that it can dilute in

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Guru
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#2
In reply to #1

Re: Math formula for "flow system" problem for a river

10/17/2007 3:33 PM

I think you are brave to even try and figure out anything ...kudos....

It would depend on how the river is flowing, if it is in it's middle to old age, the contamination could just go downstream in a fairly homogenousfairly laminar flow without mixing too much. If it's seeping into a raging torrent obviously it will mix more.

I'd fish it out quick!

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Guru
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#3

Re: Math formula for "flow system" problem for a river

10/18/2007 3:34 AM

interesting

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Guru
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#4

Re: Math formula for "flow system" problem for a river

10/18/2007 8:28 AM

Ratio of Pesticide Leaking Rate : River Flow Rate

= 1o mg/sec : 20 L /sec

= 10 mg/sec : 20 x (1 kg)/sec

= 10 mg/sec : 20 x (1000 mg)/sec

= 10 part : 20 000 part

= 1x 500 part : 2000x 500 part

= 500 part : 1000 000 part

= 500 PPM

So, the moment at which the pesticide concentration can reach 1 PPM shall not be attained if the pesticide leakage rate still the same.

After finishing of full draining of 10 kg of pesticide, the concentration shall be zero.

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Guru
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#8
In reply to #4

Re: Math formula for "flow system" problem for a river

10/19/2007 5:06 AM

Sorry, there is a correction .....

Ratio of Pesticide Leaking Rate : River Flow Rate

= 10 mg/sec : 20 L /sec

= 10 mg/sec : 20 x (1 kg)/sec ( for water, L = 1 Kg)

= 10 mg/sec : 20 x (1000 g)/sec

= 10 mg/sec : 20 x (1000 000 mg)/sec

= 10⁄20 part : 1 000 000 part

= 0.5 part : 1 000 000 part

= 0.5 PPM

So, the moment at which the pesticide concentration can reach 1 PPM shall not be attained if the pesticide leakage rate still the same.

Note 1. To attain 1 PPM :

A. By increasing the Pesticide Leaking Rate to be twice, i.e. 20 mg/sec instead of 10 mg/sec, or

B. By reducing the River Flow Rate to be 10 L /sec instead of 20 L /sec.

Note 2.

A. After full draining of 10 kg of pesticide, the concentration shall be zero.

B. The duration for draining of 10 Kg of pesticide shall be :

= (10 Kg ) / (10 mg/sec)

= (10 000 000 mg) / (10 mg/sec)

= 1 000 000 sec

= 16 666.67 min

= 277.7778 hr

= 11.57 day

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#5

Re: Math formula for "flow system" problem for a river

10/18/2007 11:43 AM

How do you have a river volume? I have never dealt with a river volume. You should research the advection-dispersion equation to solve this problem. One question i do have you could solve from the data provided is the approximate cross-sectional area of the river at the point of measurement of flow rate and average speed. I am coming up with 0.0072 m^2. Pretty small river cross-section.

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Associate

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#6

Re: Math formula for "flow system" problem for a river

10/18/2007 5:08 PM

Hi EVERYBODY

I dont know if the definition of PPM= mg substance/liter of water.

If this is correct then PPM=[10mg/20L]this a control volume at t=1sec. =[0.5 ppm]pesticide in the river.

Israel Barron

ibarron@sfmex.com

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#7
In reply to #6

Re: Math formula for "flow system" problem for a river

10/19/2007 4:40 AM

<PPM= mg substance/liter of water>

It assumes the density of water is 1000kg/m3, which is good enough for all practical purposes.

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#9

Re: Math formula for "flow system" problem for a river

10/19/2007 5:15 AM

All the calculations are meaningless regarding the distance the pesticide could travel. It could easilly remain as a 'stream within a steam' if the flow is even vaguely laminar and travel much further.

Interestingly many 'answers' don't mention the distance...which is (I believe the question)

This is 'bad science' if indeed it is science.

It is 'worthless arithmetic' as it doesn't qualify as maths.

Sorry to be so grumpy but this really is bonkers.

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Guru

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#10
In reply to #9

Re: Math formula for "flow system" problem for a river

10/19/2007 9:19 AM

At the risk of greatly inflating Del's ego, he is 100% correct. Here in Pittsburgh, we have much barge traffic on the rivers. Spills often occur and they stay together enough that we can usually shut off the drinking water intakes a short time before the spill arrives and back on a short time after the spill moves on down river. Sometimes spills remain defined as far as the Mississippi.

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#11
In reply to #9

Re: Math formula for "flow system" problem for a river

10/19/2007 11:14 AM

Hi

If we calculate the PPM, is because we calculated the distance "traveled" already, but in this case the question has an error, and how calculate the distance traveled by the water,does not depend at all in the correct way to calculate PPM of pesticide in the water.

The distance traveled by the water, depends on the time we are feeding the pesticide in the stream.

More comments.

And if we suppose that the river has geometrical surface like half cylinder.

Q=AV

A=20/10[L/SEC//KM/HR]=0.0072M2 cross sectional area.

with a radius=4.7873cm=1.88 in. really small.

Israel Barron

ibarron@sfmex.com

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Guru
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#12
In reply to #11

Re: Math formula for "flow system" problem for a river

10/19/2007 12:52 PM

This explains what I mean by the age of the river.

None of my points have been answered.

If this is a 'theoretical' question then I fear it will stay that way, with no real value.

If it is a 'real world' question then I feel dangerous assumptions are being made on a poorly worded question with insufficient information.

I feel the 'wetted perimeter' of a rive is unlikely to be a semicircle and is generally chracterised by the age of the river. If one must aproximate then a rectangular cross section with width = 2x depth may be more appropriate.

I do not profess to be a expert on this subject by any means. But I do recognise when people are out of their depth!

Del

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#13
In reply to #12

Re: Math formula for "flow system" problem for a river

10/19/2007 2:11 PM

True and direct.

And without a solubility rate of the said material, monkeys on typewriters can be more accurate. If the pesticide is oil based it may be difficult to mix with water. Some chemicals like MTBE (fuel oxygenator?) are said to disperser faster than the flow of water due to osmotic pressure. So after accurate conditions, multiply by >0 to 2 maybe.

Brad

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#14
In reply to #9

Re: Math formula for "flow system" problem for a river

10/21/2007 12:34 AM

You're a kind of rough, this is a (n) 15points on a very serious exam

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Guru
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#15
In reply to #14

Re: Math formula for "flow system" problem for a river

10/21/2007 3:11 AM

LOL

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Abdel Halim Galala (2); Anonymous Poster (1); bcassa (1); cnpower (1); Del the cat (4); Israel (2); PWSlack (1); techno (1); TVP45 (1); U V (1)

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