Math formula for "flow system" problem for a river

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

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!

interesting

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.

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

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.

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

<PPM= mg substance/liter of water>

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

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.

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.

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