Mixing Salt and Water - First Order Differential Equations

My 200th Video! Thank you for your support. 6.5K subscribers and 1.7 million views as of December 10, 2018. My goal is to double that in 2019.

In this video, we use first order, linear, ordinary differential equations to solve a mixing problem. We have a 3000L tank that is being filled and drained at the same time at 10L/min.

The solution filling the tank has a salt concentration of 0.02 kg/L, while the tank has an initial quantity of salt of 15kg. Our problem is to find the amount of salt in the tank at any given time.

Thanks for watching. Please give me a "thumbs up" if you have found this video helpful.

Please ask me a maths question by commenting below and I will try to help you in future videos.

[youung.hyun]

Oh my Jesus, thank you teacher Finally I understood what I have to do in nixing problem. I appreciate it.

[scottboyer]

This video explains the topic much better than my professor! Thank you for uploading this

[suchithsunku]

Thanks for explaining a problem to me 3:00 in the morning really saved my butt!

[steveying]

very good explanation, and i think this problem is indeed quite tricky

[ryantan]

very helpful, thanks. Im gonna show my mates now

[pipertripp]

Nice presentation. Bonus points for plotting the tank concentration v time at the end. That was a nice way to wrap it up.

[starbeoms]

why leave out /min?
dy/dt = 0.2[kg/min] - y/300[kg/min]
i think dt is time and /min too.

[filipomarcellino]

thank you soo much this really helped me

[rodericksibelius]

I don't understand how you got a '-1' under the 'ln (60 -y) / -1' ....

[kaokaoylan]

THANKS, GREAT HELP FOR MY REVISIONS!!~

[afiqhaiqal]

Hi sir, what if the rate in and rate out is different? Can we use your method?

[SuperMtheory]

It seems that this process could be generalized. For example: The tank hold L liters of fluid, with K kg of salt, etc. Doing so would provide a general solution. I wonder how the general solution would look.

[RefinerSimilitude]

I just flopped this part of the exam because I tried to include the existing salt in the tank with my rate out. Since I didn't do that correctly, I couldn't perform the next 2 follow up questions. Practice, practice, practice.

[pipertripp]

Quick question, how much nastier does the problem get if the volume of solution is changing with time as well? Say we started with 1500L of brine and then let the tank fill to a max volume of 3000L. Volume would be a function of time too so would be an interesting ODE. I can think of how I'd solve this numerically, but a look at an analytical solution would be interesting.

[EEAMD-conw]

honestly thought it was JackFrags talking, a big gaming youtuber

[hydr]

I loved how you demonstrated this concept! Thanks for the visual at the beginning.

[stilljamming-oraangaataan-maan]

why is there is negative 1 (-1) on 5:35

[hamadkhan]

i would not understand the graph clearly

[ajonjon]

Like it, but got a message that I disliked the video. I dont know what happened...I Like it. Thank you

[collinsmamadumetja]

A 1000-litre holding tank catches runoff from a chemical process. The tank initially
holds 800 litres of water with 2 grams of pollution dissolved in it. Polluted water,
containing 5 grams per litre of pollution, flows into the tank at a rate of 3 litres per
hour. At the same time, the well-mixed solution leaves the tank at 3 litres per hour.
When the amount of pollution in the holding tank reaches 500 grams, the inflow of
polluted water is cut off and fresh water enters the tank at a decreased rate of 2 litres
per hour, while the outflow is increased to 4 litres per hour. Determine the amount of
pollution in the tank at any time 𝑡.
HINT: Your answer will be a piecewise-defined function. Please solve for me.