calculus 2 mixing problem, CSTR, differential equation application

The mixing problem is an application in separable differential equation. This is also known as continuous stirred tank reactor (CSTR).

@bprpcalculusbasics

[gnikola]

Recently, you've been uploading the videos I needed in the moment I needed them!

[dorothyfinn]

Thank you so much. This is the only way I have understood how to set up the equations.

[taruntomar]

ooohhhh its the best channel on youtube

[flyingbicycles]

I'm in calculus II right now and I though he was gonna do some shenanigans to solve it. I got really giddy when I figured out what he was doing was actually pretty straightforward.

[wduandy]

Those problems are amazing, please do more!!

[dogukankaradag]

The best tutorial of all!! Please keep up the good work. Everyting is explained, nothing without explanation. That one example was like 10 examples. Thank you so much. Please keep doing tutorials sir..

[briancruz]

I was studying this for hours, then I watched your video and it all made sense, thank you!

[jacksonmpumpa]

nice english, nice presentation, nice explation BE BLESSED BROTHER

[paultello]

Im so glad I watched this video. The C trick is really clever and I will definetely use it

[gamerpedia]

On a pedantic note, it doesn't ask for the amount of alcohol, it asks for the percentage of alcohol, or rather, the concentration of alcohol. So the final answer should be roughly 32%.

[LL-knde]

I finally understood this concept! Thank you!

[calebjones]

Thankyou so much for this! This is exactly what we are learning in Specialists Maths (Australia) in year 12 right now and is perfect for revision for our upcoming exams. Are you able to do a D.E. where the tank is changing volume but pure water is being added to the mixture instead. Thankyou! c:

[allswellinendwell]

In practice you'd never feed from the top and drain from the bottom. It's far easier to feed from the bottom and let it overflow the top. That way you always have equal mass out for the mass in.

Signed an old chemical engineer.

[girthjob]

Your videos are very interesting, I learn so much from them :) Keep up the great work :D

[matthewgiallourakis]

You could skip the constant term manipulation by setting the limits of integration from 0 to 10 on the time side and 9 to A|t=10 on the amount side.

[TheGiladklos]

You can avoid the undefined integral with the constant by doing a difined integral from t equals to 0 to t equals yo 10 and a equals to a(0) to the new A

[Zaytoven]

I loved the approach in this solving problem, i always have a hard time interpreting the question, your house analogy was good.
there's one more method of solving these types of differential equations of the form dy/dx + Py=Q which uses the integrating factor method, Could you please please solve this using that method too?

[bigjazbo]

Actually, alcohol-water is a bad example. When you mix them, the volume of the solution is less than the volumes put in. This " volume of mixing" effect varies with concentration, making the true solution very complicated.

[derekpoon]

Hi blackpenredpen, it's worthwhile to mention that the final concentration of tank is same as incoming solution.

[jeromesnail]

It is really interesting how you solve differential equations because that's not how we learn to solve them at all in France.