Mixing Problems and Separable Differential Equations - Calculus 2
In this video, I will go over many examples about typical mixing problem that students often see in Calculus 2 classes. There is also another kind of mixing problem that involves percentages. I will cover this type of mixing problem in the next video. There are three formulas that you need to know. They will result in a separable differential equation that you can easily solve.
A tank contains 20 kg of salt dissolved in 5000 L of water.
Brine that contains 0.03 kg of salt per liter of water enters the tank at a rate of 25 L/min.
The solution is kept thoroughly mixed and drains from the tank at the same rate.
How much salt will there be in the tank after half an hour?
A vat with 500 gallons of beer contains 4% alcohol (by volume).
Beer with 6% alcohol is pumped into the vat at a rate of 5 gal/min.
The mixture is pumped out at the same rate.
The solution is kept thoroughly mixed.
What is the percentage of alcohol after an hour?
A tank contains 1000 L of pure water.
Brine that contains 0.05 kg of salt per liter of water enters the tank at a rate of 5 L/min
Brine that contains 0.04 kg of salt per liter of water enters the tank at a rate of 10L/min
The solution is kept thoroughly mixed and drains from the tank at a rate of 15 L/min.
How much salt is in the tank:
(a) after t minutes
(b) after 1 hour?
A tank contains 1000L of brine with 15 kg of dissolved salt.
Pure water enters the tank at a rate of 10 L/min.
The solution is kept thoroughly mixed and drains from the tank at the same rate.
How much salt is in the tank a) after t min? b) after 20 min?
Пікірлер: 24
Seriously one of the best tutors on KZread, and I love how you do so many different examples!
@QuocDatPhung
3 ай бұрын
Thank you RollingInTheDeep!! I'm really glad you enjoyed my video! I would really appreciate if you could share with your classmates or kindly subscribe ~ you can find all of my Calculus II videos in this link: kzread.info/head/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
Ok my god many thanks for that it was very too simple I have struggled for some time ! Many thanks for this simple and clear info
After one week I have final and really I was feeling stressed because I don’t understand this, now am feeling better thank you❤
You are a best tutor in this life you are a star
@QuocDatPhung
4 ай бұрын
Thank you very much! Don't forget to share with your classmates to help them as well and kindly subscribe to support me! You can also find all of my Calculus II videos here: kzread.info/head/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
This is really helpful!! Thanks!!
@QuocDatPhung
8 ай бұрын
Thanks Yihong! You can find the rest of my Calculus II videos here: kzread.info/head/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
thank you so much🥰
@QuocDatPhung
3 ай бұрын
You're welcome Tumelomokgojane :)!! I'm really glad you enjoyed my video! I would really appreciate if you could share with your classmates or kindly subscribe ~ you can find all of my Calculus II videos in this link: kzread.info/head/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
Wow, very understandable. God bless you sir 🎉🎉
@QuocDatPhung
5 ай бұрын
Thanks Dhelly Ghyde! You can find all of my Calculus 2 videos here (don't forget to share and subscribe!): kzread.info/head/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
Can you please give some examples of when the rate in more than the rate out and vide versa
@QuocDatPhung
4 ай бұрын
You can use the same formula :) in the video
Great video! However it would be nice to see more diversity in the questions for example what happens when the flow rate is not equal, and when the tank will be empty/overfill.
@QuocDatPhung
8 ай бұрын
Thanks Anthony! I will look for those problems! As well, if you like my Calculus videos, you can find all of them in this playlist here: kzread.info/head/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
where is the part where the rate in is equal to the rate out like your thumbnail?
@QuocDatPhung
4 ай бұрын
At 0:36 for y'(t). Let me know if you see it!
Here I have question to you I have got a problem like this ( water tank of pure water has 60l of it a salty water of 1 kg per l with rate of 2L per minute, and comes out with a rate of 4 kg/l his equation was dq/dt= 2-4 Qt /60-2t but according to your calculations there should not be 60-2t it should be only 60 please explain I am too confused
@QuocDatPhung
4 ай бұрын
that is strange... you should ask your professor why there is the 60-2t
i love you
@QuocDatPhung
6 ай бұрын
Thank you very much! You can find all of my Calculus 2 videos here: kzread.info/head/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA
damnnnnn ..... that was something
@QuocDatPhung
4 ай бұрын
Thanks Paypal! You can find all of my Calculus II videos in the following link (don't forget to share with your classmates and kindly subscribe also!): kzread.info/head/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA