Calculate Work to Pump Liquid Out of Tanks - Calculus 2

A tank is full of water. Find the work required to pump the water out of a the spout/faucet/nozzle of a spherical tank.
In this video, I will show you how to calculate the work to pump water out of a three dimensional circular tank with a spout. There will be five videos like this to help you guys practice.
Basically, the idea behind calculating the work to pump water from one point to another is to use the work formula: Work equals the integral from top to the bottom of density times distance times area.
In simple words, to pump water out of the tank, you consider all the layers of water and pump each layer to the top.
The first step is to place the x and y axis on the top of the box. The second step is to determine where the top and bottom values are. The third step is to determine the density. If the problem provides the length of the tank in meters, then the density is 9880, and once you find the work, the unit is in Joules. In contrast, if the problem provides the length of the tank in ft, then the density is 62.5, and the unit of work is ft-lbs.
I hope this video will help you find these types of problems easier and be able to calculate the amount of work it takes to pump water out of tanks. Make sure to watch all the five videos on this topic to get as much practice as possible.
Please comment below if you have questions, and don't forget to subscribe!
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[@TheHyperRoar]

I wish I had found this sooner! My exam is in an hour but this was so helpful. You've been the only KZbinr I can find that goes into depth with these types of pumping liquid problems that is easy to follow. Hopefully it sticks long enough for the exam, haha! Thank you!

[@QuocDatPhung]

Good luck on your exam Kiki! Please don't forget to subscribe ! And also, all of my calculus videos are here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA There's 5 second way to know when you have to use cylindrical shell v.s dish washer: kzbin.info/www/bejne/g2mYkKVppb9oj6M

[@darcash1738]

Did you win? 😏

[@paperbeatsrock_]

You speak clearly and you're enjoyable to listen to. Thanks for explaining this subject so simply!

[@QuocDatPhung]

Thank you very much! I really appreciate your comment :) I actually have an entire playlist for Calculus II, which you can find it here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@EnderAnimals4]

You're a real one, my professor quickly went over ONE example problem in my CALC 1 class and is putting this on the final.

[@QuocDatPhung]

Thanks Jillian! Please kindly subscribe and share my Calculus playlist here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@al-waleedal-salti161]

Thank you for the thorough explanation. I hope one day you get the recognition you deserve.

[@QuocDatPhung]

Thanks so much Al-Waleed! Please hit the subscribe button, and you can find more of my Calculus videos here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA Please also share with your classmates! I hope this will help them too!

[@dohUofR]

thank you so much! this was a great intro video for understanding work to pump liquids out of a tank, drawing the axis really helps

[@QuocDatPhung]

You're so welcome Daniel! Please kindly subscribe and share, and you can find the rest of my Calculus videos in the playlist here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@SN-ow1bp]

phenomenal video, I'm finally understanding this concept, thanks!

[@QuocDatPhung]

Thank you for your kind words SN! Don't forget to subscribe and share with others! You can also find the rest of my Calculus videos here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@David-gk9lk]

Found you recently and I am glad I did!!

[@QuocDatPhung]

Thank you David! Please don't forget to share with your classmates and kindly subscribe ~ you can find all of my Calculus II videos in this link: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@dhruvshah143]

I have an exam in an hour also, bless you for being such a GOAT, calc 2 is gonna be an A because of u.

[@QuocDatPhung]

That's great to hear Dhruv! If you enjoy my videos, don't forget to subscribe and share with others! As well, you can find all of my Calculus videos in this playlist: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@tylersprague-bj9jd]

Thank you!

[@QuocDatPhung]

You're welcome Tyler! If you like my Calculus II videos, you can find the rest of them here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@Skindust.007..]

Very helpful.

[@QuocDatPhung]

Thanks very much Skindust! Please kindly subscribe and share! You can also find all of my Calculus II videos here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@x1stzz127]

Awesome tutor! You just saved my life!!!

[@QuocDatPhung]

You're very welcome! Please kindly subscribe and share! You can also find the rest of my Calculus 2 videos here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@ALLEAHLUMBAN-pk9zm]

thankyou!

[@QuocDatPhung]

You're very welcome Alleahlumban! Please don't forget to share with your classmates and kindly subscribe ~ you can find all of my Calculus II videos in this link: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@alihmohammed96]

Thank you mathematician of our time.More power to your elbow. Could you help us with pumping water into truncated tank @ certain depth or level to prevent overflow.Thank you.

[@QuocDatPhung]

You're very welcome Ali! Please kindly subscribe! You can also find the rest of my Calculus II videos here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@beatsalad1]

amazing video! thank you so much.

[@QuocDatPhung]

You're very welcome beatSalad! You can find the rest of my Calculus II videos here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@RobertoRodriguez-ob2ig]

This is great! First midterm in a couple of days

[@QuocDatPhung]

Good luck on the midterm Roberto! Note that these questions are taken from the midterm itself when I took it. Please consider each example carefully and let me know if you understand. And pls also share with your classmates to help them as well and subscribe to support me. Thank you again.

[@RobertoRodriguez-ob2ig]

@@QuocDatPhung Already have an tried solving them myself as I went watching it too, very nicely explained, now moving onto some other topics 😄

[@QuocDatPhung]

@@RobertoRodriguez-ob2ig That's great to hear! What's your next topic?

[@RobertoRodriguez-ob2ig]

@@QuocDatPhung I'm now moving onto reviewing some center of mass problems, then volume by cylindrical shells, then hydrostatic force and all I'll have left for studying is the practice midterms I've found 💪

[@QuocDatPhung]

@@RobertoRodriguez-ob2ig Sounds good! Let me know if you have questions. I've done some of those topics you mentioned which you can find here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@HenrySeward]

Very helpful, thank you

[@QuocDatPhung]

You're so welcome Henry! Please kindly subscribe and share with your friends my Calculus II videos in this playlist: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@na.1221]

thanks teacher it is useful for me please continue

[@QuocDatPhung]

Thank you so much Nardos! :)))))

[@QuocDatPhung]

Nardos, you can find my English series here: kzbin.info/aero/PLeTO6OT3-FKk9JscVeO1hNqTyb3WcGGCn I will post more English videos in January since I'm now in exam season.

[@Deristrome]

why is the triangular base prism problem y (height of water at any point) + 1 (extra height), but on sphere problem 4 (max height from origin) - y ( water height) couldn't you do y (height of water at any point) + 1(extra height) again?

[@QuocDatPhung]

For the sphere problem, the distance to pull the slice of water to the top of the spherical tank is 3-y (see diagram). Then we add 1 because it has to go out of the spout. So, 3-y+1 = 4-y.

[@Deristrome]

@@QuocDatPhung thank you!

[@keyz6380]

The 9800 comes from the density times the acceleration, correct? As opposed to it just being the density. I was confused because the density of water is ~1000 g/cm^3, and when he said it was 9800, I was a bit lost for a second.

[@QuocDatPhung]

Yeah it has to do with gravity acceleration as well. For the Calculus course you only need to know the number. Only the Physics classes will ask you where it comes from.

[@QuocDatPhung]

If you like my Calculus II videos, you can find the rest of them here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@nic4090]

How come you put 2x for here: 28:26. Is that because of the formula?

[@QuocDatPhung]

Actually I was drawing on the diagram to show where 2x comes from. Please watch 28:25 to 28:45 again but this time look at the diagram on the left. You will understand right away.

[@phillipengelbrecht4699]

Hey there why is the x-axis placed at the top of the cone? Does it matter where you place the x-axis?

[@QuocDatPhung]

Placing it on top of the cone is the best idea, because you're trying to pull each layer of water to the top of the cone. So, it matters where you place the x-axis. Please let me know if that makes sense.

[@phillipengelbrecht4699]

@@QuocDatPhung that you it really does!!!! I have tried both methods of putting the x-axis on top and the bottom to see if it works and it does! But thank you so much 😊

[@NYlivinginTN]

How are you accounting for the top two meters in the inverted cone?

[@QuocDatPhung]

Hi there! Please let me know the specific timestamp of the video you're referring to.

[@NYlivinginTN]

@@QuocDatPhung @8;35 could you use 10-y for the distance?

[@vezqi]

@@NYlivinginTN It should be 10-y

[@Kirtoisplayz]

Just leaving a comment here to tell people that instead of using slope you can also do similar triangles for plugging in x

[@QuocDatPhung]

Thanks very much! I find that the slope method is easier to understand. Note that the similar triangle method fails when the shape is a 3D trapezoid, that's why I use the slope method!

[@deroxasangelmariep.3334]

You made it look so easy!

[@QuocDatPhung]

Thanks so much! Please kindly subscribe and share! As well, you can find the rest of my Calculus videos in this playlist here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@deroxasangelmariep.3334]

Sure sure, I just have a question. What if the question says that the tank is a combination of cylindrical body and hemispherical shape on one end? What should I do with the area?

[@QuocDatPhung]

@@deroxasangelmariep.3334 Good question. These types of questions are beyond the scope of our Calculus II textbook :)

[@deroxasangelmariep.3334]

Thank you so much.

[@gravysnake78]

Why did you place the y-direction inversely?

[@QuocDatPhung]

It's the way the formula works :) Out of many different methods of solving, this one is the easiest. The only catch is placing the y direction inversely, but it's actually not that bad

[@mikidees]

W

[@QuocDatPhung]

Thanks Miki! You can find the rest of my Calculus II videos here (pls subscribe too!): kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@rylanwhitworth4641]

all these problems are just copied and pasted from blackpenredpens channel. at least change the numbers

[@QuocDatPhung]

I took these problems from the textbook "Early Transcendentals - 9th Edition" by James Steward. It's a famous textbook used by many teachers and professors.