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 YouTuber 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!

[paperbeatsrock_]

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

[EnderAnimals]

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.

[David-gklk]

Found you recently and I am glad I did!!

[al-waleedal-salti]

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

[dhruvshah]

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.

[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

[SN-owbp]

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

[nic]

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

[na.]

thanks teacher it is useful for me please continue

[alihmohammed]

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.

[RobertoRodriguez-obig]

This is great! First midterm in a couple of days

[xstzz]

Awesome tutor! You just saved my life!!!

[keyz]

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.

[Kirtoisplayz]

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

[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?

[gravysnake]

Why did you place the y-direction inversely?

[phillipengelbrecht]

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

[NYlivinginTN]

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

[rylanwhitworth]

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