Calculate Work to Pump Water Out of Inverted Cone

A tank has the shape of an inverted circular cone with height 10 m and base radius 4 m. It is filled with water to a height of 8 m. Find the work required to empty the tank by pumping all of the water to the top of the tank.
In this video, I will show you how to calculate the work to pump water out of a rectangular tank. 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!
LIKE & SUBSCRIBE:
🔴 My Channel: / quocdatphung
🔴 My second channel: / @purifynature8479
MY EQUIPMENT:
✅Camera: Samsung Galaxy J7
✅Recording Equipment: obsproject.com/​
✅Editing Software: Shotcut

[@ptyptypty3]

I've seen alot of videos on these WORK problems.. and All of your problems and videos ARE THE BEST!!! I said it before, your videos are PERFECTION !! thank you Quoc !!! I'm enjoying watching all your videos!!.. You are truly Talented!!

[@QuocDatPhung]

Great to hear! Thank you thank you and thank you! If you know anyone else taking Calculus, please send theses videos to them too! This week I'm releasing two more work problem videos on pumping water out of tanks. First, what happens if there is a spout on the top of the tank and the problem asks us to pump the water OUT of the spout and not to the top of the tank. The second video will be about pumping water out of a sphere (this is a bit harder and will likely be on tests). Let me know if there's any topic you'd like me to do :D

[@ptyptypty3]

by the way, I see that the density of water is 997 Kg /m^3 .. I'm trying to figure out where you have density at 9800 ..

[@QuocDatPhung]

Excellent question! The textbook that we're using in class (Calculus: Early Transcendentals 9th Edition) tells us to assume that the density of water is 1000 kg/m^3. So where does 9800 come from? We know that the acceleration force of gravity is 9.8. The textbook just takes 9.8 x 1000 to get the weight of each layer of water. So, 62.5 also comes from the same logic but they converted it to the imperial system. In a nutshell, students just need to remember these two numbers and how to use them on exams. Tests won't ask the students where these numbers come from so don't worry too much haha :D

[@chrisi302]

Quoc, YOU ROCK!!!!

[@QuocDatPhung]

THANK YOU Chris! Please don't forget to share with your classmates and subscribe!

[@thitamhieple9818]

Well explained!

[@QuocDatPhung]

Thank you!

[@jgorf5874]

How do you calculate the amount of work if the water is only pumped out half the tank?

[@QuocDatPhung]

You adjust the bottom and top values according to your specific needs :)

[@benjajajajamin]

Hi! Thanks for your videos! They have been very informative. I just had 1 question, how do we know when to have our origin at the top of the shape? I watched your spherical tank work video, but does it depend on the question? I think you used the y+ pointing down so far for anything non-spherical, is that how it usually is?

[@QuocDatPhung]

Hi Veronica! For the work problems pumping liquid out of tanks, you always put the origin at the top of the shape. The only exception is when the tank is circular. Let me know if that makes sense :)

[@QuocDatPhung]

When the tank is circular, the origin is at the center of the tank.

[@TheTigerBin]

👌

[@QuocDatPhung]

Thanks!

[@0.p_tlt935]

Du ma u my goat

[@QuocDatPhung]

Thank you! You can find all of my Calculus lessons here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA