Calculus Work Pump Water From a Circular Swimming Pool

This video shows how to calculate the work required to pump water out of a circular swimming pool.

[@piperlickteig8384]

Absolutely amazing video. Explanation was so clear and you helped me understand this process so much better

[@crowsmathclass]

Thank you. Glad it helped.

[@1light4love]

never seen your videos before, but love how slow and thorough you were (not skipping any minor steps and explaining why numbers and terms were appearing /changing!!) i missed this class for a BDAY hockey game, and was looking at the homework like... 🤤'wait.... what??' 🤔 Thanks again!! I'll be back for more as the semester rolls on! 🤓👍

[@crowsmathclass]

Thank you. Glad it helped. Good luck in your class.

[@briannapeatrowsky7141]

Thank you for your simple explanation and walk through of how to do not only this problem, but getting the idea of how to do problems like this. This video was exactly what I needed. Thanks again!

[@crowsmathclass]

You’re welcome. Glad it helped.

[@bittersweet5869]

FYI: An alternate way of writing the integral is as follows (to my knowledge this works only if the water is not at the tippity top): (144pi)(62.5)(5-y)(dy) You can eventually pull out 9000pi as Steve did because 144pi times 62.5 is a constant no matter which way you look at it! This way of writing it takes the bottom of the water to be 0 (c) and the top to be 4 (d), hence the integral from c to d (because it's within respect to y). The 5 represents the total height of the tank and the y is the distance pumped at any given y). :3 Enjoy.

[@1dred]

Thanks for the video!!! Very well explained!!!

[@crowsmathclass]

You’re welcome. Glad it helped.

[@AnitaSpliff]

Thank you Mr. Mackey.

[@jasperjohnson83]

Thank you very much. The explanation was thorough and there were no "magic" moments when figures are generated out of the blues. The speed of explanation was also very good. Please more videos. At times, I wonder if there are no simpler ways of explaining calculus when everybody is just skipping steps. Textbooks are worse. This whole thing can be very interesting if we have people like you explain to us. But what we see are textbooks and professors that will show an example of 1+1 and give you homework to determine how many infinities are in the moon when Jamie is walking home at 9pm from Florida to Texas which are 700miles apart N and S. Very funny.

[@crowsmathclass]

You’re welcome. Glad it helped. Thank you for the comment.

[@XoIoRouge]

Thank you ! I kept thinking I needed to account for gravity when using US units.

[@crowsmathclass]

You’re welcome.

[@Jasmine-ih3mr]

Nice video, I easily followed! Can I ask why the distance is just "x," instead of "5-x" for each slice to travel?

[@crowsmathclass]

Thank you. You could make it 5-x but then that would change other things. I just made it x because I think it makes it easier.

[@glennrickelton4093]

Lovely explanation

[@crowsmathclass]

Thank you.

[@glennrickelton4093]

@@crowsmathclass You are welcome. It was nice that you didn't hurry through the example and took things step by step

[@operationcrazy2696]

A true G

[@chrisr.m.8240]

How is the force = volume x weight ? Where did that formula come from

[@crowsmathclass]

Density X Volume The density is the weight of water in lbs/cu ft.

[@lindseylybbert5427]

Force is measure in a distance times a weight

[@AhsanRafi-nk8lo]

​​@@crowsmathclassbut you didn't multiply acceleration with mass. In order to find the force you need the product of mass and acceleration which is 32 ft/s^2 here

[@hungrypenguino1827]

Thanks for the vid but can someone explain at the end why the lower bound of the derivative is 1 and not 0? The water starts at the bottom of the cylinder so how would it be 1?

[@crowsmathclass]

It’s the distance the water has to travel to the top of the tank. The top of the water is 1 foot from the top and the bottom of the water is 4 feet from the top. So the bounds on the integral are 1 to 4.

[@hungrypenguino1827]

@@crowsmathclass Ohhh okay that makes sense, thank you so much for responding I know this is a really old video lol but you helped me so much. I have an exam tomorrow and I'd probably fail without your help

[@triciagoodman1084]

The disks of water are lifted against gravity. How come gravity is not used when building the force equation?

[@crowsmathclass]

You would if the measurements were in meters and kg. We don't have to since we are in ft and pounds. If have another video on pumping water from an inverted cone were the units of measurement are in metric. Check it out.

[@TheHisisi]

Weight is the force of gravity is pulling your mass towards the earth. When the metric system is being used, they are speaking in terms of mass and not weight, which is why they always include the force of gravity. If you would like more info on the difference I would watch this video www.khanacademy.org/science/physics/centripetal-force-and-gravitation/gravity-newtonian/v/mass-and-weight-clarification I hope this helped.

[@zulhasnitamuhamad3418]

@@crowsmathclass if the measurements in m and kg, can we find the work done? If can using what formula?

[@crowsmathclass]

kzbin.info/www/bejne/nHWXd6N_npp9odU

[@shark8160]

I think you forgot to times “g” to your force function. mass is volume times density but force is mass time acceleration, in this case being g which is 9.8

[@crowsmathclass]

No. Because we are in pounds.

[@jeffreystockdale8292]

Wrong.

[@jasperjohnson83]

No wrong, very correct

[@jasperjohnson83]

Not wrong, very correct

[@haileyspark3844]

nope

[@MJ-rc6bt]

tanks for the video but can you explain a bit faster... cause my god you talk slow.

[@haileyspark3844]

nope it was a perfect speed

[@FunnyAnimatorJimTV]

Look up how to increase the speed on a youtube video