Calculus 1 - Derivatives and Related Rates (5 of 24) Water in a Funnel

Visit ilectureonline.com for more math and science lectures!
I will calculated the dy/dt=? of aater runner out of a funnel, r=3ft, at the moment of the water level of h=4ft and DV/dt=-0.1ft^3/s.
Next video in this series can be seen at:
• Calculus 1 - Derivativ...

[@lindaduong6371]

I have been trying to find a video to help me understand related rates, and I must say, I have found a holy grail of them! Thank you so much for making it easy to understand in something I struggle so much in!

[@thebearman6065]

This one put up a fight, none of the other 7 videos I watched were laid out in a way that was usable with my numbers. Nicely done!

[@MichelvanBiezen]

Glad you found it helpful.

[@yours_kiran]

Much love from India sir!

[@MichelvanBiezen]

Thank you. Welcome to the channel! 🙂

[@MichelvanBiezen]

We substituted r = (1/3)h

[@ptyptypty3]

and due to Similar Triangles we have R/H = r/h Voila!! (wow, I am LEARNING!!) :D

[@vanhoumin]

I love how he makes it seem so easy. My 75 year old professor can't relate. 😂😂 he makes everything seem like neuroscience.

[@icoalshd2358]

age shaming your teacher is not an excuse to your failures

[@klasichik1747]

@@icoalshd2358 IDK that it is something related to age shaming!! Infact it is related to the teaching skills.

[@GermanSnipe14]

Hey Mr. van Biezen, great video! Just wanted to ask, who is to say that the relationship between R and H is 1/3? How do we know it is simply a ratio and not a function that relates the two? For example, how do we know R doesn't equal sqrt(H)? That works for this example right?

[@MichelvanBiezen]

The ratio between R and H were simply given. It could have been a different ratio if the problem was stated differently.

[@GermanSnipe14]

Ah ok, thanks!

[@Kiki-ny7qr]

This helps a lot. Thank you!!

[@MichelvanBiezen]

Glad it helped!

[@user-zo1dv4in8d]

Bruh my math book skips almost half of the steps and numbers appear together without explanation whats the use of the goddamn book if it doesn’t show u the steps

[@MichelvanBiezen]

I agree that a lot of text books skip steps in their examples, which is a real shame. When I look at some examples it also takes me a while to figure out what the missing steps are. It is a lot of wasted and frustrating times. Part of the reason why we make these videos.

[@user-zo1dv4in8d]

@@MichelvanBiezen i really do appreciate the effort u do to make these vids as i see how hard and busy the life of a teacher is but what i appreciate even more is teachers like u taking the time to help out students rather than just do their jobs. Truly a legend.

[@MichelvanBiezen]

Thank you for your kind words. But most of the thanks should go to my wife. She came up with the idea and she puts in a lot of work filming, editing, producing, and uploading the videos and for making all the amazing thumbnails.

[@hym1751999]

Hi Mr. van Biezen, I would like to know whether r/h applies to cylindrical as well or just triangles?

[@MichelvanBiezen]

Yes, you can use that for triangles as well

[@hunterwillson518]

had a calc quiz with very similar numbers online today and this video got me through one of three problems and i had no fuckin idea what i was doing. thanks a lot

[@henkoegema6390]

Great video. Can you extend this video, taking into account that the rate of water going out of the funnel is depending on the height of the water level.

[@MichelvanBiezen]

It would add some complexity, but it could be done.

[@henkoegema6390]

@@MichelvanBiezen I can't do it. 😟 But you can. 😀

[@MichelvanBiezen]

That will have to be for another time. I am very busy at work at the moment.

[@henkoegema6390]

@@MichelvanBiezen I have a LOT of patience.

[@MichelvanBiezen]

HaHa, that was funny! We are planning for a course in fluid mechanics, but I will first have to retire to find the time to do it.

[@hate7896]

I don't get it in the part why did u have to isolate or eliminate first the r?

[@MichelvanBiezen]

When you take the derivative you have to take it relative to one independent variable. Since the volume has 2 independent variable (r and h), it is better to express one in terms of the other.

[@sandhiyasabitha1784]

@@MichelvanBiezen what happens if we solve , without expressing two independent variables interms of one

[@ptyptypty3]

by the way.. LOL!!! at Snoopy falling over and you picking him back up!!..

[@MichelvanBiezen]

You noticed!

[@MichelvanBiezen]

I, Mike's wife, absolutely loved Snoopy growing up.

[@ptyptypty3]

I guess that means YOU, mike's wife, Don't like the Red Barron? :D .... perhaps Red Barron Pizza?.... I think Michel's Menagerie of "Creatures" or Vehicles is a HOOT.. lol.. thanks for the laughs... and the Education!! :D... by the way.. I did notice some editing in cutting Michel out of Replacing Snoopy.. :D ...

[@chrisbouwhuis6039]

Ok somehow I'm missing how h became h^3

[@MichelvanBiezen]

We substituted r= (1/3)h

[@CaptainCalculus]

Why are calculus people obsessed with water leaving a funnel?

[@ahmedmatouk4383]

It is important application