Hydrostatic Force Problems - Calculus 2

In this video, I will show you how to calculate the hydrostatic force using Calculus 2. I go through many examples where the object submerged in the water is a rectangle, trapezoid, triangle, and circle, and we have to calculate the force created by the hydrostatic pressure on one side of this object. This video shows you the calculus formula to calculate hydrostatic force which involves integrals and the answer or the force will be in Newtons or pounds,.
So that's it for calculating the hydrostatic fluid force using integral calculus. In the next video, I will show you how to calculate the moments and the center of gravity or mass and the centroid of shapes.

[@quinnpuffer7901]

Your method of solving these problems is so comprehensive and easy to follow! Thank you so much!

[@QuocDatPhung]

You're so welcome Quinn! Please kindly subscribe if you enjoy my content! As well, you can find the rest of my Calculus 2 videos in this playlist here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@christianherrera4729]

The way you teach is so intuitive. Its annoying how the text books will try to transition from finite (delta y) to infinite (dy) in the middle of solving. You show the entire problem as dy which is so much more intuitive. Thank you!

[@QuocDatPhung]

Thank you very much! I'm really happy to hear that ;D

[@robbydonaldson6232]

Your video was super helpful and you explained everything very well! Thanks!

[@QuocDatPhung]

Thank you so much Robby! You can find the rest of my Calculus videos in this playlist here (don't forget to subscribe too!): kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@Capitan_Chaos]

Thanks for helping me get through calc 2. I just finished calc 3 a couple weeks ago and it wasn’t as bad except something that I couldn’t understand that KZbin didn’t have as much, was changing order of integration of triple integrals.

[@lucasolsen-jh4oc]

Thank you, this was really helpful!

[@QuocDatPhung]

You're most welcome!! Here are rest of my Calculus videos in this playlist here (don't forget to subscribe too!): kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@AJ-et3vf]

Great video sir. Thank you!

[@QuocDatPhung]

You're so welcome AJ! Please kindly subscribe , also you can find all of my Calculus 2 videos here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@Kabir-dv6xb]

Superb and simple explanation. Thank you so much!!

[@QuocDatPhung]

You're very welcome Kabir!! I'm glad you enjoyed my video! I would really appreciate if you could share with your classmates or kindly subscribe ~ also you can find all of my Calculus II videos in this link: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@vutuan4308]

Thank sir, your video is very helpful

[@QuocDatPhung]

Thank you Vũ Tuấn! Please kindly subscribe and you can also find the rest of my Calculus 2 videos here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@r2k314]

Love your enthusiasm for maths. Where can I see derivation of integral equation. It is not intuitively obvious to me why the only way to account for the depth is by adding another factor of Y to the integrand, such that it adds a quadratic factor to the formula's solution.

[@kadencronick6796]

16:00 Why is the length 2x rather than 6?

[@QuocDatPhung]

If you look at the diagram on the left at 16:00, place your finger on the vertical axis (anywhere you'd like as long as you're inside the circle). Now, move your finger slowly to the right until you touch the circle. That distance you just travelled with your finger is called x. Does that make sense? I drew it in the diagram on the left. Now, put your finger on the vertical axis again, and slowly move your finger to the left until it touches the circle. That distance is also x. So the length is if you draw a line from the circle on the left until it touches the boundary of the circle on the right. This is the same as x + x = 2x = length. Let me know if it makes sense.

[@QuocDatPhung]

I see, you ask why it is 2x rather than 6. If y = 0, then the length is 6 indeed. If y = 1, the length is less than 6 and so on. So, the length varies as you move along the y axis. If the length varies, it must be a variable. Therefore, the length cannot be 6 because you're saying that it's always a constant. Does this make sense?

[@hoilhod]

Great video!! ❤❤

[@QuocDatPhung]

Thank you Hoilhod!! Don't forget to share and kindly subscribe to support me! You can find all of my Calculus II videos here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@gregoryshouldice4054]

amazing! you made it make sense. just subscribed

[@QuocDatPhung]

You're very welcome GregoryShouldice!! You can find all of my Calculus II videos in this link below (don't forget to share with your friends!): kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@gregoryshouldice4054]

@@QuocDatPhung thank you! I showed all of my friends this video. Helped on our exam yesterday !

[@QuocDatPhung]

@@gregoryshouldice4054 Thanks Gregory! I'm happy to hear that it was helpful!

[@William_D_Frog]

You use a slope for the length of a triangle submerged in water(6:32), my teacher taught us to compare similar triangles(one is the object and the other is made when the object is submerged and the base is the water line) to find the width(length) in terms of x, have you dealt with that method? If so, is it any good?

[@QuocDatPhung]

Very good question! I do know that method. However, I prefer the slope method. At the end of the day, you can use whichever one you like.

[@William_D_Frog]

@@QuocDatPhung thank you for such a quick response, I find your method much easier and will see if I can use it on my test tomorrow.

[@jameskao5633]

Good job

[@QuocDatPhung]

Thanks James! If you enjoy my videos, don't forget to subscribe and share! As well, you can find all of my Calculus videos in this playlist: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@worldofsportscars4650]

Why does solving for slope and the equation of thr line work for the length x of thr triangle and trapezoid problem?

[@QuocDatPhung]

Good question! It works because we have the x and y axis so we can use it to measure any length.

[@ArlenGriswold]

legend

[@QuocDatPhung]

Thanks Arlen! 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

[@3dprintwiz378]

Why is it when I apply the equation of the empirical formula for hydrostatic Force : F = d(Hw/2)(area) = 62.5 * (8+3)/2*(8*2) = 5000 lbf d = force density of water, Hw = Height of water, Area = area of exposed surface to water I only get 5000 lbf instead of 7000 lbf as you computed using calculus. Is there something wrong with the empirical formula?

[@QuocDatPhung]

Please let me know the timestamp of the problem that you are referring to. All of these problems and solutions are taken from the textbook, and the answers are triple checked :) At the end of the day, I recommend using the method shown in the video rather than the empirical formula.

[@3dprintwiz378]

@@QuocDatPhung At 1:07 first problem shown is what I mean. I just wanted to check if our engineering formulas are correct compared to a more comprehensive calculus approach. Thank you for your response.

[@QuocDatPhung]

@@3dprintwiz378 Thank you for your question. I'm sorry that I can't confirm whether your engineering formula is correct or not. The calculus way requires you to use integration. The example at 1:07 shows a rectangle (where the width doesn't change) but if you have something like a triangle, the width changes as you go up and down the triangle. I'm confident with the calculus way.

[@chukki9385]

Thank you so much , it was really helpful 🥲

[@QuocDatPhung]

Glad it helped, Chukki! Please kindly subscribe and share with your friends my Calculus playlist: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@davenjadem.maglacas9595]

hello, do you have the solution for the practice problem ? Thank you

[@QuocDatPhung]

Yes, you can see the answer at the top right of the screen at 20:42 Let me know if this is what you meant.

[@davenjadem.maglacas9595]

@@QuocDatPhung I'm looking for the actual solution. I got the wrong answer when I tried answering it. Figured out I have done some errors in determining the depth. Found it later on. Thank you for this tutorial!

[@QuocDatPhung]

@@davenjadem.maglacas9595 Yep I'm happy that you got it right now! You can find the rest of my Calculus 2 videos here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@WOLF_XXX0]

11:35 can some one explain me this part?? Plss

[@QuocDatPhung]

Hi, you're finding the slope at 11:35. Let me know if you have any other questions.

[@wuuna]

du ma mai