Hydrostatic Force Problems - Calculus 2

[@TheOrganicChemistryTutor]

Application of Integration - Free Formula Sheet: bit.ly/3ZdKSnK Final Exams and Video Playlists: www.video-tutor.net/ Next Video: kzbin.info/www/bejne/h3ykZXuEetxml7s

[@evanmai6195]

Whoa

[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for a solid explanation of Hydrostatic Force problems in Calculus Two. Drawing a picture is a great way to solved Hydrostatic Force Problems in Calculus. There is an error in this video at about the 7:26 minute mark therefore, I will rewatch this video from start to finish.

[@nebilnebastro552]

yeah his way of finding slope is not right

[@mksjnd]

@@nebilnebastro552 FOR THOSE WHO GOT TRIPPED UP LIKE ME: Actually Organic Chemistry Tutor is completely correct. Keep in mind that we have to find slope in terms of y, not x, since we are integrating by dy. I also got tripped up at the value for b because I originally solved for b by adding 3 to both sides. However, the correct way to find b is how Organic Chemistry Tutor described it. You can test this by inputting y=-3/2x-3, the slope in terms of x in Desmos, Geogebra, or another algebra program. If you also input x=-2/3y+3, the incorrect way to find slope in terms of y, you will see that slope is equivalent, but that the y-intercepts do not match. If you input x=-2/3-2, you will find that the y-intercepts AND slopes between the aforementioned equation and y=-3/2x-3 do indeed match. Hope this helps someone else who became stuck on this concept like me. Add a little mental note that b cannot always be solved for by adding its value to both sides when in terms of y.

[@emilyberry360]

I know why the slope is -2/3 and not -3/2. The equation of the slope in terms of x is y=-3/2x - 3. However, you want to rearrange the equation so that x is by itself. Therefore, using algebra, y=-3/2x - 3 y+3 = -3/2x -2/3y - 2 = x Writing this as L(y) L(y) = -2/3y - 2

[@Smile-et3fe]

F = yhA y = unit weight (9.8kN/m³ or 62.4lbs/ft³) h = distance from water surface to centroid of the shape A = area of the shape

[@saberspeed77]

why is this in calc 2. this is gonna take me at least 6 hours to master.

[@faisalmohamed4595]

This is in calculus 1

[@randomreplays]

@@faisalmohamed4595calc 2

[@katkrasher]

This is easy

[@katkrasher]

Alright after working a couple of problems this is not easy i retract my statement

[@mrbanana6464]

Applied calculus requires a deep understanding of calculus and the problem. If you didn't understand the definition of the integral you will not understand how to do this but will instead be doomed to copy formulas.

[@winsurely7083]

Seems to be confusion in the comments section, slope is not "rise over run." In this case, it is better to think of slope as change in (function) over change in (variable), just like how rise over run is delta f(x) over delta x. Hope this helps!

[@dylanarmstrong3569]

For the example with the trapezoid, wouldn't your slope calculation be wrong because you don't actually know the length of the top half on your grid, you only know it's 12 ft + some amount on the x axis?

[@RameshKumar-li2rp]

Thank you so much I understood it Lots of love from Nepal

[@jp9523]

Great explanation but for me it would be better to locate the origin at the base of the figure so that the limits will be more easier to calculate (if you don't want to use calcu)

[@Exoulos]

At 8:33, the function for length of the strip should be: L(y) = -(2/3) * (y+3) ; because y = -(3/2)x - 3 Hope this helps someone out

[@vinceojeda9120]

Thank you so much Sir for this Video it really saves me in understanding the concept, rather than just reading it in the textbook . more power.

[@mdavis5011]

Confused on how you got slope. Looks like this is change in x divided by change in y instead of change in y divided by change in x.

[@navaerick86]

I also think I see a mistake here, not sure tho

[@Anonymous51701]

Cuz you need to change from y=mx+b to x=my+b. Solve for x and you’ll see its the slope he gets

[@graceful522]

I love you, sir. When I have money one day, I will be sure to support you.

[@georgebartman3824]

youtube > Univercity bro you saved me so many times

[@kensielwell]

Thank you thank you thank you this made no sense until I watched this vid

[@kyanisekaildelmonte928]

I don't understand the second example. As far as I rememberit's rise over run so isn't it supposed to be -3/2?

[@avalon_I]

I think because we're finding l(y), you have to find it in terms of y. Just as when you find f(x), you find it in terms of x.

[@TchallaKilmonger]

​@@avalon_Iyep, I had that issue

[@Kyle-pj2vc]

Thank you so much, bringing these videos for my final in a few hours.

[@noelforde237]

how'd it go?

[@Kyle-pj2vc]

@@noelforde237 Got a perfect score on my Calc 2 final last semester.

[@IdleHawk7]

@@Kyle-pj2vcWOOOOH!

[@teersa]

Why did you not integrate for the trapezoid?

[@User-ci3su]

Isn't the slope at 7:40 -3/2? since it's y2-y1 / x2 - x1 ?

[@jhononillgalvez950]

I also got -3/2

[@christiancarter255]

@@jhononillgalvez950 same

[@sleepsy1522]

The thing is we are replacing X with y and L with Y so instead of y=mx+b and y2-y1/x2-x1 it is L=my+b because we substituted this values we must substitute them into the slop formula as well so it would be L2-L1/y2-y1

[@makenzie2353]

Shouldn't the slope be -3/2 at 7:26? 6 and 0 are x-values and should be in the denominator since the slope formula is (y2-y1)/(x2-x1)

[@riley.the.engineer]

That is what I calculated as well. I do not understand.

[@edisunyoto6256]

the slope are -2/3 because it's the function of y

[@comic4relief]

Yes, i thought so also. -9/6 is the slope. What's up?

[@hberry69]

@@edisunyoto6256 no it should still be -3/2 slope is rise over run, y/x, no matter what.

[@milesmathews7579]

Not exactly, I believe he calculated the change between the length of the triangle and y. Slope calculates the average change in a function, and our function is L(y).@@hberry69

[@DzahierulAliemy]

How about finding hydrostatic pressure, P and then multiply it with the area of the shape, A, we will still obtain the hydrostatic force, F right?

[@HeadlessHoursemanMC]

Can you do a video like a qna for us to get to know you better I like attachments to people that teach me????!!!

[@yungzed]

lol

[@scottsanoria1386]

Why other h(y) is not just "-y". Others have "number -y". Example is "10-y", "6-y" etc. why?

[@SuperStruct]

Semicircular Dam Force Question: How come the h(y) doesn't have to be a (10-y)? Is it the h(y)=-y solely on axis placement? (0-y) I think I luckily got this right on the exam by just assuming the total distance dy(opposite gravity--parallel to y-axis) had to be multiplied by y because I thought h(y) was just y, just because it seems like y is the height at every point dy.

[@JensenPlaysMC]

depends on where you place 0,0 it will change the limits of integration and distances but should be the same result

[@laurenbrandt7164]

Thank you so much this video saved me

[@Theadventurelane]

why are you using the -y and negative values for the {c,d} when you can use the positive values for c and d and positive y?

[@MrApplepieforlife]

I read these comments and I thought I was going insane when I was working it out, it barely came out correctly on some of them and the others he flips things over. Just center the at 0,0 from the middle at the bottom and integrate.

[@btwags]

Why don’t you have to multiply the 62.4lb/ft by gravity?

[@CauseAndEfex]

Pounds is already a weight, it has the F(g) built in.

[@muniradanish8510]

Thank you so much

[@beep4050]

Thanks!

[@galligula4742]

thanks! For some reason the trapezoid was just giving me trouble lol

[@YiqianLiang-y3k]

sorry why is h(y) negative y?

[@user-vv1do1wg1j]

because it is in the negative axis below the axis line, positive X (to the right) and negative Y (below)

[@dr1lltrckz147]

why are you unnecessarily using negative values, the height could simply be y and you can integrate from 2-4 not -2 to -4. Also you could set the height to (2-y) and integrate from 0 to 2.

[@sleepsy1522]

@16:53 wouldn’t the X be equal to -square root 100-y^2 because it is below the x axis

[@ev9356]

Hey, so how come when y = 0, L = 12, 11:30 ? If the top is 12 ft long and the bottom is 20 ft long, wouldn't you need to account for 4 extra ft at the top (to the right and the left of the top space) in addition to the 12 ft if you are counting from the origin? so at y = 0, L would be 16 ? Anyway not sure, could be wrong, only noticed it because I tried working out the problem before watching you do it. Thanks btw, awsome vid!

[@yungzed]

idk

[@hyperstorm8662]

I think you have to think about it as just the length not as a coordinate

[@hocnguyen5115]

Thank you so much. Always come back to the same place for the help i need

[@graoliveira6688]

You are amazing!!! Many thanks!!

[@JoelBalasaJr.]

isn't slope equals to change of y/change of x?

[@eltariquaye6928]

How would you do this if you do this if you had to calculate for a rectangle would it be the same?

[@hkatbamna1]

Abolish calculus II

[@friedhegg8874]

skill issue

[@Lalit_Sharma_20]

Sir , why force on vertical plate (question 1 ) is not uniformly distributing ?

[@hunterpresby1090]

Different levels of depth produce different hydrostatic force bc of gravity, i.e. hydrostatic force at the top will probably be less than on the bottom...i think.

[@vashon100]

Isn't the hydrostatic force on the other side of the plate equal (ie the same), thus net zero? It's not like a dam where there is water on one side.

[@achillesarce6397]

Can you solve for a parabola?

[@carlkpsplucky5554]

Great and all, but how to you find the sides of a triangle when you only have 1 leg and 1 angle?

[@meji4966]

inverse trig

[@isaacrogers6420]

its -3 not -2

[@sepehrramshini6411]

Why h = - y? Doesn't pressure depend on the height?

[@sepehrramshini6411]

@Ye Htet Aung but that's wrong... Doesn't work for all questions

[@Kyle-pj2vc]

@@sepehrramshini6411 I think it's h = (height-y)

[@NightcoreXenovia]

Because the origin is above the object or in -y axis

[@edwardzheng5050]

Height changes as you integrate from -12 to -3

[@sleepsy1522]

You are thinking of hydrostatic pressure this is hydrostatic force though they are similar they are not the same

[@kurtneylove]

Where did he get the -2 and -4 on the first problem?

[@wilfredoperez9260]

He made them up, just to give it a value (Range).

[@meji4966]

I finally understand!!!

[@rin-me9wt]

I dont understand why it's okay to use L(y) =my + b if it's a trapezoid and not a straight line.

[@kennycao9334]

Erin West because the width is going to be whatever the x value of the equation is based on the slope that you found from the triangle given

[@DzahierulAliemy]

Why h(y) equal to -y? Why not 3m or something?

[@saberspeed77]

Because the pressure increases the further you go down in depth and isn't a constant 3m.

[@vaderanomaly1573]

why arent we doing this in calc 2? is this honors?

[@usctrojanfreak]

depends on the professor I guess. Currently doing it right now lol :(

[@kevsh4997]

10:04 I don't understand how it got 2,381,400N .

[@fritzschwartz3295]

hey buddy, not sure what im doing wrong, but i keep getting 9096.5 lbs.

[@fritzschwartz3295]

On 14:12

[@fritzschwartz3295]

So sorry! For W. I kept putting 16.4, instead of 64.4. My bad! U da MAn

[@fritzschwartz3295]

*62.4

[@piper-brawlstars6899]

Thanks for the video but shouldn’t c and d be positive?

[@JamesBond-nk1zj]

You put the coordinate system at the center of a circle or semi circle

[@alim-1558]

h should not be -y here it's y

[@jonathanjeffrymulyana4390]

Same thing

[@billg1236]

best of the best

[@bryllethe13]

2,381,400 ??

[@lucasbuddeke7101]

Anyone else getting 28,454 for the third one?

[@salaxsalaxan9218]

I want to hug you my lovely sir

[@medoutube1]

Shouldn't the slope be RISE over RUN, you flipped it by finding -2/3 when it should be -3/2. Kinda confused, beside that great video, much thanks!

[@haruharudude]

It's flipped because it's in terms of y

[@vinceojeda9120]

@@haruharudude is it getting the x value in the slope intercept formula because if that's the case it has to be minus B,just asking.

[@JamesBond-nk1zj]

17:37 I think you should multiply by pi cos the area of the cross section is pi times r squared and isn’t that why you’re using L(y) times d(y) (A=Lw)

[@fookiebear1]

i love you!!!!!!!!!!!!!!!

[@SYEDSHORABALI]

this is confusing

[@kylereed2445]

Side lemf

[@SYEDSHORABALI]

brother with all respect you should have represented function in terms of x and y rather than L(y) and H(y)

[@stephennellas7441]

thaaankkkk yoouuuuuuu

[@talharizwan1226]

ily

[@janethompson3208]

I love you

[@josewui414]

I love your accent lol

[@marvalousmarvette]

At 1418 mins I did the problem copied it and did not get your answer

[@marvalousmarvette]

Oh wait I think i forgot -(-8)^3 and that messed me up

[@kylevillepo9093]

cracked

[@MolotovWithLux]

#HYDROSTATICPRESSURE