Solved Exam Problem: Hydrostatic Forces on a Curved Gate

MEC516/BME516 Fluid Mechanics: A solved exam problem of hydrostatic forces on a curved gate.
All of the videos in this course, sample exams with solutions, and a copy (pdf) of this solution can be downloaded at:
www.drdavidnayl...
Course Textbook: F.M. White and H. Xue, Fluid Mechanics, 9th Edition, McGraw-Hill, New York, 2021.
#fluidmechanics #fluiddynamics

[@alvicgruta5763]

I love you dont use the concept of imaginary water. such a big help sir 🎉

[@gulchinaliyeva8608]

i have been suffering with a single question in my book for an hour... Your video made me understand everything, thank you so so much!!

[@idg_studios]

Thank you so much for your videos. My professor does not give us examples in class and his hand written notes/diagrams are hard to understand. Your stuff is super straightforward with organized diagrams and I greatly appreciate your work

[@FluidMatters]

Glad to help. Best of luck with your studies.

[@airsoft5005]

Amazing video, something that seems so weird and complicated made simple and intuitive. You are so good at explaining the theory and “how to attack” a problem in a easy to understand way. Please post more similar content, thank you! =)

[@FluidMatters]

Thanks. Glad to hear it was helpful.

[@nanodynamics5203]

Awesome and detailed solution. Thanks Dr. David

[@FluidMatters]

Glad to hear it was helpful. Thanks for the kind words.

[@schwarzmann1]

Thank you so much for this example, helped immensely

[@MuhammadDaniyalMechietobe]

Thank youuu Sirr , your way of explanation is tooo good..

[@FluidMatters]

Thank you so much. Glad it was helpful.

[@cutscop]

thanks dr.david for providing the solution of fluid mechanics as pdf on your website

[@MuhammadQasim-th3ed]

Sir you are great 👍💛 ... please keep sharing your knowledge with us 💛🌼😊

[@FluidMatters]

Thanks. Glad to hear the video was helpful.

[@lessssssgooooo]

Thanks Dr.David i understand the topic well now after watching your Video on it greetings from Germany.

[@FluidMatters]

Glad to help!

[@Frenzyfish]

Dear sir, at 11:55 you say that there is a uniform distribution load and therefore the Fbc acting on R/2. Why is that? Isn't the load distribution also acting in a circular way? which implies the Fbc from C is 4R/3Pi ?

[@FluidMatters]

The load on BC is NOT "acting in a circular way". Surface BC is a plane (flat) surface that is at a constant depth of R. The pressure vectors on this surface are uniform (gamma*R) and all point upward. This uniform pressure distribution is replaced by the total force at the center of the pressure distribution (at R/2). I hope that helps.

[@Amanda-le8qe]

im finally able to solve my school's past quiz examples, i can go sleep now :) thankyouu

[@FluidMatters]

Glad to hear my video was helpful. Sleep well!

[@Amanda-le8qe]

@@FluidMatters hey just wanted to let u know that i scored an A for the test! many thanks from NUS😃

[@FluidMatters]

@@Amanda-le8qe Congratulations! You obviously put in the work.

[@pizzag1940]

how is the F bc force not cancelled out by the weight force of the water? Im trying to wrap my head around how there is left over force when you take the weight away. So there is force down because of the weight, and also force down because of the fluid pressure, but isnt the fluid pressure just because of the weight?

[@pizzag1940]

OOHH the height x Area for the fluid pressure is different from the volume of the actual water! so there is a discrepancy there! Equal force on horizontal, so it is like a square of hydrostatic pressure. Thanks

[@FluidMatters]

I think you've got it. Best of luck.

[@A.Hisham86]

thank you for the video! really informative.
But, what about the weight of the gate, is it negligeable in the calculus? and why?

[@FluidMatters]

The main reason is so students can focus on fluid mechanics. Including in the gate weight is trivial statics, which adds unhelpful complexity when it comes to learning hydrostatic analysis. Also it will be generally true that the gate weight will be quite low compared to the hydrostatic forces. You can easily check this -- assume a 0.5 inch curved steel plate, for example.

[@dioutoroo]

Thank you for the explanation, Sir. I have a question, when you calculate the X bar, you take CW as (-) and CCW as (+). However, when you did the sum of moment at B you did the other way around. Why is it?

[@FluidMatters]

It makes no difference. The direction is an arbitrary choice. So, there no reason -- and no need to be consistent either.

[@dioutoroo]

@@FluidMatters I see. Thank you, Sir

[@craig7878]

Hi, when finding F_bc, since it is a vertical force, wouldn't the formula be F_bc = pgV ?

[@FluidMatters]

no. F_BC is the a fluid weight. F_BC is the upward pressure force on plane surface BC. The entire surface BC is a depth R. The pressure at this depth is rho*g*R, which gets multiplied by the surface area. I hope that helps.

[@johnangelo3992]

Thank you so much!

[@FluidMatters]

Glad it was helpful.

[@ferrariessegi9726]

Thanks a lot

[@xmainul_]

Dear Sir, why do you count Fbc pressure force.?
Usually, I saw teachers concern about the weight of the water up to free surface to find vertical force.
I only find in your all of the video you count vertical pressure force, why sir?

[@FluidMatters]

You can use the missing "water approach". It is equivalent. I show this at the very end of the solution (about 15:00). But it can be tricking to find the line of action,. The method in this video is the most general approach. I hope that helps.

[@mohamedabdhul9736]

9:19 how is Ycp=-1.333m didn't you take your origine from the surface?

[@FluidMatters]

y_cp is measured downward from the centroid. See my intro video: ua-cam.com/video/pIK_ywo10Qc/v-deo.htmlsi=_uR8Ucdri3isyM0b

[@HashemAljifri515]

Should FV = the weight of the fluid?? How do you know that there is a force FBC?? Some questions never include this force I can't concentrate??!

[@FluidMatters]

Surface BC is at depth R in the water. So, there will be hydrostatic pressure at this depth, equal to rho*g*R. That's how we know there is a force F_BC. Note that the weight of the water is downward and the force of the water on the gate is clearly upward, as seen from the pressure distribution (at 1:08). So, F_v cannot be equal to the weight of the water. I hope that helps.

[@HashemAljifri515]

@@FluidMatters But in similar problems this is not the case ?? You mean that there is a pressure from the ground due to depth and it is upward ??!

[@FluidMatters]

@@HashemAljifri515 Not "due to the ground". It's the pressure in the water at that depth (at the ground-water interface). Local pressure acts in all directions. Once you define a control volume (as done in this problem) the pressure force acts inward and normal to the boundary (see video 1, Chapter 2) --- hence upward in this case.

[@hiamberger]

Thank you so much!😊😊😊

[@FluidMatters]

Glad to hear you found it helpful.

[@salmankhanmohmand9174]

Sir where can i get its theory part...

[@FluidMatters]

Here's the theory lecture for hydrostatic forces on curved surfaces:
ua-cam.com/video/LdbEpRXUpOQ/v-deo.htmlsi=DoySt3zv_nYTipHn
You can find all the lectures as www.drdavidnaylor.net

[@gujjargujjarlion6240]

Great explanation sir😂

[@FluidMatters]

Thanks. Glad to hear it was helpful. Good luck with your studies.

[@jezrylgelacio595]

Is the Area always (b)(h)?

[@FluidMatters]

It depends. Your question needs to be more specific (e.g give a time) for me to help.

[@engineeringknowledge54]

Elegance

[@FluidMatters]

Thanks. Glad to hear it was helpful.