Solved Example: Hydrostatic Forces on a Vertical Gate

MEC516/BME516 Fluid Mechanics: A simple solved exam problem of hydrostatic forces on a flat vertical gate. The solution includes locating the line of action i.e, the center of pressure.
All of the videos in this course, sample exams with solutions, and a copy (pdf) of this solution can be downloaded at www.drdavidnaylor.net
Minor Correction: There is a "typo" at 6:46. h_cg=2.8m (not 1.8m) . But the value of y_cp and the problem answers are all ok.
Course Textbook: F.M. White and H. Xue, Fluid Mechanics, 9th Edition, McGraw-Hill, New York, 2021.
#fluidmechanics #fluiddynamics #fluidstatics

[@shenanigansonyoutube2901]

In 7 minutes I have learned more about Fluid Mechanics than I have in an entire semester so far with my professor. Thank you.

[@FluidMatters]

Thanks. Happy to help.

[@dramoyoedward9229]

Very clear explanation...thanks🙏

[@Amanda-le8qe]

thanks for the video though was very well explained, i understood it immediately as opposed to my lecturer that rambled for 2 hours straight

[@schwabioso]

thx for the video- little mistake at 06:48, hcg=2,8m !

[@FluidMatters]

Thanks. Yes That's a "typo". The value of y_cp is correct. I will make a note of this correction in the description. That's probably better than deleting this video. Thanks again.

[@naveedrehman6083]

true

[@FranciscoJLI]

OMG no way i just three hours until i just saw your comment.

[@Amanda-le8qe]

me attemping to learn this at 3 am and my exam is in 5hours 😪😪

[@garrettsanford1493]

Did you pass? Boutta take my final in 8 hours

[@MaximusLX]

Thanks for this, very clear explanation

[@FluidMatters]

Glad to hear it was helpful.

[@vihanga4141]

Very well explained

[@FluidMatters]

Thanks. Glad to hear it was helpful.

[@aitorag1114]

well explained, thank you.

[@FluidMatters]

Glad to hear it was helpful

[@gameoboy2]

How would I go about finding the reaction forces at points A and B?

[@FluidMatters]

Basic statics: Once you have the horizontal force at B, then set the sum of the forces in the x-direction equals zero to get F_Ax and set the sum of the forces in the y-direction equals zero to get F_Ay. Actually, F_Ay is zero by observation.

[@AJMusicUganda]

thanks . please share the link for the first culculation videos.thanks

[@FluidMatters]

All the videos are available at my website www.drdavidnaylor.net I hope that helps.

[@_AlfiansyahMalikN]

I'm confused, why is the value of Ixx divided by 12?

[@FluidMatters]

The second moment of area of a rectangle about a horizontal axis through its centroid is the width*height^3/12. Google "second moment of area of a rectangle"

[@sindiswahadebe1070]

For the last question why is the equation not : ycp = Ixx/hA +h

[@FluidMatters]

ycp is measured from the center of gravity, not the free surface. It's the the distance from the h_cg, with the negative sign indicating its below the cg. So, the distance from the free surface to the center of pressure is h_cg + abs(y_cp). I hope that helps.

[@abdullahoz7813]

At the end, Why did we write 1.8 intead of 2.8 ?

[@FluidMatters]

See the comment in the video description.

[@abdullahoz7813]

Thanks ✋🏻

[@violetgray4264]

02:05 , free surface has Pa, a little correction i think??

[@FluidMatters]

No correction is needed because Pa also acts on the right side of the gate. So, the effect of atmospheric pressure cancels out.

[@A.Hisham86]

Well, I was expecting you to use the prism way to resolve it too. :)

[@FluidMatters]

Yes. That works too.

[@HashemAljifri515]

What is the distance 1.8 meters??

[@FluidMatters]

In the video description: Minor Correction: There is a "typo" at 6:46. h_cg=2.8m (not 1.8m) . But the value of y_cp and the problem answers are all ok.

[@ambroseongom5345]

I was looking for the correction. Thanks for the correction