Solved Exam Problem: Hydrostatic Forces on a Curved Gate

MEC516/BME516 Fluid Mechanics: A solved exam problem of hydrostatic forces on a curved gate from a past midterm exam. This problem has been reposted without a detailed discussion of the theory because many students are only seeking solved problems.
All the videos in this course and a copy (pdf) of this presentation can be downloaded at: www.drdavidnayl...
Course Textbook: F.M. White and H. Xue, Fluid Mechanics, 9th Edition, McGraw-Hill, New York, 2021.
#fluidmechanics #fluidstatics #hydrostatics

[@FluidMatters]

All the videos for this introductory Fluid Mechanics course, pdfs of the presentations, solved exams and problem sets can be downloaded at: www.drdavidnaylor.net

[@hexene6679]

this type of videos are really helpful 🎉 currently studying for my first exam on Fluid Mechanics for CE. Thanks a lot !!!

[@FluidMatters]

Glad the hear the video was helpful. Good luck on the exam

[@MonkeyPoida]

Thank you! Very well presented. The clear explanations and graphics make it easy to understand.

[@FluidMatters]

Glad to hear that you found it helpful

[@balakayshorts949]

Why do we not include the weight of the water and Fab when taking moments around A?

[@FluidMatters]

Because you would be double counting. The forces on the gate are caused by the weight of the water. Another way to think about it. This is a free body diagram of the gate, which includes only forces on the gate. Forces on the water are not part of the FBD for the gate. That's going back to basic statics.

[@divyanshupratik826]

Why haven't you considered F due to pressure (rho*g*h) downwards on the gate?

[@FluidMatters]

See the free body diagram (at 2:25). I'm not sure what you mean. The weight of the water is the source of the downward force and the downward pressure on the gate. I hope that helps.

[@divyanshupratik826]

@@FluidMatters what I meant to ask was why you didn't consider an downward hydrostatic force due to depth h

[@FluidMatters]

@@divyanshupratik826 That would be double counting the force F_v. The downward component of the hydrostatic pressure distribution on the gate (shown at 1:08) is caused by the weight of the semi-circle of water. So, I DID "consider an downward hydrostatic force due to depth h". That's why the pressure vectors (in red) get bigger with depth.

[@ksvinit5732]

Sir I think centre of pressure should be taken from top becuz here 1.33m seems less than 1m in diagram at 8:38
2-0.6667 = 1.333 is lying below the centre

[@FluidMatters]

"1.33m seems less than 1m" doesn't make sense. Clarify and add a time stamp, if you have a real question.

[@許文赫-l5c]

Thanks OWO

[@FluidMatters]

Glad it was helpful.