Solved Exam Problem: Hydrostatic Force on a Semi-circular Plane Gate
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- Опубликовано: 13 сен 2024
- MEC516/BME516 Fluid Mechanics: Solution to the hydrostatic force on a plane gate. This is a typical exam-type question.
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Course Textbook: F.M. White and H. Xue, Fluid Mechanics, 9th Edition, McGraw-Hill, New York, 2021.
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Thank you for sharing your knowledge, this video has helped me start to get a better grasp on these kinds of problem. I'm not sure how but I ended up with a yCP value of 2.63. I used the equation from the FE exam reference handbook: yCP = yC + IxC/yC*A. My yC value was 2.6 which I got from adding the centroid distance to the slant distance from edge of gate to edge of water. I had the same IxC and A values. Any idea where I went wrong? My handbook doesn't include the formulas you were using but I was able to solve for the normal force to the gate using my version of that formula.
Sorry, it's super hard to debug solutions with just a comment to go by, often with different nomenclature (i.e., yC).
when do we use the area of the projection to calculate the horizontal force? in some exercises hey use the area of the projection and in others like yours they use the area of the initial shape. i don't know when we must you each of them
Note that the force F is normal to the gate. If you the projection (into the vertical plane) you would get the horizontal force. So, you can use the technique often used for curved gates here too, if you want.
you’re the best
What is the equation for yr?
yr? I suggest giving a time marker, as I a don't know what you are referring to.
I think that Yc = Yg + Ixx'/A×Yg
And Ixx' = 3,14×r²/ 4
So I don't understand what you did
Ixx is the 2nd moment of area about the horizontal axis through the centroid of the semi-circle. It is correct in this solution for sure. Note that Ixx must be proportional to R^4. Your formula for Ixx (with R^4) looks like it is for a full circle, rather than a half-circle. That's the best I can do for you.
@@FluidMatters yes that's true. Thanks a lot but for the formula of Yc. Is it correct?
@@Gaelleda Difficult to say, as you are using a different nomenclature that me.
@@FluidMatters I come up with this Ixx = πr⁴/8 = 0.3927r⁴
@@user-gw3bv3fn8o This is not the second moment through the centroid of the area. Your formula is about the wrong axis location (the base of the semi-circle.