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The question is about sphere like surfaces, like the hemispherical base of a cylinder as shown. enter image description here

The cylinder is filled with fluid till the given height $h$, and the density of the fluid is $\rho$ and the system is static.I need to find the force due to pressure on the hemispherical portion at the base. I know that the pressure experienced by a ring of thickness, say, $dx$, if the area it contains is parallel to the top of the cylinder, will be equal throughout the ring. And also, the pressure in the hemispherical region changes from $\rho gh$ to $\rho g(h+r)$ (from the disk at the top to the infinitesimal one at the bottom).

(I've tried to find the Force by integrating $PdA$ over each ring, with their radii ranging from $R$ to $0$, and the pressure varying like I mentioned above, but that apparently is not the right way to do it.)

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I guess the force due to pressure on the hemispherical portion at the base is equal to the weight of the fluid. You can just calculate the volume of the fluid and multiply by $\rho g$.

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  • $\begingroup$ I did try that but apparently it isn't the answer I'm supposed to get! $\endgroup$ – Hritik Narayan Apr 5 '15 at 14:25
  • $\begingroup$ @Hritik Narayan: So what answer did you get in this way? $\endgroup$ – akhmeteli Apr 5 '15 at 14:29
  • $\begingroup$ $\rho g\pi R^2(h+2R/3)$. Is that what you intended me to find? $\endgroup$ – Hritik Narayan Apr 5 '15 at 14:34
  • $\begingroup$ @Hritik Narayan: Looks fine to me. Could you give the exact wording of the problem and "the answer you're supposed to get"? $\endgroup$ – akhmeteli Apr 5 '15 at 14:42
  • $\begingroup$ I've included all the details of the question in what I've typed up. Apparently the answer is $\rho g \pi R^2 (h-R/3)$. $\endgroup$ – Hritik Narayan Apr 5 '15 at 14:46

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