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How to Determine Centroid of Gate Hydrostatics

  1. May 1, 2017 #1
    1. The problem statement, all variables and given/known data
    In this image :
    http://ezto.mheducation.com/13252703414204806874.tp4?REQUEST=SHOWmedia&media=2.83qs.jpg
    Why does the weight of the gate have a centroid at 2R/pi away from the force F?

    2. Relevant equations

    The centroid for a half circle in both x and y directions is = 4r/3pi


    3. The attempt at a solution
    why isn't the centroid location in regards to the x axis 4r/3pi? How do we get to 2R/pi?
     
  2. jcsd
  3. May 1, 2017 #2
    Can you please provide a word for word statement of this problem? Thank you.
     
  4. May 1, 2017 #3
    I solved this problem by two different methods, and got the same result for the force F. Here are some intermediate results for the moments about point B:

    counterclockwise moment exerted by normal pressure force from base = ##\rho g r^3/2##

    counterclockwise moment exerted on right vertical side = ##\rho g r^3/6##

    clockwise moment exerted by weight of fluid in quarter circle = ##\rho g \frac{\pi r^2}{4}\left(r-\frac{4r}{3\pi}\right)##

    clockwise moment of force F = ##rF##
     
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