# How to Determine Centroid of Gate Hydrostatics

1. May 1, 2017

### ScareCrow271828

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. May 1, 2017

### Staff: Mentor

Can you please provide a word for word statement of this problem? Thank you.

3. May 1, 2017

### Staff: Mentor

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 = $rF$