How to Determine Centroid of Gate Hydrostatics

In summary, the weight of the gate has a centroid at a distance of 2R/pi away from the force F. This is determined by calculating the moments about point B using different methods and obtaining the same result. The moments include the counterclockwise moment exerted by normal pressure force from the base, the counterclockwise moment exerted on the right vertical side, the clockwise moment exerted by the weight of the fluid in the quarter circle, and the clockwise moment of force F.
  • #1
ScareCrow271828
22
0

Homework Statement


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?

Homework Equations



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

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?
 
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  • #2
ScareCrow271828 said:

Homework Statement


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?

Homework Equations



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

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

Related to How to Determine Centroid of Gate Hydrostatics

1. How is the centroid of gate hydrostatics determined?

The centroid of gate hydrostatics is determined by calculating the average height of the gate and multiplying it by the area of the gate. This calculation takes into account the weight of the water above and below the gate and determines the point at which the gate would balance if it were placed on a pivot.

2. What factors affect the determination of centroid of gate hydrostatics?

The factors that affect the determination of centroid of gate hydrostatics include the shape and size of the gate, the density and depth of the water, and the angle at which the gate is positioned. These factors can alter the distribution of weight and affect the location of the centroid.

3. Why is it important to determine the centroid of gate hydrostatics?

Determining the centroid of gate hydrostatics is important for calculating the stability and equilibrium of the gate. It also helps in designing and constructing gates that can withstand the forces of hydrostatic pressure and stay in place without tipping over.

4. How does the determination of centroid of gate hydrostatics relate to buoyancy?

The determination of centroid of gate hydrostatics is directly related to buoyancy. The centroid is the point at which the gate would balance if it were placed on a pivot, and this point is also the center of buoyancy. This means that the gate will be stable and will not tip over as long as the centroid is kept below the center of gravity.

5. Are there any limitations to the determination of centroid of gate hydrostatics?

Yes, there are some limitations to the determination of centroid of gate hydrostatics. This method assumes that the gate is a simple geometric shape and that the water is at a uniform density and depth. It also does not take into account any external forces acting on the gate, such as wind or currents, which can affect its stability. Additionally, the accuracy of the determination depends on the precision of the measurements and calculations used.

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