# How to calculate the volume of a partially submerged horizontal cylinder and the center of buoyancy?

I was wondering how it was possible to calculate the volume of partially submerged horizontal cylinders and the center of buoyancy considering that these horizontal cylinders are just the supporting units of the overall structure.

Above is just a very rough sketch showing a four cylinders in water, how would I go about this I am very confused and possibly out-matched for this type of calculation?

Please let me know if there is any more info needed.

• calculate the volume by measuring them... perhaps you mean something else. Mar 8, 2023 at 14:09

## 1 Answer

Assuming balanced loading, meaning the results of the load placed on the buoy and its weight are passing through the CG of the buoy the 4 cylinders are submerged equally to a depth of H such that the buoyancy of the 4 segments of cylinders is equal to load plus the weight of the buoy. in this case, the center of buoyancy is at the CG of the float at a distance from the center of the cylinder of $$D= 4r/3(\frac{sin^3 \theta/2}{\theta- sin\theta})$$

If the resultant forces do not pass through the CG of the float then the float sinks more toward the off-balance direction to provide balance, which can be solved by iterations of stepwise increase in the angle of tilting of the float.

In the balanced case, the buoyancy of each cylinder is equal to the volume of the segment of the cylinder under the water surface. assuming a density of water= 1kg/l.

• cylinder radius r
• cylinder length L
• Area of submerged segment A
• $$\theta$$ angle of the sector as per the figure in degrees

$$F_b=4*A*L$$ A= (area of the sector as per figure)- (Area of the triangle)

$$A=(\theta /360) *\pi r^2 -1/2 r^2 sin \theta$$

There are analytical solutions as well but they are a bit too long for hand calculations.

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