How to Calculate Metacentric Height for Stability of a Floating Body?

In summary, the user is struggling with calculating the Metacentric height for a pontoon assembly with given weights and dimensions. They are seeking help and clarification on how to work out the calculation, as well as potentially needing assistance with determining the center of gravity for the loaded pontoon. They also mention potential discrepancies with units used in the given data.
  • #1
thebest99
33
0
Hi

i am not goin goin going to lie Fluid Mechanics is not my strongest subject.

Im struggling to calculate the Metacentric height.

Ive got the following:

Total weight of assembly (W) = 2.447kgf
Ajustible weight (w) = 0.204kgf
Breadth of pontoon (L) = 360mm
Height of metacentre above centre of buoyancy = 1.041m
Depth of immersion =3.33
Depth of centre of buoyancy = 19.4mm

i have other calcs, but need someone to show how to work out to get Metacentric height.

Any help will be great. Thanks
 
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  • #2
I've forgotten anything I learned in fluid mechanics. :redface: but I do remember the term Metacentric Height! Wiki reminds me that MH is the distance of the metacentre above the centre of gravity. So, looks like it comes down to pinpointing the centre of gravity of your loaded pontoon.

Can those other data give any help to this?

BTW, are you lacking care with units? You have m, mm, and none mixed in there.
 

1. What is the stability of a floating body?

The stability of a floating body refers to its ability to maintain its equilibrium or stay upright while floating on the surface of a liquid. This is affected by factors such as the shape and weight distribution of the body, as well as the density and surface tension of the liquid.

2. How is the stability of a floating body determined?

The stability of a floating body is determined by its metacentric height, which is the distance between the body's center of buoyancy (the point at which the buoyant force acts) and its metacenter (the point at which the body becomes stable). A larger metacentric height indicates a more stable body.

3. What is a stable floating body?

A stable floating body is one that has a low center of gravity and a high metacentric height. This means that the body will return to its original upright position if it is tilted or disturbed, making it less likely to capsize or sink.

4. How does the shape of a floating body affect its stability?

The shape of a floating body plays a crucial role in its stability. A body with a wider base or a lower center of gravity will have a larger metacentric height and thus be more stable. On the other hand, a body with a narrow base or a higher center of gravity will have a smaller metacentric height and be less stable.

5. How does water density affect the stability of a floating body?

Water density affects the stability of a floating body because it determines the amount of buoyant force acting on the body. A denser liquid will exert a greater buoyant force, making it more difficult for a body to maintain its equilibrium. This is why objects tend to float more easily in saltwater (which is denser) than in freshwater.

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