Centroid and centre of pressure

[Pietair]

Homework Statement

Explain why the distance between the centroid and the centre of pressure for a plane submerged fluid decreases as the depth of fluid increases.

I know that the centre of pressure for a plane submerged fluid is located below the centroid because pressure increases with depth.

But why is the distance between centroid and centre of pressure decreasing as the depth of fluid increases?

 

[Pietair]

Anyone?

 

[MisterOL]

Well I am looking for same answer and what I found out is if there is not a conrete example that you actullay tried to solve there is not much help on the basics on this forum...

 

[iq97ca]

its because y'cp=density*sin(theta)*I_xx/(P_CG*A) as the depth increases the P_CG increases causing the y'cp (the distance between the two points) to decrease

 

[rwisz]

The distance between the centroid and centre of pressure for a plane submerged in fluid decreases as the depth of the fluid increases due to the changing pressure distribution within the fluid. As the depth of the fluid increases, the pressure at the bottom of the plane increases, causing the centre of pressure to shift downwards towards the centroid. This is because the pressure at any point in a fluid is directly proportional to the depth of the fluid above it. Therefore, at greater depths, the pressure at the bottom of the plane is higher, causing the centre of pressure to move closer to the centroid. This decrease in distance between the two points is a result of the increasing pressure acting on the bottom of the plane, and is consistent with the principles of fluid mechanics.