Centroid and centre of pressure

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    Centroid Pressure
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The distance between the centroid and the center of pressure for a submerged plane decreases with increasing fluid depth due to the relationship between pressure and depth. As depth increases, the pressure at the centroid (P_CG) rises, influencing the position of the center of pressure. The formula y'cp = density * sin(theta) * I_xx / (P_CG * A) indicates that as P_CG increases, the distance y'cp diminishes. This relationship highlights the effect of hydrostatic pressure on the positioning of these two points. Understanding this concept is crucial for applications in fluid mechanics and engineering.
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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?
 
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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...
 
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
 

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