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Case Studies in Fluid Mechanics with Sensitivities to Governing Variables

M. Kemal Atesmen
M. Kemal Atesmen
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ASME Press
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In this chapter we will analyze the stability of a right circular cone-shaped object floating in water. The untipped position of a floating cone is shown in Figure 3.1. H is the height of the cone from its apex to its base, R is the cone’s base radius, h is the submerged height of the cone from its apex to the water’s surface, and r is the right circular cone’s radius at the water’s surface. Since the center of buoyancy, B, is below the center of gravity, G, some portion of the cone is above the surface of the water. Excessive tipping of the cone under these conditions can create unstable conditions for the cone and tip it over. However, if there is sufficient restoring torque from the shifting buoyancy forces, then the cone will not tip and will restore to its original position. The vertical distance G to M is called the metacentric height. Large metacentric heights mean more restoring torque and therefore more stability. See Ref. [16], chapter 3 for a detailed analysis of stability.

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