Problem *3.106[Difficulty: 4]FBW FLFUx y Given:Data on sphere and tank bottomFind:Expression for SG of sphere at which it will float to surface;minimum SG to remain in positionAssumptions:(1) Water is static and incompressible(2) Sphere is much larger than the hole at the bottom of the tankSolution:Basic equationsFBρg⋅V⋅=andΣFyFLFU−FB+W−=whereFLpatmπ⋅a2⋅=FUpatmρg⋅H2R⋅−()⋅+⎣⎦π⋅a2⋅=FBρg⋅Vnet⋅=Vnet43π⋅R3⋅πa2⋅2⋅R⋅−=WSGρ⋅g⋅V⋅=withV43π⋅R3⋅=Now if the sum of the vertical forces is positive, the sphere will float away, while if the sum is zero or negative the sphere will stayat the bottom of the tank (its weight and the hydrostatic force are greater than the buoyant force). HenceΣFypatmπ⋅a
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