A solid sphere of uniform density is released from rest

PHYSICS · Subjective · Fermi University Physics · Fluids & Continuum Physics · Kinematics, conservation laws and ideal flow · Kinematics, conservation laws and ideal flow

Fluid Dynamics, Ch Potential flow, conformal mapping and the finite wing

Problem

A solid sphere of uniform density 400 kg m−3400\,\mathrm{kg\,m^{-3}} is released from rest, fully submerged, in still water (ρ=998 kg m−3\rho = 998\,\mathrm{kg\,m^{-3}}). Using the added mass of a sphere, ma=12ρVm_a = \tfrac12\rho V, and neglecting viscous drag and vortex shedding at this initial instant, find the magnitude and direction of the sphere's initial acceleration.

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