An axisymmetric body of cross-sectional area a moves steadily down a tube of crosssectional area A, which is filled with a fluid of constant density ρ, as shown in Figure P4.48. The flow over the main part of the body is streamlined, but the flow separates over the rear part of the body such that the pressure over the section x-x immediately downstream of the base is uniform. Neglecting viscous shear forces at the wall, show that the velocity of the body is given by
where F is the force necessary to keep the body moving at a constant speed.
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