Question

4. A cylindrical message capsule is propelled at a constant speed V through a metal tube by a pressure force as shown in the figure below. A lubricating fluid fills the small gap between the capsule and the tube. Assuming that the velocity profile in the liquid is linear: a. Draw the free-body diagram on the capsule showing all the forces acting on the capsule (ignorethe weight of the capsule) b. Determine a formula for the speed of the capsule, V in terms of pressure difference, Ap = p1–P2 >0, geometry (parameters in the figures) and viscosity, µ of the liquid. State any assumptions made clearly.

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