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Unformatted text preview: ed a sleeve. The two cylinders are separated by a small distance ﬁlled with water. The sleeve is
quite long such that the driver can fall from the acceleration of gravity until it reaches a terminal velocity and hammer
into hard ground and form a hole. If designed properly the outer diameter of the driver d and and inner diameter of the
sleeve D are designed to as similar as possible so the driver stays on track. The small that distance D − d the slower
the driver falls under gravity. The inner cylinder is hardened steel with mass of m and length L. Treat this problem as a
simple Couette ﬂow. Provide an analytical expression for the terminal velocity (the steady state velocity that the cylinder reaches at long time, i.e. zero acceleration) of the inner cylinder. Whatever forces you neglect to obtain a solution
should be clearly articulated. How does the terminal velocity depend on the controlling parameters (l, d, D, m, µ), and
what is the most effective way to increase the velocity of the driver? d"
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