Problem 2–17. Fluid Statics. Pool drains can be dangerous things: There was a tragic case recently in this area in which a child was stuck in a drain on the bottom, plugging it, and drowning as a result. Here we look at a somewhat simpler problem. Suppose a ball of radius R is plugging a drain of diameter D at the bottom of a pool of depth h as shown in the figure. Obviously, R > D/2 or the ball goes down the drain! Determine the conditions under which the net force on the ball is zero. Assume that the pressure distribution in the drain is just atmospheric pressure, and that in the water is governed by the hydrostatic pressure distribution. If R is 1 ft and D is 6 in, what is the corresponding depth? h R D

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Problem 2–17. Fluid Statics. Pool drains can be dangerous things: There was a tragic
case recently in this area in which a child was stuck in a drain on the bottom, plugging it,
and drowning as a result. Here we look at a somewhat simpler problem. Suppose a ball of
radius R is plugging a drain of diameter D at the bottom of a pool of depth h as shown in
the figure. Obviously, R > D/2 or the ball goes down the drain! Determine the conditions
under which the net force on the ball is zero. Assume that the pressure distribution in the
drain is just atmospheric pressure, and that in the water is governed by the hydrostatic
pressure distribution. If R is 1 ft and D is 6 in, what is the corresponding depth?
h
R
D
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Transcribed Image Text

Problem 2–17. Fluid Statics. Pool drains can be dangerous things: There was a tragic case recently in this area in which a child was stuck in a drain on the bottom, plugging it, and drowning as a result. Here we look at a somewhat simpler problem. Suppose a ball of radius R is plugging a drain of diameter D at the bottom of a pool of depth h as shown in the figure. Obviously, R > D/2 or the ball goes down the drain! Determine the conditions under which the net force on the ball is zero. Assume that the pressure distribution in the drain is just atmospheric pressure, and that in the water is governed by the hydrostatic pressure distribution. If R is 1 ft and D is 6 in, what is the corresponding depth? h R D