Very small objects, such as dust particles, experience a linear drag force, D? =

Question

Very small objects, such as dust particles, experience a linear drag force, D?  = (bv, direction opposite the motion), where b is a constant. That is, the quadratic model of drag of the equation given below fails for very small particles. For a sphere of radius R, the drag constant can be shown to be b=6??R, where ? is the viscosity of the gas.

D?  = (12CAv2, direction opposite the motion).

Suppose a gust of wind has carried a 52-?m-diameter dust particle to a height of 290m . If the wind suddenly stops, how long will it take the dust particle to settle back to the ground? Dust has a density of 2700 kg/m3, the viscosity of 25?C air is 2.0

Explanation / Answer

Formula for terminal velocity = 2gR^2(Ddust - Dair)/9*u

v = 0.794 m/s

Time taken = 290 /v = 364.79 seconds

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