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Find the settling velocity of an 8 μm diameter particle with density 1500 kg/m3. If this...

  1. Find the settling velocity of an 8 μm diameter particle with density 1500 kg/m3. If this particle had been hurled to a height of 7000 m during a volcanic eruption, estimate the time required to reach the ground (at sea level). You may assume that the viscosity of air does not change enough with altitude to be important. If winds average 8.0 m/s, how far away (horizontally) would it travel on its way down?

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Answer #1

Diameter of particle, d = 8 μm = 8 * 10-6 m

Density of particle, = 1500 kg/m3

Height during volcanic eruption, h = 7000 m

Viscosity of air, = 0.0172 * 10-3 kg/ms

Settling velocity, v = (d2**g) / (18)

= [ (8 * 10-6 m)2 * 1500 kg/m3 * 9.8 m/s2 ] / [18 * 0.0172 * 10-3 kg/ms ]

= 3.03 * 10-3 m/s

Time to reach ground = h/v = 7000 m / 3.03 * 10-3 m/s = 2310231.023 s

Horizontal wind speed = 8 m/s

Horizontal distance travelled by the particle = 8 m/s * 2310231.023 s

= 18481848.18 m

= 18481.84 km

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