Question

A volcanic plume puts ash into the atmosphere to altitude of 10000m. The characteristic ash particle...

A volcanic plume puts ash into the atmosphere to altitude of 10000m. The characteristic ash particle is a sphere with a diameter of 40 mum and has a density of 1000 kg/m^3. Consider a single ash particle in isolation that is travelling vertically at its terminal velocity (i.e. no acceleration). Assume the density and kinematic viscosity of the air are independent of altitude and is given rho = 0.7 kg/m^3 and nu = 1.5 times 10^-5 m^2/s. The drag coefficient is given by Stoke's relation: C_D = 24/Re. Which of the following answers is closest to the length of time it takes for the particle to settle to the ground? 2 hours 53 hours 33 hours 21 hours

Solution:

Settling velocity is used to determine the approximate time for the ash particle to settle down from 10000m,

Vs = (9.81* (1000-0.7)* 40 E-06 ) / 18 = 0.02178 m/s

so it takes 33 hours approx for the ash particle to settle down

Option (B) 53 hours.

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