p.209 in Henry and Heinke. A coal-fired electric generating station has a 100-m

Question

    p.209 in Henry and Heinke.

A coal-fired electric generating station has a 100-m high stack from which particles are emitted and rise an additional 100 m due to plume thermal buoyancy. The average horizontal wind speed between the earth surface and the 200-m level is 10 m/s. Estimate the distance downstream from the stack that a 15-um particle of density 2 g/cm3 will travel before it reaches the earth surface. You may assume that the vertical settling velocity of the particle may be calculated using Stokes Law: ut = (pp -p) g dp2 / 18 u, where pp = particle density, p = air density, g = acceleration of gravity, dp= particle diameter, and u = air viscosity. [From Appendix A, p.771 in Davis and Masten, p = 1.2 g/L and u = 1.8x10-5 kg/m-s.]

Explanation / Answer

pp = 2g/cm3 = 2000Kg/m3

p = 1.2 kg/m3

ut = (2000-1.2)*9.8*(15*10^-6)^2 /(18*1.8*10^-5) = 0.0136 m/s

so, time required for the particle to come down = 200/0.0136 = 14702.69 seconds

so, distance downstream from the stack = 10*14702.69 = 147026.9 m = 147.026 Km

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