Question

Spherical particles of pollen are shaken up in wate are allowed to settle. The depth of water is ` 2 xx 10^(-2)m`. What is the diameter of the largest paricle remaining in suspension for one hour later? Density of pollen = `1.8 xx 10^(3) kg m^(-3)`, vescosity of water = `1 xx 10^(-2)` deca poise and density of water = `1xx 10^(3) kgm^(-3)`.

Answer 1

Terminal velocity of the spherical of pollen, falling through water is
`upsilon=(2 (rho -rho_(0))gr^(2))/(9 eta)` ..(i)
The paricle will not be reaching the bottom in a time t if
`upsilon le d/t = (2 xx 10^(-2)m)/(1 hour) = (2 xx 10^(-2)M)/(60 xx 60s) = (10^(-4))/(18) ms^(-1)`
from (i), ` r = [(9 eta upsilon)/(2(rho - rho_(0))g)]^(1//2)`
`=[(9 xx 10^(-2) xx (10^(-4)//18))/(2[(1.8 xx 10^(3)-1 xx 10^(3))xx9.8])]^(1//2)`
`=5.6 xx 10^(-6)m`.