Suppose that an erosion event disperses sand, silt, and clay size soil particles

Question

Suppose that an erosion event disperses sand, silt, and clay size soil particles into a pond. You wish to estimate how long it will take for the particles to settle to the bottom of the 25 cm deep pond. In reality these problems are complicated by water currents and temperature variations causing turbulence, but for this approximation assume that the pond is calm with a uniform temperature (9 C). If the particles are initially distributed uniformly and have a maximum diameter of 1.80 mm, calculate the maximum particle diameter D remaining in suspension as a function of time. Plot D(t) for 24 hrs. Report the times at which all the sand and all the silt sized particles have settled to the bottom.

Explanation / Answer

The particles settles followin the stokes law, the heavier particles settle first and then the lighter particles.

The settling velocity of soil is given by stokes law

V2=1/18((Ps-pf)gd2/u

where ps= density of soil=1.35g/cm3( average density of soil)

pf= density of fluid=1g/cm3

g=9.8 m/s2=980 cm/s-2

d=1.80mm=180 cm

u= visocity of fluid=0.0135 sq cms-1

Now stokes velocity=1/18(1.35-1)*980*180/(0.0135)

=1/18(0.35*980*180^2/0.0135

=1/18(0.35*980*32400)/0.0135

=1/18(11113200/0.0135)

=1/18(823,200,000)

=45,733,333.33

Now, time taken for all particles to settle=distance/ speed or settling velocity

Distance=25 cm

Speed=45733,333.33cm/s

time=25/45733,333.33

=5.4*10-7s

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