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You and your friend have begun working on the Klamath River. During high water events in the spring, the river becomes turbid and carries a substantial burden of fine grain sediment. The river shed drains from both clay-rich and sandy-rich soils. Clay soils shed sediment grains 0.002 mm and less in diameter. Sandy soils shed silt sediment with a size from 0.002 and 0.060 mm. You realize that these different sediments will settle in water at different velocities. You devise an experiment to fill a 1 m tall glass cylinder and time how long it takes for the column of water to visibly change in opacity and indicate particle settlement. Clay and silt are both comprised of silicate minerals with a mass density of about 2,650 kg/m3.
a)Calculate the settling velocity (terminal velocity)of particle at the break point size between silt and clay.
b) Calculate the time to see a substantial visible change in opacity in your cylinder if silt rather than clay.
settling speed of particles is given by
v = 2(rhop - rhof)gR^2/9mu
whew mu is viscosity of fluid, rhof is density of fluid, rhop is density of particles, R is radius of oarticels, g is acceleration due to gravity
for r = 0.002 mm = R
mu = 8.9*10^-4
rhop = 2650 kg/m^3
rhof = 1000 kg/m^3
a. v = 1.616629*10^-5 m/s
b. for sand, r = 0.06 mm
hence v = 0.0145496 m/s
as the speed for clay and sand has an order of magnitude difference of over 900
for average r = (0.06 + 0.002)/2 = 0.031
hence v = 0.00388
hecne for average samd particel, the speed of silt is order of magnitude, 240 times
hence to fall a depth of 5 cm in a beaker, time taken by sand = 5*10^-3/0.00388 = 1.288 s
hence in about 1.2 s we can see a visible change in opacity
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