Your oceanographer friend has a seafloor sample collected last September from ou
ID: 485425 • Letter: Y
Question
Your oceanographer friend has a seafloor sample collected last September from out in the Pacific from a depth of 3,000 m. Your friend studies diatoms and collected this sample during that month to investigate the diatoms that settled from the previous summer, knowing that diatoms live in the light-rich photic zone then die and fall to the seafloor. You wonder just how long it would take diatoms to settle to that depth and if the diatoms on top of the sample in September would give a fair representation of the summer diatom production at the surface above the sample site. From your time in Phyx 118 you can do this! Diatoms range in size from about 10–150 m, and your friend studies a type about 50 m in diameter. I found an article in the Journal of Plankton Research (van Ierland and Peperzak 1983) that reported diatom have a mass density around 1.1 g cm-3.
a) Calculate how long it would take for typical diatoms to settle to the bottom of your friend’s study site, and comment on if you can confidently consider them to have fallen during the summer just before the sample collection. (Hint: you have to see diatoms with a microscope, and remember to consider buoyancy in your calculation.)
b) Based on your calculation in part a), select a reasonable velocity for oceanic currents and make an estimate of the distance from a location on the surface directly above the collection site to a possible location on the ocean surface where those diatoms might have lived before they died and began falling.
Explanation / Answer
Depth of sea, H = 3000 m
Size of diatoms = 50 µm
Radius of diatoms, R = 50 /2 = 25 µm = 25 x 10-6 m
Density of diatoms, d = 1.1 g/cm3 = 1100 kg/m3
Density of water, w = 1 g/cm3 = 1000 kg/m3
At 20 °C
Viscosity of water, µ = 10-3 Pa.s
Stoke settling velocity, v = 2 * (d - w) * g * R2 / (9 * µ)
= 1.3625 x 10-4 m/s
a)
Time taken to fall, t = H / v
= 3000 / 1.3625 x 10-4 = 2.2 x 107 s
= 2.2 x 107 / (3600 *24) days
= 254.8 days ~ 8.5 months
September to sample collection time ~ 9.5 months
Yes, the typical diatoms would have fallen before the sample collection.
b)
Considering average oceanic current velocity (u) of 5 cm/s or 0.05 m/s
Distance = u * t
= 0.05 * 2.2 x 107 = 1.1 x 106 m
~ 1100 kms
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