SME
Physical Geology · Problem type
Settling speed of silt and clay
Use this for “Silt grains 0.02 mm across settle in still water. How fast do they sink, and how long do they take to fall 1 m?”
Chart
w(0.02) ≈ 0.036
This is an example. Type your own values to start a new problem.
w (cm/s)
=
(
ρₛ (kg/m³)
−
1,000
kg/m³)
×
g
×
(
d (mm)
)
2
÷
(18
×
μ (mPa·s)
)
ρₛ is the density of the grains themselves, and μ is the water’s viscosity.
t
Time to sink 1 m
calculated
Formulas
w
=
(ρₛ
−
1,000)
×
9.81
×
d
2
18 ×
μ
÷
10
0.03597
=
(2,650
−
1,000)
×
9.81
×
0.02
2
18 × 1
÷
10
t
=
100
w
2,780
=
100
0.03597
Formulas are worked in s. The step-by-step shows the conversions.
Assumptions
•
Stokes’ law holds for grains finer than about 0.1 mm, each sinking alone through still water.
•
g = 9.81 m/s² and water is 1,000 kg/m³; with d in mm and μ in mPa·s the rule gives mm/s, so ÷ 10 gives cm/s.
•
The grain reaches w almost at once, so 1 m (100 cm) takes 100 ÷ w seconds.
Step-by-step
WE KNOW
d = 0.02 mm, ρₛ = 2,650 kg/m³, μ = 1 mPa·s
FIND
settling speed (w), time to sink 1 m (t)
Step 1 · Find settling speed (w)
Use w = (ρₛ − 1,000) × 9.81 × d² ÷ (18 × μ) ÷ 10
Stokes: the grain’s weight less its buoyancy, against the water’s drag, sets its steady speed.
w
=
(2,650
−
1,000)
×
9.81
×
0.02
2
18 × 1
÷
10
w
=
1,650
×
9.81
×
0.02
2
18
÷
10
w
=
1,650
×
9.81
×
0.0004
18
÷
10
w
=
16,186.5
×
0.0004
18
÷
10
w
=
6.4746
18
÷
10
w
=
0.3597
10
w
=
0.03597
cm/s
Step 2 · Find time to sink 1 m (t)
Use t = 100 ÷ w
1 m is 100 cm; divide it by the speed in cm/s.
t
=
100
0.03597
t
=
2,780.0945
s
Step 3 · Convert the answers
Change each answer back to the unit you chose.
t = 2,780 s = 46.3 min (1 min = 60 s)
Check
Put the numbers back in. Both sides should match.
0.03597
=
(2,650
−
1,000)
×
9.81
×
0.02
2
18 × 1
÷
10
✓
2,780
=
100
0.03597
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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