SME
Physical Geology · Problem type
Shear stress under a glacier
Use this for “Ice 300 m thick has a surface slope of 3°. What is the shear stress at its bed?”, or the thickness for 100 kPa on 2°.
Diagram
Basal shear = ρgH sin α = 917 × 9.81 × 300 × sin 3° ÷ 1000 = 141.2 kPa
At or past about 100 kPa: the ice deforms and flows.
The slab is long next to its depth; the depth is not drawn to scale.
This is an example. Type your own values to start a new problem.
τb (kPa)
=
ρ (kg/m³)
×
g
×
H (m)
×
sin(
α
°)
Formulas
τb
=
ρ
×
9.81
×
H
×
sin(
α
°)
1,000
141
=
917
×
9.81
×
300
×
sin(3°)
1,000
Assumptions
•
The slope is the ice surface’s, not the bed’s; the glacier is long next to its thickness.
•
g = 9.81 m/s²; the ÷ 1,000 turns pascals into kilopascals.
•
Ice flows when the basal shear nears about 100 kPa, so thickness and slope adjust toward it.
Step-by-step
WE KNOW
H = 300 m, α = 3°, ρ = 917 kg/m³
FIND
basal shear stress (τb)
Step 1 · Find basal shear stress (τb)
Use τb = ρ × 9.81 × H × sin(α°) ÷ 1,000
The
ice
column’s
weight
per
area,
ρgH,
times
its
share
along
the
slope,
sin
α
,
in
kPa.
τb
=
917
×
9.81
×
300
×
sin(3°)
1,000
τb
=
917
×
9.81
×
300
×
0.052336
1,000
τb
=
8,995.77
×
300
×
0.052336
1,000
τb
=
2,698,731
×
0.052336
1,000
τb
=
141,240
1,000
τb = 141 kPa
Check
Put the numbers back in. Both sides should match.
141
=
917
×
9.81
×
300
×
sin(3°)
1,000
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Related lessons
Surface processes
Main lesson
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?”
Landforms and the agent that made them
Use this for “Which agent of erosion and deposition formed an esker, a cirque or a barchan dune?”