SME
Oceanography · Problem type
Volume transport in sverdrups
Use this for “A current 80 km wide and 400 m deep flows at 1.2 m/s. What is its transport in sverdrups?”
Diagram
The cross-section is A = w × d = 80,000 × 400 = 32,000,000 m².
Each second the water moves 1.2 m, so the slab passing is 32,000,000 × 1.2 = 38,400,000 m³: Q = 38,400,000 m³/s.
This is an example. Type your own values to start a new problem.
A (m²)
=
b (km)
×
d (m)
Q (Sv)
=
A (m²)
×
u (m/s)
N
Times the Amazon’s flow
worked out (not typed)
Formulas
A
=
b
×
d
32,000,000 = 80,000 × 400
Q
=
A
×
u
38,400,000 = 32,000,000 × 1.2
N
=
Q
210,000
182.8571
=
38,400,000
210,000
Formulas are worked in m, m³/s. The step-by-step shows the conversions.
Assumptions
•
The current is taken as a box of one width and depth moving at its mean speed.
•
One sverdrup (Sv) is 10⁶ m³/s.
•
The Amazon, the largest river, carries about 0.21 Sv (210,000 m³/s) to the sea.
Step-by-step
WE KNOW
b = 80 km, d = 400 m, u = 1.2 m/s
FIND
cross-section area (A), volume transport (Q), times the Amazon’s flow (N)
Step 1 · Convert to the formula’s units
The formulas don’t work directly in the units you chose, so convert first (to m, m³/s).
b = 80 km = 80,000 m (1 km = 1000 m)
Step 2 · Find cross-section area (A)
Use A = b × d
The cross-section is the width times the depth.
A
=
80,000
×
400
A
=
32,000,000
m²
Step 3 · Find volume transport (Q)
Use Q = A × u
Each
second
a
slab
of
water
u
long
passes
through
the
cross-section.
Q
=
32,000,000
×
1.2
Q
=
38,400,000
m³/s
Step 4 · Find times the Amazon’s flow (N)
Use N = Q ÷ 210,000
Compare with the Amazon’s 210,000 m³/s.
N
=
38,400,000
210,000
N
=
182.8571
Step 5 · Convert the answers
Change each answer back to the unit you chose.
Q = 38,400,000 m³/s = 38.4 Sv (1 Sv = 10⁶ m³/s)
Check
Put the numbers back in. Both sides should match.
32,000,000 = 80,000 × 400 ✓
38,400,000 = 32,000,000 × 1.2 ✓
182.8571
=
38,400,000
210,000
✓
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