SME
Grade 12 Science · Problem type
A stream’s discharge
Use this for “A stream is 12 m wide and 1.5 m deep and flows at 0.8 m/s. What is its discharge?”
Diagram
The cross-section is A = w × d = 12 × 1.5 = 18 m².
Each second the water moves 0.8 m, so the slab passing is 18 × 0.8 = 14.4 m³: Q = 14.4 m³/s.
This is an example. Type your own values to start a new problem.
Q (m³/s)
=
w (m)
×
d (m)
×
v (m/s)
A
Cross-section area
worked out (not typed)
Formulas
A
=
w
×
d
18 = 12 × 1.5
Q
=
A
×
v
14.4 = 18 × 0.8
Assumptions
•
Discharge is the volume of water that flows past a point each second.
•
The channel is taken as a rectangle, and the speed is the average across it.
•
Discharge rises in a flood, and a faster, fuller stream carries more sediment.
Step-by-step
WE KNOW
w = 12 m, d = 1.5 m, v = 0.8 m/s
FIND
cross-section area (A), discharge (Q)
Step 1 · Find cross-section area (A)
Use A = w × d
The cross-section is a rectangle, width by depth.
A
=
12
×
1.5
A
=
18
m²
Step 2 · Find discharge (Q)
Use Q = A × v
Each
second
a
slab
of
water
v
meters
long
and
A
square
meters
across
passes.
Q
=
18
×
0.8
Q
=
14.4
m³/s
Check
Put the numbers back in. Both sides should match.
18 = 12 × 1.5 ✓
14.4 = 18 × 0.8 ✓
← Previous lesson
Weathering, erosion, groundwater, glaciers and wind
Next lesson →
Mechanical or chemical weathering?
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.