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River cross-section & discharge

Use Q = A × v to calculate river discharge in m³/s from cross-sectional area and flow velocity. Review suitability for your learners before teaching.

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Worksheet StudioPractice pack · Ages 10-12

River cross-section & discharge

Take your time. Show your thinking.

1. A river channel has a wet cross-sectional area of 23 m² and an average flow velocity of 2 m/s. Use Q = A × v to calculate its discharge.
23 m · 2 m/s · River cross-section & disc…
2. A river channel has a wet cross-sectional area of 18 m² and an average flow velocity of 6 m/s. Use Q = A × v to calculate its discharge.
18 m · 6 m/s · River cross-section & disc…
3. A river channel has a wet cross-sectional area of 12 m² and an average flow velocity of 5 m/s. Use Q = A × v to calculate its discharge.
12 m · 5 m/s · River cross-section & disc…
4. A river channel has a wet cross-sectional area of 5 m² and an average flow velocity of 5 m/s. Use Q = A × v to calculate its discharge.
5 m · 5 m/s · River cross-section & disc…
5. A river channel has a wet cross-sectional area of 17 m² and an average flow velocity of 6 m/s. Use Q = A × v to calculate its discharge.
17 m · 6 m/s · River cross-section & disc…
6. A river channel has a wet cross-sectional area of 17 m² and an average flow velocity of 4 m/s. Use Q = A × v to calculate its discharge.
17 m · 4 m/s · River cross-section & disc…
7. A river channel has a wet cross-sectional area of 13 m² and an average flow velocity of 2 m/s. Use Q = A × v to calculate its discharge.
13 m · 2 m/s · River cross-section & disc…
8. A river channel has a wet cross-sectional area of 7 m² and an average flow velocity of 3 m/s. Use Q = A × v to calculate its discharge.
7 m · 3 m/s · River cross-section & disc…
9. A river channel has a wet cross-sectional area of 4 m² and an average flow velocity of 4 m/s. Use Q = A × v to calculate its discharge.
4 m · 4 m/s · River cross-section & disc…
10. A river channel has a wet cross-sectional area of 4 m² and an average flow velocity of 1 m/s. Use Q = A × v to calculate its discharge.
4 m · 1 m/s · River cross-section & disc…
11. A river channel has a wet cross-sectional area of 3 m² and an average flow velocity of 2 m/s. Use Q = A × v to calculate its discharge.
3 m · 2 m/s · River cross-section & disc…
12. A river channel has a wet cross-sectional area of 20 m² and an average flow velocity of 1 m/s. Use Q = A × v to calculate its discharge.
20 m · 1 m/s · River cross-section & disc…

12 questions · Seed 44 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 10-12

River cross-section & discharge

Answers and reasoning. Review before teaching.

1. A river channel has a wet cross-sectional area of 23 m² and an average flow velocity of 2 m/s. Use Q = A × v to calculate its discharge.
46 m³/s
Discharge Q = cross-sectional area × velocity = 23 m² × 2 m/s = 46 m³/s.
2. A river channel has a wet cross-sectional area of 18 m² and an average flow velocity of 6 m/s. Use Q = A × v to calculate its discharge.
108 m³/s
Discharge Q = cross-sectional area × velocity = 18 m² × 6 m/s = 108 m³/s.
3. A river channel has a wet cross-sectional area of 12 m² and an average flow velocity of 5 m/s. Use Q = A × v to calculate its discharge.
60 m³/s
Discharge Q = cross-sectional area × velocity = 12 m² × 5 m/s = 60 m³/s.
4. A river channel has a wet cross-sectional area of 5 m² and an average flow velocity of 5 m/s. Use Q = A × v to calculate its discharge.
25 m³/s
Discharge Q = cross-sectional area × velocity = 5 m² × 5 m/s = 25 m³/s.
5. A river channel has a wet cross-sectional area of 17 m² and an average flow velocity of 6 m/s. Use Q = A × v to calculate its discharge.
102 m³/s
Discharge Q = cross-sectional area × velocity = 17 m² × 6 m/s = 102 m³/s.
6. A river channel has a wet cross-sectional area of 17 m² and an average flow velocity of 4 m/s. Use Q = A × v to calculate its discharge.
68 m³/s
Discharge Q = cross-sectional area × velocity = 17 m² × 4 m/s = 68 m³/s.
7. A river channel has a wet cross-sectional area of 13 m² and an average flow velocity of 2 m/s. Use Q = A × v to calculate its discharge.
26 m³/s
Discharge Q = cross-sectional area × velocity = 13 m² × 2 m/s = 26 m³/s.
8. A river channel has a wet cross-sectional area of 7 m² and an average flow velocity of 3 m/s. Use Q = A × v to calculate its discharge.
21 m³/s
Discharge Q = cross-sectional area × velocity = 7 m² × 3 m/s = 21 m³/s.
9. A river channel has a wet cross-sectional area of 4 m² and an average flow velocity of 4 m/s. Use Q = A × v to calculate its discharge.
16 m³/s
Discharge Q = cross-sectional area × velocity = 4 m² × 4 m/s = 16 m³/s.
10. A river channel has a wet cross-sectional area of 4 m² and an average flow velocity of 1 m/s. Use Q = A × v to calculate its discharge.
4 m³/s
Discharge Q = cross-sectional area × velocity = 4 m² × 1 m/s = 4 m³/s.
11. A river channel has a wet cross-sectional area of 3 m² and an average flow velocity of 2 m/s. Use Q = A × v to calculate its discharge.
6 m³/s
Discharge Q = cross-sectional area × velocity = 3 m² × 2 m/s = 6 m³/s.
12. A river channel has a wet cross-sectional area of 20 m² and an average flow velocity of 1 m/s. Use Q = A × v to calculate its discharge.
20 m³/s
Discharge Q = cross-sectional area × velocity = 20 m² × 1 m/s = 20 m³/s.

12 questions · Seed 44 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

River cross-section & discharge

Take your time. Show your thinking.

1. A river channel has a wet cross-sectional area of 23 m² and an average flow velocity of 2 m/s. Use Q = A × v to calculate its discharge.
23 m · 2 m/s · River cross-section & disc…
2. A river channel has a wet cross-sectional area of 18 m² and an average flow velocity of 6 m/s. Use Q = A × v to calculate its discharge.
18 m · 6 m/s · River cross-section & disc…
3. A river channel has a wet cross-sectional area of 12 m² and an average flow velocity of 5 m/s. Use Q = A × v to calculate its discharge.
12 m · 5 m/s · River cross-section & disc…
4. A river channel has a wet cross-sectional area of 5 m² and an average flow velocity of 5 m/s. Use Q = A × v to calculate its discharge.
5 m · 5 m/s · River cross-section & disc…
5. A river channel has a wet cross-sectional area of 17 m² and an average flow velocity of 6 m/s. Use Q = A × v to calculate its discharge.
17 m · 6 m/s · River cross-section & disc…
6. A river channel has a wet cross-sectional area of 17 m² and an average flow velocity of 4 m/s. Use Q = A × v to calculate its discharge.
17 m · 4 m/s · River cross-section & disc…
7. A river channel has a wet cross-sectional area of 13 m² and an average flow velocity of 2 m/s. Use Q = A × v to calculate its discharge.
13 m · 2 m/s · River cross-section & disc…
8. A river channel has a wet cross-sectional area of 7 m² and an average flow velocity of 3 m/s. Use Q = A × v to calculate its discharge.
7 m · 3 m/s · River cross-section & disc…
9. A river channel has a wet cross-sectional area of 4 m² and an average flow velocity of 4 m/s. Use Q = A × v to calculate its discharge.
4 m · 4 m/s · River cross-section & disc…
10. A river channel has a wet cross-sectional area of 4 m² and an average flow velocity of 1 m/s. Use Q = A × v to calculate its discharge.
4 m · 1 m/s · River cross-section & disc…
11. A river channel has a wet cross-sectional area of 3 m² and an average flow velocity of 2 m/s. Use Q = A × v to calculate its discharge.
3 m · 2 m/s · River cross-section & disc…
12. A river channel has a wet cross-sectional area of 20 m² and an average flow velocity of 1 m/s. Use Q = A × v to calculate its discharge.
20 m · 1 m/s · River cross-section & disc…

12 questions · Seed 44 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

River cross-section & discharge

Answers and reasoning. Review before teaching.

1. A river channel has a wet cross-sectional area of 23 m² and an average flow velocity of 2 m/s. Use Q = A × v to calculate its discharge.
46 m³/s
Discharge Q = cross-sectional area × velocity = 23 m² × 2 m/s = 46 m³/s.
2. A river channel has a wet cross-sectional area of 18 m² and an average flow velocity of 6 m/s. Use Q = A × v to calculate its discharge.
108 m³/s
Discharge Q = cross-sectional area × velocity = 18 m² × 6 m/s = 108 m³/s.
3. A river channel has a wet cross-sectional area of 12 m² and an average flow velocity of 5 m/s. Use Q = A × v to calculate its discharge.
60 m³/s
Discharge Q = cross-sectional area × velocity = 12 m² × 5 m/s = 60 m³/s.
4. A river channel has a wet cross-sectional area of 5 m² and an average flow velocity of 5 m/s. Use Q = A × v to calculate its discharge.
25 m³/s
Discharge Q = cross-sectional area × velocity = 5 m² × 5 m/s = 25 m³/s.
5. A river channel has a wet cross-sectional area of 17 m² and an average flow velocity of 6 m/s. Use Q = A × v to calculate its discharge.
102 m³/s
Discharge Q = cross-sectional area × velocity = 17 m² × 6 m/s = 102 m³/s.
6. A river channel has a wet cross-sectional area of 17 m² and an average flow velocity of 4 m/s. Use Q = A × v to calculate its discharge.
68 m³/s
Discharge Q = cross-sectional area × velocity = 17 m² × 4 m/s = 68 m³/s.
7. A river channel has a wet cross-sectional area of 13 m² and an average flow velocity of 2 m/s. Use Q = A × v to calculate its discharge.
26 m³/s
Discharge Q = cross-sectional area × velocity = 13 m² × 2 m/s = 26 m³/s.
8. A river channel has a wet cross-sectional area of 7 m² and an average flow velocity of 3 m/s. Use Q = A × v to calculate its discharge.
21 m³/s
Discharge Q = cross-sectional area × velocity = 7 m² × 3 m/s = 21 m³/s.
9. A river channel has a wet cross-sectional area of 4 m² and an average flow velocity of 4 m/s. Use Q = A × v to calculate its discharge.
16 m³/s
Discharge Q = cross-sectional area × velocity = 4 m² × 4 m/s = 16 m³/s.
10. A river channel has a wet cross-sectional area of 4 m² and an average flow velocity of 1 m/s. Use Q = A × v to calculate its discharge.
4 m³/s
Discharge Q = cross-sectional area × velocity = 4 m² × 1 m/s = 4 m³/s.
11. A river channel has a wet cross-sectional area of 3 m² and an average flow velocity of 2 m/s. Use Q = A × v to calculate its discharge.
6 m³/s
Discharge Q = cross-sectional area × velocity = 3 m² × 2 m/s = 6 m³/s.
12. A river channel has a wet cross-sectional area of 20 m² and an average flow velocity of 1 m/s. Use Q = A × v to calculate its discharge.
20 m³/s
Discharge Q = cross-sectional area × velocity = 20 m² × 1 m/s = 20 m³/s.

12 questions · Seed 44 · Age guidance, not curriculum certification