- 2073 Bhadra · 8 marks
Discharge from depth and mean velocity data
Short answer
Mid-section method with strip widths determined from adjacent distances. Multiplying each strip width by depth and given mean velocity, then summing gives total discharge ≈ 232 m³/s.
At known distances from an initial point on the stream bank, the measured depth and velocity of a river are shown in table. Calculate the corresponding discharge at this location.
| Distance from initial point (m) | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 99 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Depth (m) | 0 | 1.0 | 1.5 | 2.0 | 2.5 | 3.0 | 3.5 | 3.0 | 2.0 | 1.5 | 0 |
| Mean velocity (m/s) | 0 | 0.6 | 0.8 | 1.0 | 1.2 | 1.4 | 1.6 | 1.3 | 1.0 | 0.5 | 0 |
Mean velocities are given directly, so the mid-section method is applied: each vertical represents a strip from halfway to the previous vertical to halfway to the next, , and .
Computation
| x (m) | Width (m) | Depth (m) | V (m/s) | Area (m²) | ΔQ (m³/s) |
|---|---|---|---|---|---|
| 10 | 10 | 1.0 | 0.6 | 10.00 | 6.000 |
| 20 | 10 | 1.5 | 0.8 | 15.00 | 12.000 |
| 30 | 10 | 2.0 | 1.0 | 20.00 | 20.000 |
| 40 | 10 | 2.5 | 1.2 | 25.00 | 30.000 |
| 50 | 10 | 3.0 | 1.4 | 30.00 | 42.000 |
| 60 | 10 | 3.5 | 1.6 | 35.00 | 56.000 |
| 70 | 10 | 3.0 | 1.3 | 30.00 | 39.000 |
| 80 | 10 | 2.0 | 1.0 | 20.00 | 20.000 |
| 90 | (99 − 80)/2 = 9.5 | 1.5 | 0.5 | 14.25 | 7.125 |
| Total | 199.25 | 232.125 |
Answer: Discharge ≈ 232 m³/s.
(By the mean-section method, averaging depth and velocity of adjacent verticals for each 10 m panel, m³/s; the mid-section result is normally reported.)
✓ Answer checked by Claude Opus 5.5 (high effort)
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