GATE CE 2023 Set 2 — Question 63
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Water Resources Engineering → Flow Measurement → Flow Measurement in Channels
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Question
The cross-section of a small river is sub-divided into seven segments of width 1.5 m each. The average depth, and velocity at different depths were measured during a field campaign at the middle of each segment width. The discharge computed by the velocity area method for the given data is _________ (round off to one decimal place).
| Segment | Average depth (D) (m) | 0.2D | 0.6D | 0.8D |
|---|---|---|---|---|
| 1 | 0.40 | -- | 0.40 | -- |
| 2 | 0.70 | 0.76 | -- | 0.70 |
| 3 | 1.20 | 1.19 | -- | 1.13 |
| 4 | 1.40 | 1.25 | -- | 1.10 |
| 5 | 1.10 | 1.13 | -- | 1.09 |
| 6 | 0.80 | 0.69 | -- | 0.65 |
| 7 | 0.45 | -- | 0.42 | -- |
Correct answer
8.4 to 8.6
Solution
The discharge is calculated using the velocity-area method:
where m is the width of each segment.The average velocity for each segment is determined as follows:
Rounding to one decimal place, .
where m is the width of each segment.The average velocity for each segment is determined as follows:
- If velocities at and are given:
- If only velocity at is given:
1.Segment 1: m, m/s.
2.Segment 2: m, m/s.
3.Segment 3: m, m/s.
4.Segment 4: m, m/s.
5.Segment 5: m, m/s.
6.Segment 6: m, m/s.
7.Segment 7: m, m/s.
Total discharge .Rounding to one decimal place, .
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