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A short reach of a 2 m wide rectangular open channel has its bed level rising in the direction of flow at a slope of 1 in 10000. It carries a discharge of 4 m³/s and its Manning’s roughness coefficient is 0.01. The flow in this reach is gradually varying. At a certain section in this reach, the depth of flow was measured as 0.5 m. The rate of change of the water depth with distance, dy/dx, at this section is ___(use g = 10 m/s²)
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- 0.0032
- 1.0032
- 2.0023
- 1.0254
Correct Option: A
0.0032
| S0 = | ||
| 10000 |
θ = 4 m³/s, n = 0.01, y = 0.5m
Rate of change of water depth, dy/dx
| Q = | AR2/3Sƒ1/2 | |
| n |
| 4 = | × (2 × 0.5) × |  |  | 2/3 | × Sƒ1/2 | ||
| 0.01 | 2 + 1 |
∴ Sf = 6.92 × 10–3
| Fr = | = | ||
| √gy | A √gy |
| = | = 1.79 | |
| (2 × 0.5) × √10 × 5 |
| ∴ | = | |||
| dx | 1 - (1.79)² |
= 3.2 × 10-3 = 0.0032
