Culvert Hydraulics on a Seasonal Stream Near Jhalawar
A new rural road must cross a seasonal stream near Jhalawar. The catchment is 1.2 km², with a 25-year, three-hour rainfall of 120 mm and a runoff coefficient of 0.45. The proposed structure is a two-cell box culvert, each cell 1.5 m wide and 1.5 m high, laid on a 1% slope. The design uses Manning’s n = 0.015 and allows a freeboard of 0.30 m. The road profile leaves only 0.45 m between the culvert soffit and the road crest. The area is known for high silt loads, and the stream carries crop residue after harvest. The executive engineer must check whether the culvert can pass the design flood, whether the freeboard is adequate, and whether a cheaper single-cell option would be safer. A nearby road was washed out two years ago when a culvert of similar size blocked with debris.
1. Estimate the peak design discharge using the rational method and state the intensity used.
Read the worked answer
Rainfall intensity = 120 mm ÷ 3 h = 40 mm/h.
Rational method in SI units: Q = 0.278 × C × I × A, with A in km² and I in mm/h. Q = 0.278 × 0.45 × 40 × 1.2 = 6.0 m³/s.
This is the 25-year design peak. The result is an estimate; the engineer should confirm the rainfall depth, catchment boundary, and runoff coefficient from local records. A culvert on a road with higher consequence should also be checked for a larger return period, but 6.0 m³/s is the design value for this check.
2. Check the full-flow capacity of the proposed two-cell culvert and comment on whether it can pass 6.0 m³/s.
Read the worked answer
For one cell: area A = 1.5 × 1.5 = 2.25 m²; wetted perimeter P = 2(1.5 + 1.5) = 6.0 m; hydraulic radius R = 2.25/6.0 = 0.375 m.
R^(2/3) = 0.375^(2/3) ≈ 0.520; S^(1/2) = 0.01^(1/2) = 0.10. V = (1/n) R^(2/3) S^(1/2) = (1/0.015) × 0.520 × 0.10 ≈ 3.47 m/s. Q per cell = 2.25 × 3.47 ≈ 7.8 m³/s; two cells ≈ 15.6 m³/s at full flow.
The design peak of 6.0 m³/s is only about 3.0 m³/s per cell, well below full capacity. Hydraulically, the two-cell culvert is adequate. The critical issue is blockage and headwater, not raw barrel capacity. With one cell blocked, the remaining cell can still pass about 7.8 m³/s, so redundancy is good.
3. Assess freeboard and debris risk, and recommend between the two-cell design and a cheaper single-cell option.
Read the worked answer
At 6.0 m³/s, each cell carries about 3.0 m³/s, roughly 38% of full-flow capacity. Using approximate rectangular-channel proportionality, depth is about 0.38^(3/5) ≈ 0.56 of full depth, or roughly 0.84 m. The road crest is 1.5 + 0.45 = 1.95 m above the invert, so the water surface has ample freeboard; 0.45 m above the soffit is more than the specified 0.30 m even before allowing for inlet head. Freeboard is not the governing problem.
Debris is. A single 3.0 m × 1.5 m cell would also pass the flow, but one blockage could stop most of the opening. The two-cell design gives redundancy: if one cell clogs, the other still has capacity above 6.0 m³/s. Recommend the two-cell culvert, with a maintained upstream debris trap or cleared approach, regular post-monsoon inspection, and a recorded maintenance plan. Do not rely on a trash rack alone, because racks can clog and increase afflux.