Unlined Distributary: Verifying the Regime Section, Diagnosing Siltation and Judging a Lining Proposal
An 18 km unlined distributary takes off from a main canal with a design head discharge of 15 m³/s to command 12,000 ha. It was designed on Lacey's regime equations with silt factor f = 1.0 and side slopes 0.5H:1V, and built to the approved bed width and depth. After three years of operation the head reach has silted about 0.6 m, the tail reach is scoured, the tail escape is not maintained, and discharge measured at the tail is 11 m³/s although all outlets are recorded as closed. A ponding test indicates a seepage loss of about 8% of the head discharge. The irrigation department proposes lining the full 18 km with 75 mm cement concrete to save the seepage, at a capital cost about 1.4 times the annual O&M budget. A consultant is asked to verify the design section, explain the behaviour, and advise on the lining.
1. Reproduce the Lacey regime section for Q = 15 m³/s, f = 1.0, and check the bed width against Lacey's perimeter relation.
Read the worked answer
Velocity: V = (Q f²/140)^(1/6) = (15 × 1/140)^(1/6) = (0.1071)^(1/6) = 0.69 m/s
Area: A = Q/V = 15/0.69 = 21.8 m²
Hydraulic radius: R = 2.5 V²/f = 2.5 × 0.476 = 1.19 m
Perimeter: P = A/R = 21.8/1.19 = 18.4 m
Check against Lacey: P = 4.75√Q = 4.75 × 3.873 = 18.4 m - consistent, so the section is a true regime section at design discharge.
Section geometry (trapezoid, side slope 0.5H:1V, so A = By + 0.5y², P = B + 2.236y):
- From P: B = 18.4 − 2.236y
- Substitute in A: 18.4y − 1.736y² = 21.8 → y = 1.36 m, B = 15.4 m
B/y ≈ 11.3, which is a wide, shallow, stable regime channel.
Slope and cross-check: Lacey slope S = f^(5/3)/(3340 Q^(1/6)) = 1/(3340 × 1.570) = 1 in 5,245. Manning with n = 0.0225 gives V = (1/0.0225) × 1.19^(2/3) × (1.907 × 10⁻⁴)^0.5 = 0.69 m/s, exactly matching the Lacey velocity - confirming the section is self-consistent and that the design is not the cause of the observed behaviour.
2. Explain the head-reach siltation and tail-reach scour. Is the section out of regime, or is the operation at fault?
Read the worked answer
Because the built section is a correct regime section at 15 m³/s, the anomalies cannot be blamed on the geometry as designed; they indicate the channel is not running at regime.
Head reach siltation: if the actual discharge in the head reach is below 15 m³/s, velocity falls below 0.69 m/s and the incoming sediment load from the main canal can no longer be transported - deposition follows. Rotation-supply operation, throttled head gates at low demand, and reduced outlet draws all do this. A 0.6 m rise on a 1.36 m depth is severe and will progressively reduce capacity.
Tail discharge of 11 m³/s against 15 m³/s: 4 m³/s (27%) is unaccounted, against a ponding-test seepage figure of only 8%. The ponding test usually underestimates real loss: it misses crack and rodent-hole leakage, the wetted perimeter in the field is larger, and it cannot see unauthorised pumping or cuttings. So expect unauthorised offtakes and leakage through outlet structures rather than uniform seepage.
Tail scour: the tail escape being out of service removes the bleed that keeps the tail reach from carrying the full fluctuating discharge; sudden gate openings send a surge through the lower reach, which is likely steeper than the regime slope (1 in 5,245). Verify with a longitudinal level survey and a sediment sample: if the actual silt is finer than f = 1.0 (say f = 0.7), the true regime velocity is only 0.61 m/s and the as-built 0.69 m/s will scour. Diagnosis must rest on measured bed levels, actual reach discharges and sediment grading, not on the assumption that the design is wrong.
3. Should the 18 km lining be approved? State the engineering checks and the alternatives you would impose.
Read the worked answer
Seepage at 8% of 15 m³/s = 1.2 m³/s. With the implied duty of 12,000 ha per 15 m³/s (800 ha per m³/s), that saved water is worth roughly 960 ha of additional irrigation - real, but the proposal must be tested before it is accepted.
Checks required:
- Replace the ponding estimate with a measured inflow–outflow balance over the full reach.
- Re-run the hydraulics with n = 0.015. At the same depth and slope: V = (1/0.015) × 1.19^(2/3) × 0.01381 = 1.03 m/s against 0.69 m/s, i.e. the lined channel would pass about 22 m³/s at the same depth. That is safe for concrete (permissible 2–3 m/s) but means the head regulator, outlet modules and the tail escape must be re-calibrated, and the reduced depth will increase freeboard - check it, do not assume it.
- Provide a drainage layer and weep holes behind the lining; uplift and slip of a 75 mm lining on a 0.5H:1V slope is the standard failure mode.
- Check the lining does not create a new scour problem at the transition back to the unlined tail.
Verdict: conditional, not blanket, approval. Line only the reaches proven permeable, restore the tail escape, and first fix the outlet control and unauthorised offtakes - because lining will not stop the head-reach siltation, which is an operational and sediment problem, not a seepage problem.