Cross drainage: canal 125, drainage 64

The drainage bed (300.00 m) is above the canal FSL (298.00 m) by 2.0 m, and the canal is much larger than the drainage (125 vs 64 m³/s). So the drainage is carried over the canal in an RCC trough: a super passage. The canal flows beneath as an open channel with a free surface.

Assumptions: RCC trough and canal waterway with $n$ = 0.015; spans 8 m with 1.2 m piers; slab 0.6 m; losses of $0.3\,\Delta h_v$ at the inlet and $0.5\,\Delta h_v$ at the outlet; downstream drainage section: bed 300.00 m, HFL 304.00 m, width 80 m.

1. Canal waterway

Normal canal: $A=(40+1\times4)\times4$ = 176 m², $V$ = 125/176 = 0.710 m/s.

Through the structure the canal is fitted with a rectangular lined section of width 32 m (depth 4 m): $A$ = 128 m², $V$ = 125/128 = 0.98 m/s (< 2 m/s), Froude number 0.16 (subcritical). Provide 4 spans of 8 m with 3 piers of 1.2 m: clear canal waterway = 32 m, overall = 32 + 3 × 1.2 = 35.6 m. This is also the length of the drainage trough.

Clearance: soffit of trough slab = 300.00 − 0.6 = 299.40 m, which is 1.40 m above canal FSL (298.00 m). Adequate (> 0.6 m free board).

2. Drainage waterway (flumed trough)

Lacey's perimeter $P=4.75\sqrt{64}$ = 38.0 m. The natural channel is 80 m wide with $V$ = 64/(80 × 4) = 0.20 m/s, so it is flumed to a rectangular RCC trough of width $B_t$ = 16 m, which keeps the velocity near 1 m/s.

The depth at the downstream end of the trough ($d_3$) follows from Bernoulli's equation with the expansion loss, taking the trough bed at the downstream bed level 300.00 m:

$$\begin{aligned} d_3 + h_{v3} &= (304.00-300.00) + h_{v4} + 0.5(h_{v3}-h_{v4}) \\ d_3 &= 4.00 + 0.5\,(h_{v4} - h_{v3}) \end{aligned}$$

By trial: $d_3$ = 3.975 m, $V_3$ = 64/(16 × 3.975) = 1.006 m/s, $h_{v3}$ = 0.0516 m. Water level at the end of trough = 303.975 m.

Friction in the trough: $R$ = 2.656 m, $S=(nV/R^{2/3})^2$ = 0.000062, $h_f$ = S × 35.6 = 0.0022 m.

3. Levels at the upstream end

• Water level at the start of trough = 303.975 + 0.0022 = 303.977 m
• Keeping the same depth 3.975 m in the trough, the trough bed at the upstream end = 300.002 m, practically 300.00 m (2 mm above the downstream end).
• Water level in the drainage just upstream of the inlet transition = 303.977 + 0.0516 + 0.3(0.0516 − 0.0020) − 0.0020 = 304.042 m, an afflux of about 0.04 m. Taking the normal 80 m drainage section (depth 4.00 m) upstream, the drainage bed just upstream of the inlet transition = 304.04 − 4.00 = 300.04 m.
• Transitions: inlet (2:1) = 80 − 16 = 64 m; outlet (3:1) = 1.5 × 64 = 96 m (splay measured on the water-surface width), with the drainage bed continuing at 300.00 m.

  HFL 304 ~~~~~~~\__________________/~~~~~~~
  drain bed 300 ---|== RCC trough ==|---
  clearance 1.4 m  | 4 x 8 m spans  |
  canal FSL 298 ---+~~~~~~~~~~~~~~~~+---
  canal bed 294 ---+----------------+---

Answer: canal waterway 32 m clear (4 × 8 m spans, overall 35.6 m); drainage flumed to a 16 m wide RCC trough (3.98 m deep); trough bed at the upstream end of the structure = 300.00 m (water level 303.98 m at the trough start); drainage bed upstream of the inlet transition = 300.04 m (water level 304.04 m).