Siphon design: canal 18, drainage 60

The drainage bed (101.50 m) is above the canal bed (100.00 m) and the drainage HFL (103.50 m) is above the canal FSL (103.00 m), so the drainage cannot be passed under the canal. The canal is carried under the drainage through closed barrels flowing full under pressure: a canal siphon (the drainage flows over the barrels as an open channel).

Assumptions: two rectangular RCC barrels; roof slab 0.5 m with its top flush with the drainage bed (101.50 m); entry loss 0.5 $V^2/2g$ and exit loss $0.5(V_b-V_1)^2/2g$; barrel length = width of drainage crossing; permissible velocity in barrels 2–3 m/s.

1. Drainage waterway

$$P = 4.75\sqrt{60} = 36.8\ \text{m}$$

Provide a pitched drainage crossing of bottom width 37 m (> 36.8 m) over the barrels. Depth at HFL = 103.50 − 101.50 = 2.0 m, velocity = 60/(37 × 2.0) = 0.81 m/s, so a pitched floor with end aprons and cut-offs is enough. The length of the barrels is therefore about 38 m (crossing width plus flanking walls).

2. Canal waterway (barrels)

Normal canal: $A_1=(6+1.5\times3)\times3$ = 31.5 m², $V_1$ = 18/31.5 = 0.571 m/s, $h_{v1}$ = 0.0166 m, top width $T$ = 15 m.

Adopting $V_b$ = 2.5 m/s, required area = 18/2.5 = 7.2 m². Provide 2 barrels, each 2 m wide × 1.8 m high, separated by a 0.6 m pier: area = 2 × 2 × 1.8 = 7.2 m², $V_b$ = 18/7.2 = 2.50 m/s, $h_v$ = 0.3186 m. Overall width = 2×2 + 0.6 + 2×0.6 = 5.8 m.

3. Bed levels and transitions

• Top of roof = 101.50 m; soffit = 101.50 − 0.5 = 101.00 m; barrel floor = 101.00 − 1.8 = 99.20 m (canal bed depressed by 0.80 m, with a slope of 1 in 4 at the inlet and outlet).
• Transitions in plan: inlet (2:1) = T − barrel width = 15 − 5.8 = 9.2 m; outlet (3:1) = 1.5 × 9.2 = 13.8 m.

Losses of head (N = 0.016, $R$ = 0.474 m for one barrel):

$$\begin{aligned} h_{f} &= \frac{N^2V_b^2L}{R^{4/3}} = \frac{0.016^2 \times 2.50^2 \times 38}{0.474^{4/3}} = 0.165\ \text{m} \\ h_e &= 0.5\,\frac{V_b^2}{2g} = 0.159\ \text{m} \\ h_x &= 0.5\,\frac{(V_b-V_1)^2}{2g} = 0.095\ \text{m} \end{aligned}$$

Total loss = 0.159 + 0.165 + 0.095 = 0.419 m.

  HFL 103.50 ~~~~~~~~~~~~~~~~~~~~~~~~~
  drain bed 101.50 ============ roof (0.5 m)
  canal FSL 103.00 --.  barrels 2 x (2.0 x 1.8)  .-- 102.58
  canal bed 100.00 ---'__________________________'--- 99.58
                       floor 99.20

Answer: drainage crossing 37 m wide; 2 barrels of 2.0 m × 1.8 m (V = 2.50 m/s); barrel floor 99.20 m; total head loss 0.419 m; downstream canal FSL 102.581 m and bed 99.581 m.