Question 9.5: Design a suitable outlet to discharge 501 s^-1 from a canal ......
Design a suitable outlet to discharge 501 {s}^{-1} from a canal with a full supply depth of 1 m. The working head available is 150 mm.
1: open flume outlet
For non-submergence of the flume, i.e. modular flow conditions, the minimum working head is approximately 0.2 times the head over the crest. Therefore the maximum head over the crest, H =0.15/0.2 = 0.75 m. Hence the throat width, b (from the weir formula) \simeq 0.05 m. Therefore, adopt the minimum value of b = 0.06 m; this gives the head, H = 0.65 m, and hence the minimum working head, h = 0.2 × 0.65 = 0.13 m, which is satisfactory, as the available head is 0.15 m. This sets H/D = 0.65/1.0= 0.65, and the flexibility, F = 0.9/0.65 > 1. The design may be acceptable but may not draw its fair share of silt from the supply canal because of the excessive sill height of 0.35 m (depth of flow-head over sill).
2: pipe and open flume outlet
An open flume type outlet is expensive, particularly if the supply canal bank is very wide, and in such cases the pipe semimodule is used. The outlet is also suitable for drawing its share of silt, with its lead pipe set at or near the bed level (Fig. 9.32). The pipe delivers the water into a tank on the downstream side, to which an open flume or an orifice semimodule is fitted.
Q={501}\,{ s}^{-1}; \quad {D}=1.0{\, m};\quad h=0.15\,\mathrm{m}.Assume a bank width of 10m and adopt a concrete pipe with a k value of 0.1 mm. The head loss through the pipe, h_{1}=(1.5+\lambda L/d)V^{2}/2g. Assuming a pipe diameter, d = 300 mm, V = 0.707 m{s}^{-1} and V²/2g = 0.0255 m. Therefore the Reynolds number, Re = 2 × 10^{5} ; k/d = 3.3 × 10^{-4} , and so λ = 0.0175 from the Moody chart. Hence the head loss = 0.0531 m, giving the available working head for the semimodule as 0.15 – 0.0531 = 0.0969 m. Therefore the maximum head over the crest, H = 0.0969/0.2 = 0.484 m. The throat width, b (from weir formula) = 0.093 m. Therefore provide a throat width of 10 cm, which gives H = 0.46 m and thus h_{\mathrm{minimum}} = 0.092 m, which is satisfactory as the available head is 0.0969 m. The layout of the proposed design of the pipe and open flume outlet is shown in Fig. 9.32(a). Two other alternative proposals which are in use are shown in Figs 9.32(b) and (c).
