Canal head regulator design, Q 200

Data and assumptions

• Discharge $Q = 200$ m³/s; pond level $= 304$ m; full supply level of canal $= 303$ m; canal bed $= 299.5$ m; u/s HFL $= 307$ m; Lacey's $f = 1$; safe exit gradient $G_E = 1/6$.
• Crest of the head regulator is kept 1.2 m above the crest of the under-sluice (300.00 m): $300.00 + 1.2 = 301.20$ m, so bed load is excluded.
• The regulator is designed as a broad-crested weir for the free-flow condition, $Q = 1.705\,L\,H^{3/2}$.

1. Crest level

$$\text{Crest level} = 301.20\ \text{m}$$

Head over the crest at pond level: $H = 304 - 301.20 = 2.80$ m. Depth of canal water over the crest: $FSL - \text{crest} = 1.80$ m, which is less than $\tfrac{2}{3}H$, so the weir is not drowned and the free-flow formula applies.

2. Waterway

$$L = \frac{Q}{1.705\,H^{3/2}} = \frac{200}{1.705\times2.80^{3/2}} = 25.04\ \text{m}$$

Provide 5 bays of 5.0 m clear width (25 m) with 4 piers 1.5 m thick; overall width $= 31.0$ m. Check: $Q = 1.705\times25\times2.80^{3/2} = 199.7$ m³/s, which is accepted as $\approx 200$ m³/s.

3. Impervious floor (Khosla's exit gradient)

Discharge intensity $q = Q/\text{width} = 200/31.0 = 6.45$ m²/s. Lacey's scour depth:

$$R = 1.35\left(\frac{q^2}{f}\right)^{1/3} = 1.35\left(\frac{6.45^2}{1}\right)^{1/3} = 4.68\ \text{m}$$

The d/s cut-off is taken down to $1.5R$ below the d/s water level: bottom level $= 303 - 1.5\times4.68 = 295.98$ m, so the d/s cut-off depth below the floor (canal bed) is $d = 299.5 - 295.98$, adopt $d = 3.6$ m. U/s cut-off $d_1 = 2.5$ m. Maximum static head (canal dry, water at pond level): $H_s = 304 - 299.5 = 4.5$ m. The gates are closed in floods; the HFL (307 m) fixes the top of the piers and gates. Exit gradient:

$$G_E = \frac{H_s}{d}\,\frac{1}{\pi\sqrt{\lambda}} = \frac{1}{6} \Rightarrow \frac{1}{\pi\sqrt{\lambda}} = \frac{3.6}{6\times4.5} = 0.1333$$ $$\lambda = 5.70 \Rightarrow \alpha = \frac{b}{d} = 10.35 \Rightarrow b = 10.35\times3.6 = 37.3\ \text{m}$$

(Using $\lambda = \frac{1+\sqrt{1+\alpha^2}}{2}$.) Check: $G_E = 0.1667 = 1/6.00$. Provide a floor of 38 m: about 1/3 on the u/s side and 2/3 downstream, thickness 1.5 m under the gates tapering to 0.8 m.

4. Other features

• Top of piers and gate: HFL + 1.0 m free-board. Vertical lift steel gates with a hoist deck.
• D/s of the floor: inverted filter and loose stone apron (length about $2D$), and wing walls splayed 45°.
• The silt excluder in the under-sluice keeps bed load away, so the regulator crest only needs to be 1.2 m above the under-sluice crest.

Summary

Conceptual sketch (longitudinal section):

 HFL / pond ~~~~~~~~~~|gates|~~~~~~ canal FSL ~~~~~
 river        ________|piers|________
 bed ________|  crest  (1.2 m above   |_____ canal bed
     |d1 u/s floor     U/S sluice crest) d/s floor | d2
       (impervious)                     inverted filter
       <------------ b (Khosla, GE = 1/6) --------->