Canal head regulator design, Q 150

Data and assumptions

• Discharge $Q = 150$ m³/s; pond level $= 254$ m; full supply level of canal $= 253$ m; canal bed $= 249.5$ m; u/s HFL $= 257$ m; Lacey's $f = 1$; safe exit gradient $G_E = 1/6$.
• The river bed is at 250.00 m; the crest is kept 1.2 m above the river bed (under-sluice crest level): $250.00 + 1.2 = 251.20$ m.
• The regulator is designed as a broad-crested weir for the free-flow condition, $Q = 1.705\,L\,H^{3/2}$.

1. Crest level

$$\text{Crest level} = 251.20\ \text{m}$$

Head over the crest at pond level: $H = 254 - 251.20 = 2.80$ m. Depth of canal water over the crest: $FSL - \text{crest} = 1.80$ m, which is less than $\tfrac{2}{3}H = 1.87$ m, so the weir is not drowned and the free-flow formula applies.

2. Waterway

$$L = \frac{Q}{1.705\,H^{3/2}} = \frac{150}{1.705\times2.80^{3/2}} = 18.78\ \text{m}$$

Provide 4 bays of 5.0 m clear width (20 m) with 3 piers 1.5 m thick; overall width $= 24.5$ m. Check: with the gates fully open, $Q = 1.705\times20\times2.80^{3/2} = 159.8$ m³/s $> 150$ m³/s, so the waterway is adequate and the gates are partly lowered to pass the design discharge.

3. Impervious floor (Khosla's exit gradient)

Discharge intensity $q = Q/\text{width} = 150/24.5 = 6.12$ m²/s. Lacey's scour depth:

$$R = 1.35\left(\frac{q^2}{f}\right)^{1/3} = 1.35\left(\frac{6.12^2}{1}\right)^{1/3} = 4.52\ \text{m}$$

The d/s cut-off is taken down to $1.5R$ below the d/s water level: bottom level $= 253 - 1.5\times4.52 = 246.22$ m, so the d/s cut-off depth below the floor (canal bed) is $d = 249.5 - 246.22 = 3.28$ m; adopt $d = 3.3$ m. U/s cut-off $d_1 = 2.5$ m. Maximum static head (canal dry, water at pond level): $H_s = 254 - 249.5 = 4.5$ m. The gates are closed during floods; the HFL (257 m) fixes the top of the piers and gates. Exit gradient:

$$G_E = \frac{H_s}{d}\,\frac{1}{\pi\sqrt{\lambda}} = \frac{1}{6} \Rightarrow \frac{1}{\pi\sqrt{\lambda}} = \frac{3.3}{6\times4.5} = 0.1222$$ $$\lambda = 6.78 \Rightarrow \alpha = \frac{b}{d} = 12.53 \Rightarrow b = 12.53\times3.3 = 41.3\ \text{m}$$

(Using $\lambda = \frac{1+\sqrt{1+\alpha^2}}{2}$.) Check: $G_E = 0.1667 = 1/6.00$. Provide a floor of 42 m: about 1/3 on the u/s side and 2/3 downstream, with thickness 1.5 m under the gates tapering to 0.8 m.

4. Other features

• Top of piers and gates: 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 at 45°.

Summary

Conceptual sketch (longitudinal section):

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