Glacis fall: crest, cistern, HGL; Q 118

A glacis fall passes the flow over a raised crest, down a sloping glacis, and into a cistern in which a hydraulic jump forms. The canal is flumed (contracted) at the crest to reduce the cost and to increase the discharge intensity, so that the jump is more stable. Here the canal width is 62 m and the fluming ratio is 75 %.

Data

$Q = 118$ m³/s, FSL u/s $209.70$ m and d/s $208.20$ m, bed u/s $207.50$ m and d/s $206.00$ m, so $D_u = D_d = 2.2$ m, bed width 62 m, fluming ratio 75 %, safe exit gradient 1/6.

1. Crest elements

• Fluming: throat width $L = 0.75\times62 = 46.5$ m.
• Approach velocity: $v = \dfrac{118}{62\times2.2} = 0.865$ m/s, $h_a = 0.0381$ m.
• Head over a broad crest: $Q = 1.705\,L\,H^{3/2}$

$$H = \left(\frac{118}{1.705\times46.5}\right)^{2/3} = 1.304\ \text{m}$$

• Crest level $= FSL_u + h_a - H = 209.70 + 0.038 - 1.304 = 208.43$ m, which is 0.93 m above the u/s bed.
• Crest width: about $2H$ to $3H$ for a broad crest; adopt 3.0 m. U/s approach slope 1:1 (ramp), glacis slope 3:1 from the crest to the cistern.

2. Cistern elements

Discharge per metre of flumed crest $q = 118/46.5 = 2.538$ m²/s. Energy above the d/s bed $E_1 = 209.70 + 0.038 - 206.00 = 3.738$ m. The conjugate depth without depression is 1.911 m, which is less than the tail water 2.20 m, so the jump is submerged and a nominal depression is adopted:

• Cistern depth $X = 0.25$ m; cistern floor level $= 206.00 - 0.25 = 205.75$ m.
• $y_1 = 0.298$ m, $F_1 = 4.97$, $y_2 = 1.954$ m.
• Cistern length $L_c = 5(y_2 - y_1) = 8.28$ m.
• Fall height from crest to cistern floor $= 208.43 - 205.75 = 2.68$ m, so the horizontal length of the 3:1 glacis $= 3\times2.68 = 8.05$ m.

3. Floor length and HGL

Maximum static head $H_s = 209.70 - 206.00 = 3.70$ m. Lacey's scour (f = 1): $R = 1.35(q^2/f)^{1/3} = 2.51$ m, so the d/s cut-off need only reach 204.43 m; adopt $d = 2.5$ m (practical minimum) below the floor.

$$\frac{1}{\pi\sqrt{\lambda}} = \frac{1}{6}\frac{d}{H_s} = 0.1126 \Rightarrow \lambda = 7.99,\ \alpha = 14.95,\ b = 37.4\ \text{m}$$

Provide a total impervious floor of 38 m.

HGL (Khosla) at the d/s pile: $\phi_E = 23.0\,\%$ and $\phi_D = 16.1\,\%$ of $H_s$. Pressure head levels:

The HGL is a straight line from 209.70 m at the u/s end to 206.85 m at the d/s pile, then falls to the exit.

 209.7 ~~~~~~~~~~
        \__ crest 208.43
 207.5 ___\___ glacis 3:1
              \_cistern_______ 206.0
          HGL: 209.7 ------------> 206.85
                                 |  d/s pile

Answer: crest level 208.43 m, crest width 3.0 m, flumed length 46.5 m; cistern depth 0.25 m, length 8.28 m; floor length 38 m.