Question

A weir across an alluvial river has a horizontal floor of length 60 m and retains 6.5 m of water under full reservoir condition. If the downstream sheet pile is driven to a depth of 6.5 m below the average bed level, the exit gradient would be ____ $\times {10}^{-2}$.

• A. 14

Answer 1

The correct option is A 14
$\text{Exit gradient}=\frac{H}{d}.\frac{1}{\pi \sqrt{\lambda }}$

$\lambda =\frac{1+\sqrt{1+{\alpha }^2}}{2}$

where,
$\alpha =\frac{b}{d}=\frac{60}{6.5}=9.23$

$\therefore \lambda =\frac{1+\sqrt{(9.23{)}^2}}{2}=5.14$

$\therefore G_E=\frac{6.5}{6.5}.\frac{1}{\pi \sqrt{5.14}}=0.14=14\times {10}^{-2}$