Question

For a Lacey channel to carry $5m^3/sec$ through a $0.5mm$ sand, the bed slope will be $1:k$. The value of $k$ is ____

• A. 3052

Answer 1

The correct option is A 3052
As per Lacey's theory,

Bed slope,
$S=\frac{f^{5/3}}{3340Q^{1/6}}$

Given,
$Q=5m^3/sec$

Also,
$f=1.76\sqrt{d_{mm}}$

$=1.76\times \sqrt{0.5}=1.24$

Hence,
$S=\frac{(1.24{)}^{5/3}}{3340\times (5{)}^{1/6}}$

$=\frac{1}{3051.68}\simeq \frac{1}{3052}$

$k=3052$