Solution :

Given :

$Q=50$ cumec

Lacey's silt factor $F=1.1$

Design steps by Lacey's theory :

1) Calculate velocity of flow,

$\begin{aligned} \qquad{V} &=\left(\frac{Q F^{2}}{140}\right)^{(1/6)}\\ &=\left(\frac{50\times 1.1^{2}}{140}\right)^{(1/6)}\\ &=0.8695 m/s \end{aligned}$

Where,

$F=$ silt factor

2) Calculation of area of cross-section of canal,

$\begin{aligned}\qquad A &= \frac{Q}{V} =\frac{50}{0.8695}\\ &=57.50 m^2 \end{aligned}$ …