Find the critical depth and critical velocity of the water flowing through a rectangular channel of width 5m, when discharge is $15 m^3/s$

Given:

width of channel, b = 5m

Discharge Q = $15 m^3/s$

$\therefore$ Discharge per unit width,

$q = \frac{Q}{b}$

$= \frac{15}{5}$

= 3$m^2/s$

Critical depth : (hc)

$hc = (\frac{q^2}{g})^1/3$

$= (\frac{3^2}{9.81}^1/3$

$= (\frac{9}{9.81})^1/3$

= 0.972m

Critical velocity : (Vc)

$Vc = \sqrt{g \times hc}$

$= \sqrt{9.81 \times 0.972}$

Vc = 3.088 m/s