Question

Two triangular channels carry discharge of 2 cumecs and 3 cumecs respectively.The apex angles for the channel are ${60}^{\circ }$and ${90}^{\circ }$respectively.The ratio of critical depth of flow is

• A. 2

Answer 1

The correct option is A 2
$Q_1=2cumecs,Q_2=3cumecs$

${\theta }_1={60}^{\circ },{\theta }_2={90}^{\circ }$

For triangular channel,
$y_c={\left(\frac{2Q^2}{g{m}^2}\right)}^{\frac{1}{5}}$

$Where,m=tan\left(\frac{\theta }{2}\right)$

$\therefore \frac{(y_c{)}_1}{(y_c{)}_2}={\left(\frac{Q_1}{Q_2}\right)}^{\frac{2}{5}}\times {\left(\frac{m_2}{m_1}\right)}^{\frac{2}{5}}$

$={\left(\frac{2}{3}\right)}^{\frac{2}{5}}\times {\left(\frac{\tan {45}^{\circ }}{\tan {30}^{\circ }}\right)}^{\frac{2}{5}}=1.06$