Question

Rectangular channel carries a discharge of 8 cumecs at a depth of 0.9m. the width of channel is 12 m, the alternate depth of flow is _____ m.

• A. 0.173

Answer 1

The correct option is A 0.173
The two depths for a given specific energy at a constant discharge are called alternate depths of flow

$y_1+\frac{V_1^2}{2g}=y_2+\frac{V_2^2}{2g}$

$y_1+\frac{Q^2}{2g{B}^2{y}_1^2}=y_2+\frac{Q^2}{2g{B}^2{y}_2^2}$

Given, $y_1=0.9m,Q=8cumecs,B=12m$

$0.9+\frac{8^2}{2\times 9.81\times (12{)}^2\times (0.9{)}^2}=y_2+\frac{8^2}{2\times 9.81\times (12{)}^2{y}_2^2}$

$0.928=y_2+\frac{0.02265}{y_2^2}$

$y_2^3-0.928y_2^2+0.02265=0$

$y_2=0.9m,-0.145m,0.173m$

$\therefore$ alternate depth of flow = 0.173 m