Question

A rectangular channel has 6m width and 0.8 m depth of flow. The channel carries discharge of 2.4 cumecs. The maximum height of hump (in m, rounded off to two decimal places) allowed at downstream section so that upstream depth will not change _______.

• A. 0.4323

Answer 1

The correct option is A 0.4323
B = 6m, y = 0.8m, Q = 2.4 cumecs

Specific energy at upstream,

$E_1=y_1+\frac{v_1^2}{2g}$

$=0.8+{\left(\frac{2.4}{6\times 1.8}\right)}^2.\frac{1}{2\times 9.81}$

$=0.8127m$

Let the maximum height of hump be $Z_c$

$Z_c=E_1-E_c$

$E_c=\frac{3}{2}{y}_c=\frac{3}{2}{\left(\frac{q^2}{g}\right)}^{1/3}$

$=\frac{3}{2}{[{\left(\frac{2.4}{6}\right)}^2.\frac{1}{9.81}]}^{1/3}$

$=0.3804m$

$\therefore Z_c=(0.8127-0.3804)m$

$=0.4323m$