Question

A rectangular channel of width 12 m carries 18 cumecs of water at a depth of 0.5 m. The change in water surface elevation at the transition where bed width is increased to 15 m is____ .(Answer in metres, rounded off to two decimal places)

• A. -0.17

Answer 1

The correct option is A -0.17
Given, B=12 m, y=0.5m, Q=18cumecs, $B^{{}^{\prime }}$=15m
Specific energy at section 1-1, $E_1=y+\frac{V^2}{2g}$
=$0.5+(\frac{18}{12\times 0.5}{)}^2.\frac{1}{2\times 9.81}$
=0.959 m
Let the water depth at section 2-2 be $y^{{}^{\prime }}$
$E_2=E_1$
$y^{{}^{\prime }}+\frac{V^2}{2g}=0.959$
$y^{{}^{\prime }}+(\frac{18}{15y^{{}^{\prime }}}{)}^2.\frac{1}{9.81\times 2}=0.959$
$y^{{}^{\prime }}+\frac{0.0732}{y^{{}^{\prime }2}}=0.959$
$y^{\prime 3}-0.959y^{\prime 2}+0.0734=0$
$y^{{}^{\prime }}=0.346m$
Change in water surface elevation=$y^{{}^{\prime }}-y$
=0.346-0.5=-0.154m