Subject: Applied Hydraulics-II

Topic: Flow Through Open Channel(Uniform Flow)

Difficulty: Medium

Solution :

Given :

Chezy's constant, $\quad C=60$

Bed slope, $\quad i=\frac{1}{2000}$

From Figure

Area, $A=$ Area $A B C D$ + Area $B E C$

$\begin {aligned} \quad &=(1.2 \times 3.0)+\frac{\pi R^{2}}{2}\\ &=3.6+\frac{(1.5)^{2}}{2}\\ &=7.134 \mathrm{~m}^{2} \end {aligned}$

Wetted perimeter, (P)

$\begin{aligned} P &=A B+B E C+C D\\ &=1.2+\pi R+1.2\\ &=1.2+\pi \times 1.5+1.2\\ &=7.11 \mathrm {~m} \end {aligned}$

Hydraulic mean depth, (m)

$m=\frac{A}{P}=\frac{7.134}{7.1124}=1.003$

Discharge, (Q) is given by,

$ \begin{aligned} Q =A C \sqrt{m i} \end{aligned} $

$ \begin{aligned} \quad=7.134 \times 60 \times \sqrt{1.003 \times \frac{1}{2000}} \end{aligned} $

$ \begin{aligned} \quad=9.59 \mathrm {~m}^3/\mathrm {~s} \end{aligned} $