Question

For a rectangular channel section, Match List - I (Geometrical elements) with List-II (Proportions for hydraulically efficient section) and select the correct answer using the codes given below the lists:

List - I	List - II
A. Top width	1. $y_e/2$
B. Perimeter	2. $y_e$
C. Hydraulic Radius	3. $2y_e$
D. Hydraulic Depth	4. $4y_e$

$y_e$ is the flow depth corresponding to hydraulically efficient section.

• A. A - 3, B - 4, C - 2, D - 1
• B. A - 3, B - 1, C - 4, D - 2
• C. A - 3, B - 4, C - 1, D - 2
• D. A - 2, B - 4, C - 1, D - 3

Answer 1

The correct option is C A - 3, B - 4, C - 1, D - 2

Let the width of rectangular channel be B and depth of flow be y.
Area of flow, A = By
Wetted perimeter,
$P=B+2y=\frac{A}{y}+2y$
For hydraulically most efficient section, P should be minimum.
$\therefore \frac{dP}{dy}=0$
$\Rightarrow \frac{-A}{y^2}+2=0$
$\Rightarrow A_e=2y_e^2$
$\Rightarrow B_e{y}_e=2y_e^2$
$\Rightarrow B_e=2y_e$
Hydraulic radius,
$A=\frac{A}{P}=\frac{2y_e^2}{2y_e+2y_e}=\frac{y_e}{2}$
Top width,
$T=B=2y_e$
Perimeter,
$P=B+2y_e=2y_e+2y_e=4y_e$
Hydraulic depth,
$D=\frac{A}{T}=\frac{2y_e^2}{2y_e}=y_e$