Question

Water surface profiles that are asymptotic at one end and terminated at the other end would include

• A. $M_{2}and{H}_2$
• B. $H_{3}and{S}_2$
• C. $M_{2}and{H}_2$
• D. $H_{2}and{S}_2$

Answer 1

The correct option is A

$M_{2}and{H}_2$

(c)
The curves which are asymptotic at one end and terminated at the other end are $M_{2}and{H}_2$

From $\frac{dy}{dx}=\frac{S_0-S_f}{1-\frac{Q^{2}T}{g{A}^3}}=S_0\frac{1-{\left(\frac{y_n}{y}\right)}^{10/3}}{1-{\left(\frac{y_c}{y}\right)}^3}$

Using Manning's equation for wide rectangular channel.

(i) $Asy\to y_0;\frac{dy}{dx}\to 0;$ i.e. the water surface approaches normal depth line asymptotically

(ii) $Asy\to y_c;\frac{dy}{dx}\to \infty ;$ i.e. the water surface meets the critical depth line vertically in region 2 and3

(iii) $Asy\to \infty ;\frac{dy}{dx}\to 0;$ i.e. the water surface meets a very large depth as horizontal asymptote in region 1.

(iv) $Asy\to 0;\frac{dy}{dx}\to \infty ;$ it means that the surface profile meets the channel bed vertically in region 3

Thus,
$M_1,M_2,S_{2}and{S}_3$meet $y_0$ line asymptotically

(ii) $M_{1}and{S}_1$ curve tend to horizontal as $y\to \infty$

(iii) $M_2,M_{3}and{S}_2$ meet $y_c$ line normally

(iv) $M_{3}and{S}_3$ meet channel bed normally.

The slope of:

$C_{1}and{C}_3$ curve comes out to be equal to critical slope of the bed, if Chezy's equation is used. Otherwise they are slightly curved.