Chapter 10, Problem 10.97P

To determine

i.

If the solution curve is mild, critical or steep slope when the local water depth is 1m.

Answer to Problem 10.97P

The required curve is mild slope M-1 curve.

Explanation of Solution

Given:

Q = 8 m³ /s

Slope = 0.1°

b = 4 m

Local depth = 1m

Concept Used:

$\begin{array}{l}Q=\frac{\alpha }{n}*A*R^{2/3}*Slop{e}^{1/2}\\ y_c={\left(\frac{q^2}{g}\right)}^{1/3}\end{array}$

Calculation:

$\begin{array}{l}Q=\frac{\alpha }{n}*A*R^{2/3}*Slop{e}^{1/2}\\ Forbrickworkn=0.015\\ A=y_n*b\\ where{y}_{n}isdepth\\ R_h=\frac{A}{P}=\frac{4y_n}{4+2y_n}\\ 8=\frac{1}{0.015}*4*y_n*{\left(\frac{4y_n}{4+2y_n}\right)}^{2/3}*{\left(\sin (0.1°)\right)}^{1/2}\\ y_n=0.960m\\ y_c={\left(\frac{q^2}{g}\right)}^{1/3}\\ y_c={\left(\frac{{\left(\raisebox{1ex}{$8$}\!\left/ \!\raisebox{-1ex}{$4$}\right.\right)}^2}{9.81}\right)}^{1/3}\\ y_c=0.742m\\ y_n>y_c\\ Theslopeismild\\ \mathrm{Sin}cethegivenlocaldepthisgreaterthan{y}_{n}and{y}_c.\end{array}$

Conclusion:

From gradually varied flow of channel flow curve, we get a mils slope curve which is M-1 curve.

To determine

ii.

If the solution curve is mild, critical or steep slope when the local water depth is 1.5 m.

Answer to Problem 10.97P

The required curve is mild slope M-1 curve.

Explanation of Solution

Given:

Q = 8 m³ /s

Slope = 0.1°

b = 4 m

Local depth = 1.5 m

Concept Used:

$\begin{array}{l}Q=\frac{\alpha }{n}*A*R^{2/3}*Slop{e}^{1/2}\\ y_c={\left(\frac{q^2}{g}\right)}^{1/3}\end{array}$

Calculation:

$\begin{array}{l}Q=\frac{\alpha }{n}*A*R^{2/3}*Slop{e}^{1/2}\\ Forbrickworkn=0.015\\ A=y_n*b\\ where{y}_{n}isdepth\\ R_h=\frac{A}{P}=\frac{4y_n}{4+2y_n}\\ 8=\frac{1}{0.015}*4*y_n*{\left(\frac{4y_n}{4+2y_n}\right)}^{2/3}*{\left(\sin (0.1°)\right)}^{1/2}\\ y_n=0.960m\\ y_c={\left(\frac{q^2}{g}\right)}^{1/3}\\ y_c={\left(\frac{{\left(\raisebox{1ex}{$8$}\!\left/ \!\raisebox{-1ex}{$4$}\right.\right)}^2}{9.81}\right)}^{1/3}\\ y_c=0.742m\\ y_n>y_c\\ Theslopeismild\\ \mathrm{Sin}cethegivenlocaldepthisgreaterthan{y}_{n}and{y}_c.\end{array}$

Conclusion:

From gradually varied flow of channel flow curve, we get a mils slope curve which is M-1 curve.

To determine

iii.

If the solution curve is mild, critical or steep slope when the local water depth is 2m.

Answer to Problem 10.97P

The required curve is mild slope M-1 curve.

Explanation of Solution

Given:

Q = 8 m³ /s

Slope = 0.1°

b = 4 m

Local depth = 2m

Concept Used:

$\begin{array}{l}Q=\frac{\alpha }{n}*A*R^{2/3}*Slop{e}^{1/2}\\ y_c={\left(\frac{q^2}{g}\right)}^{1/3}\end{array}$

Calculation:

$\begin{array}{l}Q=\frac{\alpha }{n}*A*R^{2/3}*Slop{e}^{1/2}\\ Forbrickworkn=0.015\\ A=y_n*b\\ where{y}_{n}isdepth\\ R_h=\frac{A}{P}=\frac{4y_n}{4+2y_n}\\ 8=\frac{1}{0.015}*4*y_n*{\left(\frac{4y_n}{4+2y_n}\right)}^{2/3}*{\left(\sin (0.1°)\right)}^{1/2}\\ y_n=0.960m\\ y_c={\left(\frac{q^2}{g}\right)}^{1/3}\\ y_c={\left(\frac{{\left(\raisebox{1ex}{$8$}\!\left/ \!\raisebox{-1ex}{$4$}\right.\right)}^2}{9.81}\right)}^{1/3}\\ y_c=0.742m\\ y_n>y_c\\ Theslopeismild\\ \mathrm{Sin}cethegivenlocaldepthisgreaterthan{y}_{n}and{y}_c.\end{array}$

Conclusion:

From gradually varied flow of channel flow curve, we get a mils slope curve which is M-1 curve.