Question

What will be the ratio of critical specific energy for two triangular channel having apex angle ${\Theta }_1$ and ${\Theta }_2$ respectively for a constant discharge ?

• A. ${\left[\frac{tan\left(0.5{\Theta }_1\right)}{tan\left(0.5{\Theta }_2\right)}\right]}^{2/5}$
• B. ${\left[\frac{tan\left(0.5{\Theta }_2\right)}{tan\left({0.5}_1\right)}\right]}^{2/5}$
• C. $\frac{tan{\Theta }_2}{tan{\Theta }_1}$
• D. $\frac{tan{\Theta }_1}{tan{\Theta }_2}$

Answer 1

The correct option is B ${\left[\frac{tan\left(0.5{\Theta }_2\right)}{tan\left({0.5}_1\right)}\right]}^{2/5}$

For triangular channel ,

$E_c=1.25y_c$

$\therefore \frac{(E_c{)}_1}{(E_c{)}_2}=\frac{(Y_c{)}_1}{(Y_c{)}_2}$

$=\frac{{\left(\frac{2Q^2}{g{m}_1^2}\right)}^{1/5}}{{\left(\frac{2Q^2}{g{m}_2^2}\right)}^{1/5}}={\left(\frac{m_2}{m_1}\right)}^{2/5}$

$={\left[\frac{tan\left({\Theta }_2/2\right)}{tan\left({\Theta }_1/2\right)}\right]}^{2/5}$