Question 12.P.10: In a rectangular open channel of 5 m width the flow rate is ......

Flow velocity, V = 10/5 × 1 = 2 m/s, Froude number = V/{\sqrt{g y}}\;=2/{\sqrt{9.81\times1}}\;=0.64

Flow is in the subcritical region.

Specific energy            ={\frac{Q^{2}}{2g A^{2}}}+y={\frac{10^{2}}{2\times9.81\times5^{2}}}+1=1.2039\,\,{\mathrm{m}}

At critical condition,  \mathrm{y}_{\mathrm{c}}=\left({\frac{Q^{2}}{g b^{2}}}\right)^{1/3}=\left({\frac{10^{2}}{5^{2}\times9.81}}\right)^{1/3}=0.7415{\mathrm{~m}}

Velocity at this condition = 10/(5 × 0.745) = 2.6971 m/s

Froude number        =2.6971/\sqrt{9.81\times0.7415}\,=\,1.0  (checks)

Minimum energy     =(3/2)\;y_{c}=1.11225\;\mathrm{m}

To determine the alternate depth,

\frac{V_{2}^{~2}}{2g}+y_{2}=1.2039,\ V_{2}^{~2}=\left(\frac{Q}{A_{2}}\right)^{2}=\frac{Q^{2}}{b^{2}y^{2}} \\ \frac{Q^{2}}{2g b^{2}y_{2}^{~2}}+y_{2}=1.2039,\,\frac{10^{2}}{2\times9.81\times5^{2}}\frac{1}{y_{2}^{~2}}+y_{2}=1.2039

Solving by trail  y_{2}=0.565\mathrm{\ m~and~}V_{_{2}}=3.5398\mathrm{\ m/s},\,F r=1.5036,

∴    Supercritical region. Check for energy :

∴             (V^{2}/2\mathrm{g})+y=1.2036  (checks).