Question

A 1m wide rectangular channel carries a discharge of 2m³/s. The specific energy-depth diagram is prepared for the channel. It is observed in this diagram that corresponding to a particular specific energy. The subcritical depth is twice the supercritical depth. The subcritical depth (in meters, up to two decimal places) is equal to ________

Answer 1

Let, Subcritical depth = y

then, super critical depth \(= \frac{y}{2}\)

Specific energy is constant at both depths

\(\begin{array}{l} \Rightarrow y + \frac{{{Q^2}}}{{2g{B^2}{y^2}}} = \frac{y}{2} + \frac{{{Q^2}}}{{2g{B^2}{{\left( {\frac{y}{2}} \right)}^2}}}\\ \Rightarrow \left( {y - \frac{y}{2}} \right) = \frac{{{Q^2}}}{{2g{B^2}}}\left( {\frac{{ - 1}}{{{y^2}}} + \frac{4}{{{y^2}}}} \right)\\ \Rightarrow \frac{y}{2} = \frac{{{2^2}}}{{2 \times 9.81 \times {1^2}}} \times \frac{3}{{{y^2}}} \end{array}\)

y = 1.07