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A 10 m wide rectangular channel carries a discharge of 20 m3/s under critical condition. Using g = 9.81 m/s2, the specific energy (in m, up to two decimal places) is _____.

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Concept:

Energy at a section is the sum of the kinetic head, potential head and datum head.

Specific Energy: It is the energy per unit weight of the fluid at a particular section considering the bottom of the bed as datum i.e. datum head is always zero.

For a rectangular section:

Critical depth \(\left( {{{\rm{y}}_{\rm{c}}}} \right) = {\left( {\frac{{{{\rm{q}}^2}}}{{\rm{g}}}} \right)^{\frac{1}{3}}}\) 

Specific energy \(\left( {{{\rm{E}}_{\rm{c}}}} \right) = \frac{3}{2}{{\rm{y}}_{\rm{c}}}\)

Calculation:

Given: Rectangular channel of width (B) = 10 m, Discharge (Q) = 20 m3/s, and g = 9.81 m/s2

For critical flow in rectangular channel:

\({\rm{q}} = \frac{{\rm{Q}}}{{\rm{B}}} = \frac{{20}}{{10}} = 2{{\rm{m}}^2}/{\rm{s}}/{\rm{m}}\)

\({{\rm{y}}_{\rm{c}}} = {\left( {\frac{{{{\rm{q}}^2}}}{{\rm{g}}}} \right)^{\frac{1}{3}}} = {\left( {\frac{{{2^2}}}{{9.81}}} \right)^{\frac{1}{3}}} = 0.741{\rm{\;m}}\)

\(\therefore {{\rm{E}}_{\rm{c}}} = \frac{3}{2}{{\rm{y}}_{\rm{c}}} = \frac{3}{2}\left( {0.741} \right) = 1.11{\rm{\;m}}\)

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