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:
\({\rm{q}} = \frac{{\rm{Q}}}{{\rm{B}}} = \frac{{20}}{{10}} = 2{{\rm{m}}^2}/{\rm{s}}/{\rm{m}}\)
\({{\rm{y}}_{\rm{c}}} = {\left( {\frac{{{{\rm{q}}^2}}}{{\rm{g}}}} \right)^{\frac{1}{3}}} = {\left( {\frac{{{2^2}}}{{9.81}}} \right)^{\frac{1}{3}}} = 0.741{\rm{\;m}}\)
\(\therefore {{\rm{E}}_{\rm{c}}} = \frac{3}{2}{{\rm{y}}_{\rm{c}}} = \frac{3}{2}\left( {0.741} \right) = 1.11{\rm{\;m}}\)