Specific energy $(E)$ in an open channel is defined as the total energy head measured relative to the channel bed as the datum: $$E = y + \frac{v^2}{2 \cdot g} = y + \frac{Q^2}{2 \cdot g \cdot A^2}$$ Where $y$ is flow depth, $v$ is mean velocity, $Q$ is total discharge, and $A$ is cross-sectional area. For a given discharge $Q$ in a rectangular channel of width $b$, critical depth $(y_c)$ occurs at minimum specific energy $(E_{min}):$ $$y_c = \left( \frac{q^2}{g} \right)^{1/3}$$ Where unit discharge $q = Q / b.$ At critical flow, the Froude number equals unity $(Fr = \frac{v}{\sqrt{g \cdot y}} = 1).$ Flow depths greater than $y_c$ represent subcritical flow $(Fr < 1),$ while depths less than $y_c$ represent supercritical flow $(Fr > 1).$ In modern urban drainage and canal fall design across India, transition zones frequently pass through critical state conditions, causing surface instability and standing waves. Engineers now utilize real-time hydro-numeric models (such a...