A hydraulic jump occurs when high-velocity supercritical flow $(Fr_1 > 1)$ transitions abruptly to subcritical flow $(Fr_2 < 1),$ dissipating excess kinetic energy downstream of spillways and sluice gates. The conjugate depth relationship across a rectangular channel jump is governed by Bélanger’s Equation: $$\frac{y_2}{y_1} = \frac{1}{2} \cdot \left( \sqrt{1 + 8 \cdot Fr_1^2} - 1 \right)$$ Where $y_1$ and $y_2$ are pre-jump and post-jump water depths, and $Fr_1 = \frac{v_1}{\sqrt{g \cdot y_1}}$ is the initial Froude number. The head loss $\Delta E$ dissipated within the turbulent roller is expressed as: $$\Delta E = \frac{(y_2 - y_1)^3}{4 \cdot y_1 \cdot y_2}$$ High-head dams in narrow Himalayan gorges encounter massive dynamic uplift forces and cavitation damage inside spillway stilling basins during extreme discharge events. Modern hydraulic engineering in India relies on standardized USBR or IS-code stilling basin designs reinforced with high-strength fiber-reinforce...