As river channels adjust their morphology to transport water and sediment supply from upstream catchments, their cross-sectional dimensions follow systematic power-law relationships. Leopold and Maddock’s Hydraulic Geometry defines channel width $(w),$ mean depth $(d)$, and mean velocity $(v)$ as functions of discharge $(Q):$ $w = a \cdot Q^b,$ $\quad d = c \cdot Q^f,$ $\quad v = k \cdot Q^m$ Continuity requires that $w \cdot d \cdot v = Q$, which dictates two fundamental coefficient constraints: $a \cdot c \cdot k = 1.0 \quad \text{and} \quad b + f + m = 1.0$ Exponents reflect boundary resistance: stable cohesive banks yield lower width exponents $(b \approx 0.1\text{ to }0.2),$ whereas easily erodible non-cohesive alluvial banks result in rapid width expansion $(b \approx 0.5).$ Unregulated sand mining and altered flow regimes below major dams across Peninsular Indian rivers (such as the Krishna and Cauvery) disrupt dynamic channel equilibrium, causing severe channel bed degr...