Culverts are short hydraulic conduits designed to convey surface runoff through highway or railway embankments. Hydraulic performance is governed by two distinct flow regimes depending on whether the control section lies at the entrance or exit: A. Inlet Control The barrel capacity exceeds the entrance capacity. Discharge is controlled solely by the inlet geometry (cross-sectional area $A$, edge roundness, and headwater elevation $HW$). Flow inside the barrel remains subcritical or supercritical with a free surface. Under unsubmerged conditions ($HW / D < 1.2$, where $D$ is culvert height): $$\frac{HW}{D} = \frac{H_c}{D} + K \cdot \left[ \frac{Q}{A \cdot \sqrt{g \cdot D}} \right]^M - 0.5 \cdot S_0$$ Where $H_c$ is critical head, $S_0$ is barrel slope, and $K, M$ are empirical inlet shape coefficients. B. Outlet Control Discharge is controlled by tailwater elevation ($TW$), barrel friction, and entrance losses. The culvert flows full or subcritically partially full over its ...