Vasslab

Bridge Lab

Explore how a bridge constriction changes river flow from ordinary backwater to pressure flow and roadway overtopping.

Free-surface method
EGL
Critical depth

About this model

Bridges can become important hydraulic controls during floods. Abutments and piers contract the active flow area, accelerate the river and can raise water levels far upstream. This matters in flood mapping, bridge design and river modelling because a short structure can influence a much longer reach.

The Energy method follows total head, E, through the reach. Friction lowers it gradually, while contraction and expansion add local losses:

\[E=z+y+\frac{V^2}{2g},\qquad h_L=C\left|\Delta\frac{V^2}{2g}\right|.\]

Momentum describes the bridge by balancing pressure, momentum flux, friction and obstruction forces, so pier drag is explicit. When subcritical and supercritical solutions coexist, the model compares their specific force locally; a change in the controlling branch identifies a hydraulic jump.

As discharge increases, the bridge can approach critical flow, shift control away from the downstream boundary or force a hydraulic jump. Low-chord interaction is a transition rather than an instantaneous switch: pressure flow is checked when the low-flow energy grade line reaches the low chord, while admissible free-surface and pressure/high-flow solutions continue to compete by required upstream head. That competition ends once the upstream energy grade overtops the roadway: roadway flow must then be included explicitly unless the whole bridge is highly submerged. The opening and roadway can therefore act as parallel flow paths:

\[Q=Q_{\mathrm{opening}}+Q_{\mathrm{road}},\qquad Q_{\mathrm{road}}=C\,L\,H^{3/2}.\]

The same bridge can therefore behave as an ordinary open-channel contraction, a critical control, a pressurised opening and a roadway weir. High tailwater can progressively drown the roadway control; once the bridge is highly submerged, the separate weir picture ceases to be useful and the model returns to an Energy-based high-flow calculation. That changing hydraulic identity is one of the most important—and least intuitive—features of bridge hydraulics.